Repository: tyt2y3/vaserenderer
Branch: master
Commit: 93d291ccc7ff
Files: 86
Total size: 385.6 KB

Directory structure:
gitextract_m2dfrshv/

├── .gitignore
├── LICENSE
├── README.md
├── cpp/
│   ├── samples/
│   │   ├── Makefile
│   │   ├── png_readwrite.cpp
│   │   ├── polyline
│   │   ├── polyline.cpp
│   │   ├── readme.txt
│   │   ├── samples
│   │   ├── samples.cpp
│   │   ├── segment
│   │   ├── segment.cpp
│   │   └── test1_base.cpp
│   ├── vaser/
│   │   ├── agg_curve4.cpp
│   │   ├── backend.h
│   │   ├── color.h
│   │   ├── curve.cpp
│   │   ├── gradient.cpp
│   │   ├── opengl.cpp
│   │   ├── point.h
│   │   ├── polyline.cpp
│   │   ├── vaser.cpp
│   │   ├── vaser.h
│   │   └── vertex_array_holder.h
│   └── workbench/
│       ├── base.html
│       ├── dragger.js
│       ├── drawer.js
│       ├── gradient_along_path.html
│       ├── knife_cut_test
│       ├── knife_cut_test.cpp
│       ├── layout.css
│       ├── outward_vector.html
│       ├── quad_reflex.html
│       ├── raphael-min.js
│       ├── readme.txt
│       ├── triangle_knife_cut.js
│       ├── triangles_dual_knife_cut.html
│       ├── triangles_knife_cut.html
│       └── vector_arc.html
├── csharp/
│   ├── Assets/
│   │   ├── Demo/
│   │   │   ├── Demo.cs
│   │   │   ├── Demo.cs.meta
│   │   │   ├── demo.unity
│   │   │   └── demo.unity.meta
│   │   ├── Demo.meta
│   │   ├── Resources/
│   │   │   ├── Vaser/
│   │   │   │   ├── Fade.mat
│   │   │   │   ├── Fade.mat.meta
│   │   │   │   ├── Fade.shader
│   │   │   │   └── Fade.shader.meta
│   │   │   └── Vaser.meta
│   │   ├── Resources.meta
│   │   ├── Vaser/
│   │   │   ├── Gradient.cs
│   │   │   ├── Gradient.cs.meta
│   │   │   ├── Polybezier.cs
│   │   │   ├── Polybezier.cs.meta
│   │   │   ├── Polyline.cs
│   │   │   ├── Polyline.cs.meta
│   │   │   ├── Vec2Ext.cs
│   │   │   ├── Vec2Ext.cs.meta
│   │   │   ├── VertexArrayHolder.cs
│   │   │   └── VertexArrayHolder.cs.meta
│   │   └── Vaser.meta
│   ├── Docs/
│   │   └── README.md
│   ├── Packages/
│   │   └── manifest.json
│   ├── ProjectSettings/
│   │   ├── AudioManager.asset
│   │   ├── ClusterInputManager.asset
│   │   ├── DynamicsManager.asset
│   │   ├── EditorBuildSettings.asset
│   │   ├── EditorSettings.asset
│   │   ├── GraphicsSettings.asset
│   │   ├── InputManager.asset
│   │   ├── NavMeshAreas.asset
│   │   ├── Physics2DSettings.asset
│   │   ├── PresetManager.asset
│   │   ├── ProjectSettings.asset
│   │   ├── ProjectVersion.txt
│   │   ├── QualitySettings.asset
│   │   ├── TagManager.asset
│   │   ├── TimeManager.asset
│   │   ├── UnityConnectSettings.asset
│   │   ├── VFXManager.asset
│   │   └── XRSettings.asset
│   └── README.md
└── docs/
    ├── API.html
    ├── getting_started.html
    ├── index.html
    └── style.css

================================================
FILE CONTENTS
================================================

================================================
FILE: .gitignore
================================================
# This .gitignore file should be placed at the root of your Unity project directory
#
# Get latest from https://github.com/github/gitignore/blob/master/Unity.gitignore
#
/[Ll]ibrary/
/[Tt]emp/
/[Oo]bj/
/[Bb]uild/
/[Bb]uilds/
/[Ll]ogs/
/[Mm]emoryCaptures/

# Never ignore Asset meta data
!/[Aa]ssets/**/*.meta

# Uncomment this line if you wish to ignore the asset store tools plugin
# /[Aa]ssets/AssetStoreTools*

# Autogenerated Jetbrains Rider plugin
[Aa]ssets/Plugins/Editor/JetBrains*

# Visual Studio cache directory
.vs/

# Gradle cache directory
.gradle/

# Autogenerated VS/MD/Consulo solution and project files
ExportedObj/
.consulo/
*.csproj
*.unityproj
*.sln
*.suo
*.tmp
*.user
*.userprefs
*.pidb
*.booproj
*.svd
*.pdb
*.mdb
*.opendb
*.VC.db

# Unity3D generated meta files
*.pidb.meta
*.pdb.meta
*.mdb.meta

# Unity3D generated file on crash reports
sysinfo.txt

# Builds
*.apk
*.unitypackage

# Crashlytics generated file
crashlytics-build.properties

# Sublime
*.sublime*

================================================
FILE: LICENSE
================================================
BSD 3-Clause License

Copyright (c) 2023 TSANG, Hao Fung (tyt2y7@gmail.com)

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this
   list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.

3. Neither the name of the copyright holder nor the names of its
   contributors may be used to endorse or promote products derived from
   this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.


================================================
FILE: README.md
================================================
> This project was started many, many years ago. The C++ implementation is a pre-OpenGL 3 relic. The C# implementation is more "modern" and uses fragment shader, which is better.

<body>
	<div class='vaser_wrap'>
		<div class='article_name'>
			<h1>VASE<span style='line-height:40px;'> renderer</span></h1>
		</div>
<h2>About</h2>
<p>VASE renderer version 0.42 (VASEr 0.42) is a tessellating library for rendering high quality 2D vector graphics. It is an attempt to address unconventional features in 2d graphics. It is intended for OpenGL 1.1+, but much of the code is API independent C++.</p>

<h2>Unconventional features</h2>
<h3>Per vertex coloring and weighting</h3>
<div style='position:relative; overflow:hidden; height:220px; float:left;'><img style='position:relative; top:-40px;' src='docs/sample_images/polyline_3.png' /></div>
<br><br>VASEr revolutionarily lets you control the color and thickness at each vertex for a polyline. This feature is unseen on any commonly available graphics library.
	<div style='clear:both'></div>

<h3>Linear gradient along curve</h3>
<div style='position:relative; overflow:hidden; height:200px; float:right;'><img style='position:relative; top:-60px;' src='docs/sample_images/bezier_2.png' /></div>
<br>A similar feature is also available to curves. Because there are so many vertices on a curve that it is impractical to specify data on each point, VASEr lets you define a linear gradient of color and thickness along the length of a curve, giving you two more degrees of freedom.
	<div style='clear:both'></div>

<h3>Feathering for brush like effects</h3>
<img src='docs/sample_images/bezier_3.png' style='float:left;' />
<img src='docs/sample_images/bezier_4.png' style='float:left;' />
<img src='docs/sample_images/bezier_5.png' style='float:left;' />
<br>VASEr must use an outsetting polygon anyway, so it is free (as in computational cost) to scale it up, and it is called feathering in VASEr.
	<div style='clear:both'></div>

<h3>Premium quality anti aliasing</h3>
<div style='background:#333; margin: 10px; border:5px solid #AAA; float:left; height: 150px; overflow:hidden;'>
<img src='docs/sample_images/fade_intro_1.png' />
<img src='docs/sample_images/fade_intro_2.png' />
<img src='docs/sample_images/fade_intro_3.png' />
<img src='docs/sample_images/fade_intro_4.png' />
</div>
<br><br>From left to right: raw polygon without anti aliasing, <br>
anti aliased with outset fade polygon, <br>
exaggerated outsetting polygon with wireframe, <br>
same as left without wireframe.
	<div style='clear:both'></div>
<p>Outset-fade polygon is the high quality, fast, portable, consistent and hassle free technique for anti aliasing. The difficulties are to calibrate the outsetting distance to achieve believable result and to perform tedious tessellation. Luckily VASEr did this for you.</p>
<p>Below are line rendering comparison between VASEr and Cairo and AGG:</p>
<div>
	<div id='ab_va'>VASEr<br><img src='docs/sample_images/ab_vaser_line_thickness1.png' /></div>
	<div id='ab_ca' style='display:none;'>Cairo<br><img src='docs/sample_images/ab_cairo_line_thickness.png' /></div>
</div>
<div>
	<div id='a_agg' style='display:none;'>AGG<br><img src='docs/sample_images/agg_line_thickness.png' /></div>
</div>
<p>There is small difference, but it is more a matter of taste than correctness. In terms of clarity VASEr is like between Cairo and AGG, and VASEr is the most crisp among the three. VASEr even do pixel alignment to 1px completely horizontal or vertical lines.</p>
<p>The flaw is, because the outsetting distance is resolution dependent, while the triangulation is unaffected under rotational transformation, fidelity will be lost under scale and sheer.</p>

<h2>Articles</h2>

+ <a href='http://artgrammer.blogspot.com/2011/07/drawing-polylines-by-tessellation.html' target='_blank'>Drawing polylines by tessellation.</a><br>
+ <a href='http://artgrammer.blogspot.hk/2011/05/drawing-nearly-perfect-2d-line-segments.html'>Drawing nearly perfect 2D line segments in OpenGL</a>

<h2>Related Work</h2>
<ul>
<li>If you only need uniform color & width and only wanted a clean mesh, you can try out <a href="https://github.com/CrushedPixel/Polyline2D">Polyline2D</a>.</li>
</ul>

<h2>Acknowledgement</h2>
<p>Bezier curve subdivision code is extracted from Anti-Grain Geometry V2.4 by Maxim Shemanarev (McSeem).</p>
<p>The open-source graphics library AGG inspired me a lot during my teenage.</p>

</body>


================================================
FILE: cpp/samples/Makefile
================================================
CPP = polyline.cpp segment.cpp samples.cpp
BIN = $(CPP:.cpp=)
VASER = ../vaser/*

all: $(BIN)

polyline: polyline.cpp png_readwrite.cpp test1_base.cpp $(VASER)
	fltk-config --use-gl --use-images --compile polyline.cpp

segment: segment.cpp test1_base.cpp $(VASER)
	fltk-config --use-gl --compile segment.cpp

samples: samples.cpp test1_base.cpp $(VASER)
	fltk-config --use-gl --compile samples.cpp

win32: $(CPP) $(VASER)
	$(foreach var,$(BIN),g++ -I/usr/local/include -mwindows -DWIN32 -DUSE_OPENGL32 -D_LARGEFILE_SOURCE -D_LARGEFILE64_SOURCE -o $(var) $(var).cpp -mwindows /usr/local/lib/libfltk_gl.a -static -lpng -lz -lglu32 -lopengl32 /usr/local/lib/libfltk.a -lole32 -luuid -lcomctl32 -static-libgcc -static-libstdc++ & )


================================================
FILE: cpp/samples/png_readwrite.cpp
================================================
#include <stdio.h>
#include <png.h>

int	// 0 on failure, 1 on success
save_png(const char *filename,	// filename
	unsigned char* buffer,		// buffer of an image
	int w,		// width of image
	int h,		// height
	int b)		// color depth/ bytes per pixel
{
	int	y;						// Current row
	const unsigned char	*ptr;	// Pointer to image data
	FILE				*fp;	// File pointer
	png_structp			pp;		// PNG data
	png_infop			info;	// PNG image info

	if ( !filename)
	{
		printf("invalid filename.\n");
		return 0;
	}
	if ( !buffer)
	{
		printf("null pointer buffer.\n");
		return 0;
	}
	
	// Create the output file...
	if ((fp = fopen(filename, "wb")) == NULL)
	{
		printf("Unable to create PNG image.\n");
		return (0);
	}

	// Create the PNG image structures...
	pp = png_create_write_struct(PNG_LIBPNG_VER_STRING, 0, 0, 0);
	if (!pp)
	{
		fclose(fp);
		printf("Unable to create PNG data.\n");
		return (0);
	}

	info = png_create_info_struct(pp);
	if (!info)
	{
		fclose(fp);
		png_destroy_write_struct(&pp, 0);
		printf("Unable to create PNG image information.\n");
		return (0);
	}

	if (setjmp(png_jmpbuf(pp)))
	{
		fclose(fp);
		png_destroy_write_struct(&pp, &info);
		printf("Unable to write PNG image.\n");
		return (0);
	}

	png_init_io(pp, fp);

	png_set_compression_level(pp, Z_BEST_COMPRESSION);
	png_set_IHDR(pp, info, w, h, 8,
	       b==3? PNG_COLOR_TYPE_RGB : PNG_COLOR_TYPE_RGB_ALPHA,
	       PNG_INTERLACE_NONE, PNG_COMPRESSION_TYPE_DEFAULT,
	       PNG_FILTER_TYPE_DEFAULT);
	png_set_sRGB(pp, info, PNG_sRGB_INTENT_PERCEPTUAL);
	png_set_sRGB_gAMA_and_cHRM(pp, info, PNG_INFO_sRGB);
	
	png_write_info(pp, info);
	
	ptr = buffer;
	
	for (y = 0; y < h; y ++)
	{
		png_write_row(pp, (png_byte *)ptr);
		ptr += w*b;
	}

	png_write_end(pp, info);
	png_destroy_write_struct(&pp, 0);

	fclose(fp);
	return (1);
}


unsigned char*	// 0 on failure, address of memory buffer on success
				// must *delete[]* the buffer manually after use
read_png( const char* filename, // filename
	int* width,			// store image width into pointer
	int* height,		// store image height into pointer
	int* channels)		// number of channels
{
	int		i;			// Looping var
	FILE		*fp;	// File pointer
	png_structp	pp;		// PNG read pointer
	png_infop	info;	// PNG info pointers
	png_bytep	*rows;	// PNG row pointers

	// Open the PNG file...
	if ((fp = fopen(filename, "rb")) == NULL)
	{
		printf( "Unable to open file %s.\n", filename);
		return 0;
	}

	// Setup the PNG data structures...
	pp   = png_create_read_struct(PNG_LIBPNG_VER_STRING, NULL, NULL, NULL);
	info = png_create_info_struct(pp);

	if (setjmp(pp->jmpbuf))
	{
		printf("Unable to read. png file %s contains errors.\n", filename);
		return 0;
	}

	// Initialize the PNG read "engine"...
	png_init_io(pp, fp);

	// Get the image dimensions and convert to grayscale or RGB...
	png_read_info(pp, info);

	if (info->color_type == PNG_COLOR_TYPE_PALETTE)
	png_set_expand(pp);

	if (info->color_type & PNG_COLOR_MASK_COLOR)
	*channels = 3;
	else
	*channels = 1;

	if ((info->color_type & PNG_COLOR_MASK_ALPHA) || info->num_trans)
	(*channels) ++;

	if ( *channels != 3 && *channels != 4)
	{
		printf("png image other than 3 or 4 channels is not supported.\n");
		return 0;
	}

	*width = info->width;
	*height = info->height;

	if (info->bit_depth < 8)
	{
	png_set_packing(pp);
	png_set_expand(pp);
	}
	else if (info->bit_depth == 16)
	png_set_strip_16(pp);

	// Handle transparency...
	if (png_get_valid(pp, info, PNG_INFO_tRNS))
	png_set_tRNS_to_alpha(pp);

	unsigned char* array = new unsigned char[(*width) * (*height) * (*channels)];

	// Allocate pointers...
	rows = new png_bytep[(*height)];

	for (i = 0; i < (*height); i ++)
	rows[i] = (png_bytep)(array + i * (*width) * (*channels));

	// Read the image, handling interlacing as needed...
	for (i = png_set_interlace_handling(pp); i > 0; i --)
	png_read_rows(pp, rows, NULL, (*height));

	#ifdef WIN32
	// Some Windows graphics drivers don't honor transparency when RGB == white
	if (*channels == 4) {
	// Convert RGB to 0 when alpha == 0...
	unsigned char* ptr = (unsigned char*) array;
	for (i = (*width) * (*height); i > 0; i --, ptr += 4)
	if (!ptr[3]) ptr[0] = ptr[1] = ptr[2] = 0;
	}
	#endif //WIN32

	// Free memory
	delete[] rows;

	png_read_end(pp, info);
	png_destroy_read_struct(&pp, &info, NULL);

	fclose(fp);

	return array;
}


================================================
FILE: cpp/samples/polyline.cpp
================================================
/*config.h is generated by fltk in your system
 * this file is used with fltk 1.3 with gl enabled.
 * compile by: fltk-config --use-gl --use-images --compile polyline.cpp
 * or something like: g++ -lX11 -lGL -lpng 'polyline.cpp' -o 'polyline'
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

#include "config.h" //config.h must always be placed before any Fl header
#include <FL/gl.h>
#include <FL/Fl_Box.H>
#include <FL/Fl_Tabs.H>
#include <FL/Fl_Window.H>
#include <FL/Fl_Value_Slider.H>
#include <FL/Fl_Radio_Light_Button.H>

namespace VASEr
{
	struct Vec2 { double x,y;};
	struct Color { float r,g,b,a;};
}
#define VASER_DEBUG
#include "../vaser/vaser.cpp"
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
#include "png_readwrite.cpp"

using namespace VASEr;
void test_draw();
#include "test1_base.cpp"

const int buf_size=20;
Vec2 AP[buf_size];
int size_of_AP=0;
Color AC[buf_size];
double AW[buf_size];

Fl_Window* main_wnd;
Gl_Window* gl_wnd;
Fl_Slider *weight, *feathering;
Fl_Button *poly, *bezi;
Fl_Button *feather, *no_feather_at_cap, *no_feather_at_core;
Fl_Button *jt_miter, *jt_bevel, *jt_round;
Fl_Button *jc_butt, *jc_round, *jc_square, *jc_rect;
Fl_Button *jc_both, *jc_first, *jc_last, *jc_none;
Fl_Button *colored, *alphaed, *weighted;
Fl_Button *skeleton, *triangulate;
Fl_Slider *bz_ap, *bz_ag, *bz_cu;

void line_update()
{
	Color cc[3];
	Color grey = {.4,.4,.4, 1};
	
	{ Color col={1 , 0, 0, 1}; cc[0]=col;}
	{ Color col={.8,.8, 0, 1}; cc[1]=col;}
	{ Color col={ 0, 0, 1, 1}; cc[2]=col;}
	
	for ( int i=0; i<size_of_AP; i++)
	{
		if ( colored->value())
			AC[i] = cc[i%3];
		else
			AC[i] = grey;
		
		if ( alphaed->value())
			AC[i].a = 0.5f;
		else
			AC[i].a = 1.0f;
			
		if ( weighted->value())
		{
			AW[i] = weight->value() * (0.05 + double(i*2)/size_of_AP);
		}
		else
		{
			AW[i] = weight->value();
		}
	}
}
void line_init( int N)
{
	switch (N)
	{
	case 2:
		AP[0].x=180; AP[0].y=270;
		AP[1].x=220; AP[1].y=30;
		size_of_AP = 2;
	break;
	
	case 3:
		AP[0].x=200; AP[0].y=100;
		AP[1].x=100; AP[1].y=200;
		AP[2].x=300; AP[2].y=200;
		size_of_AP = 3;
	break;
	
	case 4:
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
		size_of_AP = 4;
	break;
	
	case 5:
		AP[0].x=60; AP[0].y=250;
		AP[1].x=120; AP[1].y=50;
		AP[2].x=180; AP[2].y=250;
		AP[3].x=240; AP[3].y=50;
		AP[4].x=300; AP[4].y=250;
		size_of_AP = 5;
	break;
	
	case 6:
		AP[0].x=280; AP[0].y=110;
		AP[1].x=200; AP[1].y=50;
		AP[2].x=100; AP[2].y=150;
		AP[3].x=300; AP[3].y=150;
		AP[4].x=200; AP[4].y=250;
		AP[5].x=120; AP[5].y=190;
		size_of_AP = 6;
	break;

	case 7:
		AP[0].x=280; AP[0].y=110;
		AP[1].x=200; AP[1].y=50;
		AP[2].x=100; AP[2].y=50;
		AP[3].x=200; AP[3].y=150;
		AP[4].x=300; AP[4].y=250;
		AP[5].x=200; AP[5].y=250;
		AP[6].x=120; AP[6].y=190;
		size_of_AP = 7;
	break;
	}
	line_update();
	gl_wnd->set_drag_target( AP, size_of_AP); 
}
char get_joint_type()
{
	if ( jt_miter->value())
		return PLJ_miter;
	else if ( jt_bevel->value())
		return PLJ_bevel;
	else if ( jt_round->value())
		return PLJ_round;
	else
		return 0;
}
char get_cap_type()
{
	char cap;
	if ( jc_butt->value())
		cap=PLC_butt;
	else if ( jc_round->value())
		cap=PLC_round;
	else if ( jc_square->value())
		cap=PLC_square;
	else if ( jc_rect->value())
		cap=PLC_rect;

	if ( jc_both->value())
		cap+=PLC_both;
	else if ( jc_first->value())
		cap+=PLC_first;
	else if ( jc_last->value())
		cap+=PLC_last;
	else if ( jc_none->value())
		cap+=PLC_none;
	return cap;
}
void np_cb(Fl_Widget* W, void*)
{
	int n=3;
	sscanf( W->label(), "%d", &n);
	line_init(n);
	if( n<4)
	{
		poly->value(1);
		bezi->value(0);
	}
	line_update();
	gl_wnd->redraw();
}
void line_bezier(Fl_Widget* W, void*)
{
	gl_wnd->redraw();
}
void drag_cb(Fl_Widget* W, void*)
{
	line_update();
	gl_wnd->redraw();
}
void exportimg_cb(Fl_Widget* W, void*)
{
	Image img = renderer::get_image();
	if( img.buf)
	{
		save_png("capture.png",img.buf,img.width,img.height,4);
		free(img.buf);
	}
}

void make_form()
{
	Fl_Tabs* tabs = new Fl_Tabs(400,0,200,300);

	{ Fl_Group* tab = new Fl_Group(400, 20, 200, 300, "config");
		Fl_Box* o = new Fl_Box(FL_NO_BOX,400,25,200,20,"general configurations");
		//weight
		weight = new Fl_Value_Slider(400,50,200,20,"weight");
		weight->type(FL_HOR_SLIDER);
		weight->bounds(0.02,30.0);
		weight->callback(drag_cb);
		weight->value(8.0);
		
		{ Fl_Group* o = new Fl_Group(400,90,200,20);
			poly = new Fl_Radio_Light_Button(400,90,100,20,"polyline");
			bezi = new Fl_Radio_Light_Button(500,90,100,20,"polybezier");
			poly->callback(line_bezier);
			bezi->callback(line_bezier);
			poly->value(1);
			o->end();
		}

		//number of points
		(new Fl_Button(400,110,80,20,"2 points"))->callback(np_cb);
		(new Fl_Button(480,110,20,20,"3"))->callback(np_cb);
		(new Fl_Button(500,110,20,20,"4"))->callback(np_cb);
		(new Fl_Button(520,110,20,20,"5"))->callback(np_cb);
		(new Fl_Button(540,110,20,20,"7"))->callback(np_cb);

		//test options
		colored = new Fl_Light_Button(400,130,60,20,"colored");
		colored->callback(drag_cb);
		colored->value(1);
		alphaed = new Fl_Light_Button(460,130,70,20,"alpha-ed");
		alphaed->callback(drag_cb);
		alphaed->value(1);
		weighted = new Fl_Light_Button(530,130,70,20,"weighted");
		weighted->callback(drag_cb);
		skeleton = new Fl_Light_Button(400,150,80,20,"skeleton");
		skeleton->value(0);
		skeleton->callback(drag_cb);
		triangulate = new Fl_Light_Button(480,150,120,20,"triangulation");
		triangulate->value(0);
		triangulate->callback(drag_cb);
		//export button
		Fl_Button *exportimg;
		exportimg = new Fl_Button(400,170,200,20,"export image");
		exportimg->callback(exportimg_cb);
	tab->end();}

	{ Fl_Group* tab = new Fl_Group(400, 20, 200, 300, "polyline");
		Fl_Box* o = new Fl_Box(FL_NO_BOX,400,25,200,20,"polyline_opt");

		//feathering
		feather = new Fl_Light_Button(400,50,100,20,"feather");
		feather->value(1);
		feather->callback(drag_cb);
		feathering = new Fl_Value_Slider(400,70,200,20,"feathering");
		feathering->type(FL_HOR_SLIDER);
		feathering->bounds(1.0,10.0);
		feathering->callback(drag_cb);
		feathering->value(1.0);
		no_feather_at_cap  = new Fl_Light_Button(430,110,170,15,"no_feather_at_cap");
		no_feather_at_core = new Fl_Light_Button(430,125,170,15,"no_feather_at_core");
		no_feather_at_cap ->value(0);
		no_feather_at_core->value(0);
		no_feather_at_cap ->callback(drag_cb);
		no_feather_at_core->callback(drag_cb);

		//joint type
		{ Fl_Group* o = new Fl_Group(400,145,200,30);
			new Fl_Box(400,145,80,15,"joint type");
			jt_miter = new Fl_Radio_Light_Button(420,160,60,15,"miter");
			jt_bevel = new Fl_Radio_Light_Button(480,160,60,15,"bevel");
			jt_round = new Fl_Radio_Light_Button(540,160,60,15,"round");
			o->end();
			jt_miter->value(1);
			jt_miter->callback(drag_cb);
			jt_bevel->callback(drag_cb);
			jt_round->callback(drag_cb);
		}
		//cap type
		{ Fl_Group* o = new Fl_Group(400,180,200,45);
			new Fl_Box(400,180,80,15,"cap type");
			jc_butt   = new Fl_Radio_Light_Button(440,195,80,15,"butt");
			jc_round  = new Fl_Radio_Light_Button(520,195,80,15,"round");
			jc_square = new Fl_Radio_Light_Button(440,210,80,15,"square");
			jc_rect   = new Fl_Radio_Light_Button(520,210,80,15,"rect");
			o->end();
			jc_butt   ->value(1);
			jc_butt   ->callback(drag_cb);
			jc_round  ->callback(drag_cb);
			jc_square ->callback(drag_cb);
			jc_rect   ->callback(drag_cb);
		}
		{ Fl_Group* o = new Fl_Group(400,230,200,45);
			new Fl_Box(400,230,80,15,"cap parts");
			jc_both   = new Fl_Radio_Light_Button(440,245,80,15,"both");
			jc_first  = new Fl_Radio_Light_Button(520,245,80,15,"first");
			jc_last   = new Fl_Radio_Light_Button(440,260,80,15,"last");
			jc_none   = new Fl_Radio_Light_Button(520,260,80,15,"none");
			jc_both->value(1);
			jc_both ->callback(drag_cb);
			jc_first->callback(drag_cb);
			jc_last ->callback(drag_cb);
			jc_none ->callback(drag_cb);
		}
	tab->end();}

	/*{ Fl_Group* tab = new Fl_Group(400, 20, 200, 300, "BZ");
		Fl_Box* o = new Fl_Box(FL_NO_BOX,400,25,200,20,"polybezier_opt");
		bz_ap = new Fl_Value_Slider(400,70,200,15,"approximation_scale");
		bz_ag = new Fl_Value_Slider(400,105,200,15,"angle_tolerance");
		bz_cu = new Fl_Value_Slider(400,140,200,15,"cusp_limit");
		bz_ap->type(FL_HOR_SLIDER);
		bz_ag->type(FL_HOR_SLIDER);
		bz_cu->type(FL_HOR_SLIDER);
		bz_ap->bounds(0.1,5.0); bz_ap->value(BZ_default_approximation_scale); bz_ap->callback(drag_cb);
		bz_ag->bounds(0.01,0.52); bz_ag->value(BZ_default_angle_tolerance); bz_ag->callback(drag_cb);
		bz_cu->bounds(0.1,5.0); bz_cu->value(BZ_default_cusp_limit); bz_cu->callback(drag_cb);
	tab->end();}*/

	/*{ Fl_Group* tab = new Fl_Group(400, 20, 200, 300, "TS");
		Fl_Box* o = new Fl_Box(FL_NO_BOX,400,25,200,20,"tessellator");
	tab->end();}*/

	tabs->end();
}
void test_draw()
{	//main rendering

	renderer::before();

	polyline_opt opt={0};
	tessellator_opt tess={0};
	opt.feather    = feather->value();
	opt.feathering = feathering->value();
	opt.no_feather_at_cap = no_feather_at_cap->value();
	opt.no_feather_at_core = no_feather_at_core->value();
	opt.joint = get_joint_type();
	opt.cap   = get_cap_type();
	opt.tess = &tess;
	tess.triangulation = triangulate->value();

	Color cc={1,1,1,1};
	if ( bezi->value())
	{
		polybezier_opt bz_opt={0};
		bz_opt.poly = &opt;
		//bz_opt.approximation_scale = bz_ap->value();
		//bz_opt.angle_tolerance = bz_ag->value();
		//bz_opt.cusp_limit = bz_cu->value();
		gradient grad = {0};
		gradient_stop stop[10] = {0};
		grad.stops = stop;
		grad.length = 10;
		stop[0].t = 0.00; stop[0].type = GS_rgba; stop[0].color = AC[0];
		stop[1].t = 0.33; stop[1].type = GS_rgba; stop[1].color = AC[1];
		stop[2].t = 0.66; stop[2].type = GS_rgba; stop[2].color = AC[2];
		stop[3].t = 1.00; stop[3].type = GS_rgba; stop[3].color = AC[3];
		stop[4].t = 0.00; stop[4].type = GS_weight; stop[4].weight = AW[0];
		stop[5].t = 0.33; stop[5].type = GS_weight; stop[5].weight = AW[1];
		stop[6].t = 0.66; stop[6].type = GS_weight; stop[6].weight = AW[2];
		stop[7].t = 1.00; stop[7].type = GS_weight; stop[7].weight = AW[3];
		polybezier( AP, &grad, size_of_AP, &bz_opt);
		Color black={0,0,0,1};
		if ( skeleton->value())
		{
			polybezier( AP, cc, 1.0, size_of_AP, 0);
			polyline( AP, black, 1.0, size_of_AP, 0); //control lines
		}
	}
	else
	{
		polyline( AP, AC, AW, size_of_AP, &opt);
		if ( skeleton->value())
			polyline( AP, cc, 1.0, size_of_AP, 0);
	}

	renderer::after();
}

int main(int argc, char **argv)
{
	main_wnd = new Fl_Window( 600,300,"VASEr - polyline and bezier example");
		make_form(); //initialize
		gl_wnd = new Gl_Window( 0,0,400,300);  gl_wnd->end(); //create gl window
		line_init(4);
	main_wnd->end();
	main_wnd->show();
	main_wnd->redraw();
	
	return Fl::run();
}


================================================
FILE: cpp/samples/readme.txt
================================================
FLTK 1.3.x is required http://www.fltk.org/
libpng is required for png support


================================================
FILE: cpp/samples/samples.cpp
================================================
/*config.h is generated by fltk in your system
 * this file is used with fltk 1.3 with gl enabled.
 * compile by: fltk-config --use-gl --compile samples.cpp
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

#include "config.h" //config.h must always be placed before any Fl header
#include <FL/gl.h>
#include <FL/Fl_Window.H>
#include <FL/Fl_Button.H>

namespace VASEr
{
	struct Vec2 { double x,y;};
	struct Color { float r,g,b,a;};
}
#include "../vaser/vaser.cpp"
using namespace VASEr;

void test_draw();
#include "test1_base.cpp"

Fl_Window* main_wnd;
Gl_Window* gl_wnd;
int current=0;

void drag_cb(Fl_Widget* W, void*)
{
	sscanf( W->label(), "sample%d", &current);
	gl_wnd->redraw();
}
void make_form()
{
	for( int i=0; i<6; i++)
	{
		char* buf=(char*)malloc(10);
		snprintf(buf, 10, "sample%d",i);
		(new Fl_Button(600,20*i,100,20,buf))->callback(drag_cb);
	}
}
void sample0()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color col={ 0.5, 0.8, 1.0, 1};
	polyline( AP, col, 8.0, size_of_AP, 0);
}
void sample1()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color AC[size_of_AP];
		{ Color col={1 , 0, 0, 0.5}; AC[0]=col;}
		{ Color col={.8,.8, 0, 0.5}; AC[1]=col;}
		{ Color col={ 0, 0, 1, 0.5}; AC[2]=col;}
		{ Color col={1 , 0, 0, 0.5}; AC[3]=col;}
	double AW[size_of_AP];
		AW[0] = 1.0;
		AW[1] = 15.0;
		AW[2] = 15.0;
		AW[3] = 1.0;
	
	polyline( AP, AC, AW, size_of_AP, 0);
}
void sample2()
{	//spectrum
	for ( int i=0; i < 20; i++)
	{
		Vec2  P1 = { 5+29.7*i, 187};
		Vec2  P2 = { 35+29.7*i, 8};
		Color C1 = { 1.0,0.0,0.5, 1.0};
		Color C2 = { 0.5,0.0,1.0, 1.0};
		double W1= 0.3*(i+1);
		double W2= W1;
		
		segment(P1,P2, C1,C2, W1,W2, 0);
	}
}
void sample3()
{	//radial spectrum
	for ( double ag=0, i=0; ag < 2*vaser_pi-0.1; ag+=vaser_pi/12, i+=1)
	{
		double r1 = 30.0;
		double r2 = 90.0;
		
		double tx2=r2*cos(ag);
		double ty2=r2*sin(ag);
		double tx1=r1*cos(ag);
		double ty1=r1*sin(ag);
		double Ox = 120;
		double Oy = 194+97;
		
		Vec2  P1 = { Ox+tx1,Oy-ty1};
		Vec2  P2 = { Ox+tx2,Oy-ty2};
		Color C1 = { 1.0,0.0,0.5, 1.0};
		Color C2 = { 0.5,0.0,1.0, 1.0};
		double W1= 0.3*(i+1);
		double W2= W1;
		
		polyline_opt opt={0};
		opt.cap = PLC_round;
		opt.joint = PLJ_round;
		segment(P1,P2, C1,C2, W1,W2, &opt);
	}
}
void sample4()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color col={ 0.5, 0.8, 1.0, 1};
	polybezier( AP, col, 12.0, size_of_AP, 0);
}
void sample5()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color AC[size_of_AP];
		{ Color col={1 , 0, 0, 0.5}; AC[0]=col;}
		{ Color col={.8,.8, 0, 0.5}; AC[1]=col;}
		{ Color col={ 0, 0, 1, 0.5}; AC[2]=col;}
		{ Color col={1 , 0, 0, 0.5}; AC[3]=col;}
	double AW[size_of_AP];
		AW[0] = 1.0;
		AW[1] = 15.0;
		AW[2] = 15.0;
		AW[3] = 1.0;
	gradient grad = {0};
		gradient_stop stop[10] = {0};
		grad.stops = stop;
		grad.length = 10;
		stop[0].t = 0.00; stop[0].type = GS_rgba; stop[0].color = AC[0];
		stop[1].t = 0.50; stop[1].type = GS_rgba; stop[1].color = AC[2];
		stop[2].t = 1.00; stop[2].type = GS_rgba; stop[2].color = AC[3];
		stop[3].t = 0.00; stop[3].type = GS_weight; stop[3].weight = AW[0];
		stop[4].t = 0.33; stop[4].type = GS_weight; stop[4].weight = AW[1];
		stop[5].t = 0.66; stop[5].type = GS_weight; stop[5].weight = AW[2];
		stop[6].t = 1.00; stop[6].type = GS_weight; stop[6].weight = AW[3];
	polybezier( AP, &grad, size_of_AP, 0);
}
void sample6()
{
}
void sample7()
{
}
void sample8()
{
}
void sample9()
{
}
void test_draw()
{
	renderer::before();
	switch (current)
	{
		case 0: sample0(); break;
		case 1: sample1(); break;
		case 2: sample2(); break;
		case 3: sample3(); break;
		case 4: sample4(); break;
		case 5: sample5(); break;
		case 6: sample6(); break;
		case 7: sample7(); break;
		case 8: sample8(); break;
		case 9: sample9(); break;
	}
	renderer::after();
}

int main(int argc, char **argv)
{
	main_wnd = new Fl_Window( 700,400,"VASEr - demo");
		make_form(); //initialize
		gl_wnd = new Gl_Window( 0,0,600,400);  gl_wnd->end(); //create gl window
	main_wnd->end();
	main_wnd->show();
	main_wnd->redraw();
	
	return Fl::run();
}


================================================
FILE: cpp/samples/segment.cpp
================================================
/*config.h is generated by fltk in your system
 * this file is used with fltk 1.3 with gl enabled.
 * compile by: fltk-config --use-gl --compile segment.cpp
 * or something like: g++ -lX11 -lGL 'segment.cpp' -o 'segment'
*/
#include <math.h>
#include <stdio.h>

#include "config.h" //config.h must always be placed before any Fl header
#include <FL/gl.h>
#include <FL/Fl_Box.H>
#include <FL/Fl_Value_Slider.H>
#include <FL/Fl_Window.H>
#include <FL/Fl_Radio_Light_Button.H>

namespace VASEr
{
	struct Vec2 { double x,y;};
	struct Color { float r,g,b,a;};
}
#include "../vaser/vaser.cpp"
using namespace VASEr;

void test_draw();
#include "test1_base.cpp"

Fl_Window* main_wnd;
Gl_Window* gl_wnd;
Fl_Slider *start_weight, *feathering;
Fl_Button *feather, *no_feather_at_cap, *no_feather_at_core;
Fl_Button *jc_butt, *jc_round, *jc_square, *jc_rect;
Fl_Button *colored, *alphaed, *weighted;

char get_cap_type()
{
	if ( jc_butt->value())
		return PLC_butt;
	else if ( jc_round->value())
		return PLC_round;
	else if ( jc_square->value())
		return PLC_square;
	else if ( jc_rect->value())
		return PLC_rect;
	else
		return 0;
}
void drag_cb(Fl_Widget* W, void*)
{
	gl_wnd->redraw();
}
void make_form()
{
	const int LD = 606;
	//weight feathering
	start_weight = new Fl_Value_Slider(LD,0,200,20,"spectrum start weight");
	start_weight->type(FL_HOR_SLIDER);
	start_weight->bounds(0.3,30.0);
	start_weight->step(0.3*20.0);
	start_weight->value(0.0);
	start_weight->callback(drag_cb);
	
	feathering = new Fl_Value_Slider(LD,40,200,20,"feathering");
	feathering->type(FL_HOR_SLIDER);
	feathering->bounds(1.0,10.0);
	feathering->callback(drag_cb);
	feathering->value(1.0);
	
	//feather, no_feather_at_cap, no_feather_at_core
	feather		   = new Fl_Light_Button(LD,80,100,15,"feather");
	no_feather_at_cap  = new Fl_Light_Button(LD+50,95,150,15,"no_feather_at_cap");
	no_feather_at_core = new Fl_Light_Button(LD+50,110,150,15,"no_feather_at_core");
	feather		  ->value(1);
	no_feather_at_cap ->value(0);
	no_feather_at_core->value(0);
	feather		  ->callback(drag_cb);
	no_feather_at_cap ->callback(drag_cb);
	no_feather_at_core->callback(drag_cb);
	
	//cap type
	{
	Fl_Group* o = new Fl_Group(LD,160,200,30);
		new Fl_Box(LD,160,80,15,"cap type:");
		jc_butt   = new Fl_Radio_Light_Button(LD+20,175,40,15,"butt");
		jc_round  = new Fl_Radio_Light_Button(LD+60,175,50,15,"round");
		jc_square = new Fl_Radio_Light_Button(LD+110,175,50,15,"square");
		jc_rect   = new Fl_Radio_Light_Button(LD+160,175,40,15,"rect");
	o->end();
	jc_butt   ->value(1);
	jc_butt   ->callback(drag_cb);
	jc_round  ->callback(drag_cb);
	jc_square ->callback(drag_cb);
	jc_rect   ->callback(drag_cb);
	}
	
	//test options
	colored = new Fl_Light_Button(LD,250,60,15,"colored");
	colored->callback(drag_cb);
	colored->value(1);
	alphaed = new Fl_Light_Button(LD+60,250,70,15,"alpha-ed");
	alphaed->callback(drag_cb);
	alphaed->value(1);
	weighted = new Fl_Light_Button(LD+130,250,70,15,"weighted");
	weighted->callback(drag_cb);
}
void test_draw()
{
	renderer::before();
	
	polyline_opt opt={0};
	opt.feather    = feather->value();
	opt.feathering = feathering->value();
	opt.no_feather_at_cap = no_feather_at_cap->value();
	opt.no_feather_at_core = no_feather_at_core->value();
	opt.cap   = get_cap_type();
	
	for ( int i=0; i<20; i++)
	{
		Vec2  P1 = { 5+29.7*i, 187};
		Vec2  P2 = { 35+29.7*i, 8};
		Color C1 = { 0,0,0, 1};
		Color C2 = C1;
		double W1= 0.3*(i+1) + start_weight->value();
		double W2= W1;
		if ( colored->value())
		{
			Color cc1 = { 1.0,0.0,0.5, 1.0};
			C1 = cc1;
			Color cc2 = { 0.5,0.0,1.0, 1.0};
			C2 = cc2;
		}
		if ( alphaed->value())
		{
			C1.a = 0.5f;
			C2.a = 0.5f;
		}
		if ( weighted->value())
		{
			W1 = 0.1;
		}
		if ( opt.cap != PLC_butt)
		{
			double end_weight = 0.3*(20) + start_weight->value();
			P1.y -= end_weight*0.5;
			P2.y += end_weight*0.5;
		}
		segment(P1, P2,       //coordinates
			C1, C2,       //colors
			W1, W2,       //weights
			&opt);        //extra options
	}
	
	const double pi=3.14159265;
	for ( double ag=0, i=0; ag<2*pi-0.1; ag+=pi/12, i+=1)
	{
		double r1 = 0.0;
		double r2 = 90.0;
		if ( !weighted->value())
			r1 = 30.0;
		if ( opt.cap != PLC_butt)
		{
			double end_weight = 0.3*(12) + start_weight->value();
			r2 -= end_weight*0.5;
		}
		
		double tx2=r2*cos(ag);
		double ty2=r2*sin(ag);
		double tx1=r1*cos(ag);
		double ty1=r1*sin(ag);
		double Ox = 120;
		double Oy = 194+97;
		
		Vec2  P1 = { Ox+tx1,Oy-ty1};
		Vec2  P2 = { Ox+tx2,Oy-ty2};
		Color C1 = { 0,0,0, 1};
		Color C2 = C1;
		double W1= 0.3*(i+1) + start_weight->value();
		double W2= W1;
		if ( colored->value())
		{
			Color cc1 = { 1.0,0.0,0.5, 1.0};
			C1 = cc1;
			Color cc2 = { 0.5,0.0,1.0, 1.0};
			C2 = cc2;
		}
		if ( alphaed->value())
		{
			C1.a = 0.5f;
			C2.a = 0.5f;
		}
		if ( weighted->value())
		{
			W1 = 0.1;
		}
		segment(P1, P2,       //coordinates
			C1, C2,       //colors
			W1, W2,       //weights
			&opt);        //extra options
	}
	
	renderer::after();
}

int main(int argc, char **argv)
{
	main_wnd = new Fl_Window( 606+200,194*2,"Vase Renderer - segment() example - fltk/opengl");
		make_form(); //initialize
		gl_wnd = new Gl_Window( 0,0,606,194*2);  gl_wnd->end(); //create gl window
	main_wnd->end();
	main_wnd->show();
	main_wnd->redraw();
	
	return Fl::run();
}


================================================
FILE: cpp/samples/test1_base.cpp
================================================
#include "config.h"
#include <FL/Fl.H>
#include <FL/gl.h>
#include <FL/Fl_Window.H>
#include <FL/Fl_Gl_Window.H>

class Gl_Window : public Fl_Gl_Window
{
	//methods
	void init();
	void draw();
	int handle(int);
	void left_mouse_button_down();
	void left_mouse_button_up();
	void leftclick_drag();
	
	//variables
	short curx,cury, lastx,lasty;
	short cur_drag; //index of point which is being draged currently
			// -1 means none
	int tsize;
	Vec2* target;

	public:
	Gl_Window(int x,int y,int w,int h,const char *l=0)
		: Fl_Gl_Window(x,y,w,h,l) { init();}
	Gl_Window(int w,int h,const char *l=0)
		: Fl_Gl_Window(w,h,l) { init();}
	void set_drag_target( Vec2* target, int size_of_target)
		{ this->target=target; this->tsize=size_of_target;}
};
void Gl_Window::init()
{
	curx=0; cury=0; lastx=0; lasty=0;
	cur_drag=-1;
	tsize=0;
	target=0;
	
}
void Gl_Window::draw()
{
	if (!valid())
	{
		glMatrixMode(GL_PROJECTION);
			glLoadIdentity();
			glOrtho( 0,w(),h(),0,0.0f,100.0f);
			glClearColor( 1.0, 1.0, 1.0, 1.0);
			glClearDepth( 0.0f);
	}
	glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
	
	test_draw();
}
void Gl_Window::left_mouse_button_down()
{
	for ( int i=0; i<tsize; i++)
	{
		const short ALW=10;
		short dx=curx-target[i].x;
		short dy=cury-target[i].y;
		if ( -ALW<dx && dx<ALW)
		if ( -ALW<dy && dy<ALW)
		{
			cur_drag=i;
			return;
		}
	}
	cur_drag=-1;
};
void Gl_Window::left_mouse_button_up()
{
};
void Gl_Window::leftclick_drag()
{
	if ( target)
	if ( cur_drag >=0 && cur_drag< tsize)
	{
		target[cur_drag].x=curx;
		target[cur_drag].y=cury;
		this->redraw();
	}
};
int Gl_Window::handle(int event)
{
	switch(event)
	{
		case FL_PUSH:
		case FL_RELEASE:
		case FL_DRAG:
		case FL_MOVE:
			curx = Fl::event_x();
			cury = Fl::event_y();
			switch(event)
			{
				case FL_PUSH:
					if ( Fl::event_button() == FL_LEFT_MOUSE)
						left_mouse_button_down();
				case FL_RELEASE:
					if ( Fl::event_button() == FL_LEFT_MOUSE)
						left_mouse_button_up();
				case FL_DRAG:
					if ( (Fl::event_state()&FL_BUTTON1)==FL_BUTTON1)
						leftclick_drag();
				case FL_MOVE:
					;
			}
			lastx=curx;
			lasty=cury;
		return 1;
		
		default:
		return Fl_Window::handle(event);
	} //end of switch(event)
};


================================================
FILE: cpp/vaser/agg_curve4.cpp
================================================
//-----------------------------------------------------------------------
// The Anti-Grain Geometry Project
// A high quality rendering engine for C++
// http://antigrain.com
// 
// Anti-Grain Geometry has dual licensing model. The Modified BSD 
// License was first added in version v2.4 just for convenience.
// It is a simple, permissive non-copyleft free software license, 
// compatible with the GNU GPL. It's well proven and recognizable.
// See http://www.fsf.org/licensing/licenses/index_html#ModifiedBSD
// for details.
// 
// Note that the Modified BSD license DOES NOT restrict your rights 
// if you choose the Anti-Grain Geometry Public License.
// 
// Anti-Grain Geometry Public License
// ====================================================
// 
// Anti-Grain Geometry - Version 2.4 
// Copyright (C) 2002-2005 Maxim Shemanarev (McSeem) 
// 
// Permission to copy, use, modify, sell and distribute this software 
// is granted provided this copyright notice appears in all copies. 
// This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
// 
// 
// 
// Modified BSD License
// ====================================================
// Anti-Grain Geometry - Version 2.4 
// Copyright (C) 2002-2005 Maxim Shemanarev (McSeem) 
// 
// Redistribution and use in source and binary forms, with or without 
// modification, are permitted provided that the following conditions 
// are met:
// 
//   1. Redistributions of source code must retain the above copyright 
//      notice, this list of conditions and the following disclaimer. 
// 
//   2. Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in 
//      the documentation and/or other materials provided with the 
//      distribution. 
// 
//   3. The name of the author may not be used to endorse or promote 
//      products derived from this software without specific prior 
//      written permission. 
// 
// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 
// IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 
// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, 
// INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR 
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 
// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING 
// IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
// POSSIBILITY OF SUCH DAMAGE.
//
//-----------------------------------------------------------------------
// Contact: mcseem@antigrain.com
//          mcseemagg@yahoo.com
//          http://www.antigrain.com
//-----------------------------------------------------------------------

#include <math.h>
#ifndef M_PI
	#define M_PI 3.141592653589793238462643
#endif

double calc_sq_distance(double x1, double y1, double x2, double y2)
{
	double dx = x2-x1;
	double dy = y2-y1;
	return dx * dx + dy * dy;
}

void recursive_bezier(   double x1, double y1, 
				double x2, double y2, 
				double x3, double y3, 
				double x4, double y4,
				unsigned level,
				double m_angle_tolerance,
				double m_cusp_limit,
				double m_distance_tolerance_square,
				void (*add_point)(void*,double,double),
				void* obj )
{
	const double curve_distance_epsilon                  = 1e-30;
	const double curve_collinearity_epsilon              = 1e-30;
	const double curve_angle_tolerance_epsilon           = 0.01;
	const int curve_recursion_limit = 32;

	if(level > curve_recursion_limit) 
	{
		return;
	}

	// Calculate all the mid-points of the line segments
	//----------------------
	double x12   = (x1 + x2) / 2;
	double y12   = (y1 + y2) / 2;
	double x23   = (x2 + x3) / 2;
	double y23   = (y2 + y3) / 2;
	double x34   = (x3 + x4) / 2;
	double y34   = (y3 + y4) / 2;
	double x123  = (x12 + x23) / 2;
	double y123  = (y12 + y23) / 2;
	double x234  = (x23 + x34) / 2;
	double y234  = (y23 + y34) / 2;
	double x1234 = (x123 + x234) / 2;
	double y1234 = (y123 + y234) / 2;

	// Try to approximate the full cubic curve by a single straight line
	//------------------
	double dx = x4-x1;
	double dy = y4-y1;

	double d2 = fabs(((x2 - x4) * dy - (y2 - y4) * dx));
	double d3 = fabs(((x3 - x4) * dy - (y3 - y4) * dx));
	double da1, da2, k;

	switch((int(d2 > curve_collinearity_epsilon) << 1) +
	int(d3 > curve_collinearity_epsilon))
	{
		case 0:
			// All collinear OR p1==p4
			//----------------------
			k = dx*dx + dy*dy;
			if(k == 0)
			{
				d2 = calc_sq_distance(x1, y1, x2, y2);
				d3 = calc_sq_distance(x4, y4, x3, y3);
			}
			else
			{
				k   = 1 / k;
				da1 = x2 - x1;
				da2 = y2 - y1;
				d2  = k * (da1*dx + da2*dy);
				da1 = x3 - x1;
				da2 = y3 - y1;
				d3  = k * (da1*dx + da2*dy);
				if(d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1)
				{
					// Simple collinear case, 1---2---3---4
					// We can leave just two endpoints
					return;
				}
				if(d2 <= 0) d2 = calc_sq_distance(x2, y2, x1, y1);
				else if(d2 >= 1) d2 = calc_sq_distance(x2, y2, x4, y4);
				else             d2 = calc_sq_distance(x2, y2, x1 + d2*dx, y1 + d2*dy);

				if(d3 <= 0) d3 = calc_sq_distance(x3, y3, x1, y1);
				else if(d3 >= 1) d3 = calc_sq_distance(x3, y3, x4, y4);
				else             d3 = calc_sq_distance(x3, y3, x1 + d3*dx, y1 + d3*dy);
			}
			if(d2 > d3)
			{
				if(d2 < m_distance_tolerance_square)
				{
					add_point(obj, x2,y2);
					return;
				}
			}
			else
			{
				if(d3 < m_distance_tolerance_square)
				{
					add_point(obj, x3,y3);
					return;
				}
			}
		break;

		case 1:
			// p1,p2,p4 are collinear, p3 is significant
			//----------------------
			if(d3 * d3 <= m_distance_tolerance_square * (dx*dx + dy*dy))
			{
				if(m_angle_tolerance < curve_angle_tolerance_epsilon)
				{
					add_point(obj, x23,y23);
					return;
				}

				// Angle Condition
				//----------------------
				da1 = fabs(atan2(y4 - y3, x4 - x3) - atan2(y3 - y2, x3 - x2));
				if(da1 >= M_PI) da1 = 2*M_PI - da1;

				if(da1 < m_angle_tolerance)
				{
					add_point(obj, x2, y2);
					add_point(obj, x3, y3);
					return;
				}

				if(m_cusp_limit != 0.0)
				{
					if(da1 > m_cusp_limit)
					{
						add_point(obj, x3, y3);
						return;
					}
				}
			}
		break;

		case 2:
			// p1,p3,p4 are collinear, p2 is significant
			//----------------------
			if(d2 * d2 <= m_distance_tolerance_square * (dx*dx + dy*dy))
			{
				if(m_angle_tolerance < curve_angle_tolerance_epsilon)
				{
					add_point(obj, x23, y23);
					return;
				}

				// Angle Condition
				//----------------------
				da1 = fabs(atan2(y3 - y2, x3 - x2) - atan2(y2 - y1, x2 - x1));
				if(da1 >= M_PI) da1 = 2*M_PI - da1;

				if(da1 < m_angle_tolerance)
				{
					add_point(obj, x2, y2);
					add_point(obj, x3, y3);
					return;
				}

				if(m_cusp_limit != 0.0)
				{
					if(da1 > m_cusp_limit)
					{
						add_point(obj, x2, y2);
						return;
					}
				}
			}
		break;

		case 3: 
			// Regular case
			//-----------------
			if((d2 + d3)*(d2 + d3) <= m_distance_tolerance_square * (dx*dx + dy*dy))
			{
				// If the curvature doesn't exceed the distance_tolerance value
				// we tend to finish subdivisions.
				//----------------------
				if(m_angle_tolerance < curve_angle_tolerance_epsilon)
				{
					add_point(obj, x23, y23);
					return;
				}

				// Angle & Cusp Condition
				//----------------------
				k   = atan2(y3 - y2, x3 - x2);
				da1 = fabs(k - atan2(y2 - y1, x2 - x1));
				da2 = fabs(atan2(y4 - y3, x4 - x3) - k);
				if(da1 >= M_PI) da1 = 2*M_PI - da1;
				if(da2 >= M_PI) da2 = 2*M_PI - da2;

				if(da1 + da2 < m_angle_tolerance)
				{
					// Finally we can stop the recursion
					//----------------------
					add_point(obj, x23, y23);
					return;
				}

				if(m_cusp_limit != 0.0)
				{
					if(da1 > m_cusp_limit)
					{
						add_point(obj, x2, y2);
						return;
					}

					if(da2 > m_cusp_limit)
					{
						add_point(obj, x3, y3);
						return;
					}
				}
			}
		break;
	}

	// Continue subdivision
	//----------------------
	recursive_bezier(x1, y1, x12, y12, x123, y123, x1234, y1234, level + 1,
		m_angle_tolerance, m_cusp_limit, m_distance_tolerance_square,
		add_point, obj); 
	recursive_bezier(x1234, y1234, x234, y234, x34, y34, x4, y4, level + 1,
		m_angle_tolerance, m_cusp_limit, m_distance_tolerance_square,
		add_point, obj); 
}

int curve4_div(double x1, double y1, 
		double x2, double y2, 
		double x3, double y3,
		double x4, double y4,
		double m_approximation_scale,
		double m_angle_tolerance,
		double m_cusp_limit,
		void (*add_point)(void*,double,double),
		void* obj )
{
	double m_distance_tolerance_square = 0.5 / m_approximation_scale;
	m_distance_tolerance_square *= m_distance_tolerance_square;
	int m_count = 0;
	add_point(obj, x1, y1);
	recursive_bezier(x1, y1, x2, y2, x3, y3, x4, y4, 0,
		m_angle_tolerance, m_cusp_limit, m_distance_tolerance_square,
		add_point, obj);
	add_point(obj, x4, y4);
}

#undef M_PI


================================================
FILE: cpp/vaser/backend.h
================================================
class backend
{
public:
	static void vah_draw(vertex_array_holder& vah);
	static void polyline( const Vec2*, Color, double W, int length, const polyline_opt*); //constant color and weight
};


================================================
FILE: cpp/vaser/color.h
================================================
float& Color_get( Color& C, int index)
{
	switch (index)
	{
		case 0: return C.r;
		case 1: return C.g;
		case 2: return C.b;
		default:return C.r;
	}
}
bool Color_valid_range(float t)
{
	return t>=0.0f && t<=1.0f;
}
Color Color_between( const Color& A, const Color& B, float t=0.5f)
{
	if ( t<0.0f) t = 0.0f;
	if ( t>1.0f) t = 1.0f;
	
	float kt = 1.0f - t;
	Color C =
	{
		A.r *kt + B.r *t,
		A.g *kt + B.g *t,
		A.b *kt + B.b *t,
		A.a *kt + B.a *t
	};
	return C;
}
void sRGBtolinear( Color& C, bool exact=false)
{	//de-Gamma 2.2
	//from: http://www.xsi-blog.com/archives/133
	if (exact)
	{
		for ( int i=0; i<3; i++)
		{
			float& cc = Color_get( C,i);
			
			if ( cc > 0.04045)
				cc = pow( (cc+0.055)/1.055, 2.4);
			else
				cc /= 12.92;
		}
	}
	else
	{	//approximate
		for ( int i=0; i<3; i++)
		{
			float& cc = Color_get( C,i);
			cc = pow(cc,2.2);
		}
	}
}
void lineartosRGB( Color& C, bool exact=false)
{	//Gamma 2.2
	if (exact)
	{
		for ( int i=0; i<3; i++)
		{
			float& cc = Color_get( C,i);
			if ( cc > 0.0031308)
				cc = 1.055 * pow(cc,1.0/2.4) - 0.055;
			else
				cc *= 12.92;
		}
	}
	else
	{	//approximate
		for ( int i=0; i<3; i++)
		{
			float& cc = Color_get( C,i);
			cc = pow(cc,1.0/2.2);
		}
	}
}
float color_max( float r,float g,float b)
{
	return r>g? (g>b?r:(r>b?r:b)) : (g>b?g:b);
}
float color_min( float r, float g, float b)
{
	return -color_max( -r,-g,-b);
}
void RGBtoHSV( float r, float g, float b, float *h, float *s, float *v )
{	//from: http://www.cs.rit.edu/~ncs/color/t_convert.html
	// r,g,b values are from 0 to 1
	// h = [0,360], s = [0,1], v = [0,1]
	//		if s == 0, then h = -1 (undefined)
	float min, max, delta;
	min = color_min( r, g, b );
	max = color_max( r, g, b );
	*v = max;				// v
	delta = max - min;
	if( max != 0 )
		*s = delta / max;		// s
	else {
		// r = g = b = 0		// s = 0, v is undefined
		*s = 0;
		*h = -1;
		return;
	}
	if( r == max )
		*h = ( g - b ) / delta;		// between yellow & magenta
	else if( g == max )
		*h = 2 + ( b - r ) / delta;	// between cyan & yellow
	else
		*h = 4 + ( r - g ) / delta;	// between magenta & cyan
	*h *= 60;				// degrees
	if( *h < 0 )
		*h += 360;
}
void HSVtoRGB( float *r, float *g, float *b, float h, float s, float v )
{
	int i;
	float f, p, q, t;
	if( s == 0 ) {
		// achromatic (grey)
		*r = *g = *b = v;
		return;
	}
	h /= 60;			// sector 0 to 5
	i = floor( h );
	f = h - i;			// factorial part of h
	p = v * ( 1 - s );
	q = v * ( 1 - s * f );
	t = v * ( 1 - s * ( 1 - f ) );
	switch( i ){
		case 0:
			*r = v; *g = t; *b = p;		break;
		case 1:
			*r = q; *g = v;	*b = p;		break;
		case 2:
			*r = p;	*g = v;	*b = t;		break;
		case 3:
			*r = p;	*g = q;	*b = v;		break;
		case 4:
			*r = t;	*g = p;	*b = v;		break;
		default:		// case 5:
			*r = v;	*g = p;	*b = q;		break;
	}
}


================================================
FILE: cpp/vaser/curve.cpp
================================================
namespace VASErin
{	//VASEr internal namespace

class polyline_buffer
{
public:
	std::vector<Vec2>   P;
	std::vector<Color>  C;
	std::vector<double> W;
	std::vector<double> L; //length along polyline
	int N;
	double path_length; //total segment length

	polyline_buffer(): P(),C(),W(),L()
	{
		N=0;
		path_length=0.0;
		L.push_back(0.0);
	}
	void point(double x, double y)
	{
		Vec2 V={x,y};
		addvertex(V);
	}
	void point(Vec2 V)
	{
		addvertex(V);
	}
	static void point_cb(void* obj, double x, double y)
	{
		polyline_buffer* This = (polyline_buffer*)obj;
		Vec2 V={x,y};
		This->addvertex(V);
	}
	void vertex(Vec2 V, Color cc)
	{
		addvertex(V,&cc);
	}
	void vertex(Vec2 V, Color cc, double ww)
	{
		addvertex(V,& cc,ww);
	}
	void set_color(Color cc)
	{
		if( !C.size())
			C.push_back(cc);
		else
			C.back()=cc;
	}
	void set_weight(double ww)
	{
		if( !W.size())
			W.push_back(ww);
		else
			W.back()=ww;
	}
	void gradient( const gradient* grad)
	{
		gradient_apply(grad,&C[0],&W[0],&L[0],N,path_length);
	}
	void draw(const polyline_opt* options)
	{
		if( !N) return;
		polyline_inopt in_options={0};
		in_options.segment_length = &L[0];
		polyline( &P[0],&C[0],&W[0],N,options,&in_options);
	}
private:
	bool addvertex(const Vec2& V, const Color* cc=0, double ww=0.0)
	{
		if( N && P[N-1].x==V.x && P[N-1].y==V.y)
			return false; //duplicate
		else
		{
			//point
			P.push_back(V);
			if( N>0)
			{
				double len = (Point(V)-Point(P[N-1])).length();
				path_length += len;
				L.push_back(len);
			}
			//color
			if( cc)
				C.push_back(*cc);
			else
			{
				if( !C.size())
					C.push_back(default_color);
				else
					C.push_back(C.back());
			}
			//weight
			if( ww)
				W.push_back(ww);
			else
			{
				if( !W.size())
					W.push_back(default_weight);
				else
					W.push_back(W.back());
			}
			//finally
			N++;
			return true;
		}
	}
};

struct polybezier_inopt
{
	bool evaluate_only;
	polyline_buffer* target;
};

void polybezier( const Vec2* P, const gradient* grad, int length, const polybezier_opt* options, const polybezier_inopt* in_options)
{
	polybezier_opt opt={0};
	polybezier_inopt inopt={0};
	polyline_opt poly={0};
	poly.joint = PLJ_bevel;
	if( options) opt = *options;
	if( in_options) inopt = *in_options;
	if( !opt.poly) opt.poly = &poly;

	polyline_buffer _buf;
	polyline_buffer& buf = _buf;
	if( inopt.target)
		buf = *inopt.target;

	const double BZ_default_approximation_scale = 0.5;
	const double BZ_default_angle_tolerance = 15.0/180*vaser_pi;
	const double BZ_default_cusp_limit = 5.0;

	for( int i=0; i<length-3; i+=3)
	{
		curve4_div(
			P[i+0].x,P[i+0].y,
			P[i+1].x,P[i+1].y,
			P[i+2].x,P[i+2].y,
			P[i+3].x,P[i+3].y,
			BZ_default_approximation_scale,
			BZ_default_angle_tolerance,
			BZ_default_cusp_limit,
			polyline_buffer::point_cb,
			&buf);
	}
	if( grad)
		buf.gradient(grad);
	if( !inopt.evaluate_only)
		buf.draw(opt.poly);
}

} //sub namespace VASErin

//export implementations

void polybezier( const Vec2* P, const gradient* grad, int length, const polybezier_opt* options)
{
	VASErin::polybezier(P,grad,length,options,0);
}

void polybezier( const Vec2* P, Color cc, double ww, int length, const polybezier_opt* options)
{
	gradient grad = {0};
	gradient_stop stop[2] = {0};
	grad.stops = stop;
	grad.length = 2;
	stop[0].type = GS_rgba; stop[0].color = cc;
	stop[1].type = GS_weight; stop[1].weight = ww;
	VASErin::polybezier(P,&grad,length,options,0);
}


================================================
FILE: cpp/vaser/gradient.cpp
================================================
namespace VASErin
{	//VASEr internal namespace

double grad_getstep(double A,double B,double t,double T)
{
	return ((T-t)*A + t*B) / T;
}

void gradient_apply(const gradient* gradp, Color* C, double* W, const double* L, int length, double path_length)
{
	if( !gradp) return;
	if( !gradp->stops || !gradp->length) return;
	const gradient& grad = *gradp;
	const gradient_stop* stop = grad.stops;

	//current stops
	int las_c=0, las_a=0, las_w=0, //last
		cur_c=0, cur_a=0, cur_w=0, //current
		nex_c=0, nex_a=0, nex_w=0; //next
	double length_along=0.0;
	if( grad.length>1)
	for( int i=0; i<length; i++)
	{
		length_along += L[i];
		double p;
		if( grad.unit==GD_ratio)
			p = length_along/path_length;
		else if ( grad.unit==GD_length)
			p = length_along;

		{	//lookup for cur
			for( nex_w=cur_w; nex_w < grad.length; nex_w++)
				if( stop[nex_w].type==GS_weight && p <= stop[nex_w].t)
					{ cur_w=nex_w; break;}
			for( nex_c=cur_c; nex_c < grad.length; nex_c++)
				if( (stop[nex_c].type==GS_rgba || stop[nex_c].type==GS_rgb ) &&
					p <= stop[nex_c].t)
					{ cur_c=nex_c; break;}
			for( nex_a=cur_a; nex_a < grad.length; nex_a++)
				if( (stop[nex_a].type==GS_rgba || stop[nex_a].type==GS_alpha ) &&
					p <= stop[nex_a].t)
					{ cur_a=nex_a; break;}
			//look for las
			for( nex_w=cur_w; nex_w >= 0; nex_w--)
				if( stop[nex_w].type==GS_weight && p >= stop[nex_w].t)
					{ las_w=nex_w; break;}
			for( nex_c=cur_c; nex_c >= 0; nex_c--)
				if( (stop[nex_c].type==GS_rgba || stop[nex_c].type==GS_rgb ) &&
					p >= stop[nex_c].t)
					{ las_c=nex_c; break;}
			for( nex_a=cur_a; nex_a >= 0; nex_a--)
				if( (stop[nex_a].type==GS_rgba || stop[nex_a].type==GS_alpha ) &&
					p >= stop[nex_a].t)
					{ las_a=nex_a; break;}
		}
		#define SC(x) stop[x].color
		#define Sw(x) stop[x].weight
		#define Sa(x) stop[x].color.a
		#define St(x) stop[x].t
		if ( cur_c==las_c)
			C[i] = SC(cur_c);
		else
			C[i] = Color_between(SC(las_c),SC(cur_c), (p-St(las_c))/(St(cur_c)-St(las_c)));
		if ( cur_w==las_w)
			W[i] = Sw(cur_w);
		else
			W[i] = grad_getstep(Sw(las_w),Sw(cur_w), p-St(las_w), St(cur_w)-St(las_w));
		if ( cur_a==las_a)
			C[i].a = Sa(cur_a);
		else
			C[i].a = grad_getstep(Sa(las_a),Sa(cur_a), p-St(las_a), St(cur_a)-St(las_a));
		#undef SC
		#undef Sw
		#undef Sa
		#undef St
	}
}

} //sub namespace VASErin


================================================
FILE: cpp/vaser/opengl.cpp
================================================
/* OpenGL 1.1 renderer and backend */

namespace VASErin
{	//VASEr internal namespace

void backend::vah_draw(vertex_array_holder& vah)
{
	if ( vah.count > 0) //save some effort
	{
		glVertexPointer(2, GL_FLOAT, 0, &vah.vert[0]);
		glColorPointer (4, GL_FLOAT, 0, &vah.color[0]);
		glDrawArrays (vah.glmode, 0, vah.count);
	}
}

void backend::polyline( const Vec2* P, Color C, double W, int length, const polyline_opt*) //constant color and weight
{
	int type=0;
	if( sizeof(Vec2)==16)
		type = GL_DOUBLE;
	else if( sizeof (Vec2)==8)
		type = GL_FLOAT;

	glColor4f(C.r,C.g,C.b,C.a);
	glLineWidth(W);
	if( type)
	{
		glEnableClientState(GL_VERTEX_ARRAY);
		glDisableClientState(GL_COLOR_ARRAY);
		glVertexPointer(2, type, 0, P);
		glDrawArrays(GL_LINE_STRIP, 0, length);
		glEnableClientState(GL_COLOR_ARRAY);
	}
	else
	{
		glBegin(GL_LINE_STRIP);
		for( int i=0; i<length; i++)
			glVertex2f(P[i].x,P[i].y);
		glEnd();
	}
	glLineWidth(1);
}

void swap_pixel(unsigned char* img, int w, int x1,int y1, int x2,int y2)
{
	const int b=4;
	unsigned char R = img[y1*w*b+x1*b];
	unsigned char G = img[y1*w*b+x1*b+1];
	unsigned char B = img[y1*w*b+x1*b+2];
	unsigned char A = img[y1*w*b+x1*b+3];
	
	img[y1*w*b+x1*b] = img[y2*w*b+x2*b];
	img[y1*w*b+x1*b+1] = img[y2*w*b+x2*b+1];
	img[y1*w*b+x1*b+2] = img[y2*w*b+x2*b+2];
	img[y1*w*b+x1*b+3] = img[y2*w*b+x2*b+3];
	
	img[y2*w*b+x2*b] = R;
	img[y2*w*b+x2*b+1] = G;
	img[y2*w*b+x2*b+2] = B;
	img[y2*w*b+x2*b+3] = A;
}

} //sub namespace VASErin

void renderer::init()
{
}

void renderer::before()
{
	glEnableClientState(GL_VERTEX_ARRAY);
	glEnableClientState(GL_COLOR_ARRAY);
	
	glDisableClientState(GL_EDGE_FLAG_ARRAY);
	//glDisableClientState(GL_FOG_COORD_ARRAY);
	glDisableClientState(GL_INDEX_ARRAY);
	glDisableClientState(GL_NORMAL_ARRAY);
	//glDisableClientState(GL_SECONDARY_COLOR_ARRAY);
	glDisableClientState(GL_TEXTURE_COORD_ARRAY);
	
	glEnable(GL_BLEND);
	glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
}
void renderer::after()
{
	glDisableClientState(GL_VERTEX_ARRAY);
	glDisableClientState(GL_COLOR_ARRAY);
	glDisable(GL_BLEND);
}
Image renderer::get_image()
{
	int res[4];
	glGetIntegerv(GL_VIEWPORT,res);
	Image im={0};
	im.width=res[2];
	im.height=res[3];
	im.buf=(unsigned char*)malloc(im.width*im.height*4);
	if( !im.buf)
		return im;
	glReadPixels(0, 0, im.width, im.height, GL_RGBA, GL_UNSIGNED_BYTE, (GLvoid *)im.buf);
	//flip horizontally
	for( int i=0; i<im.height/2; i++)
		for( int j=0; j<im.width; j++)
			VASErin::swap_pixel(im.buf,im.width,j,i,j,im.height-i-1);
	return im;
}



================================================
FILE: cpp/vaser/point.h
================================================
class Point : public Vec2
{
public:
	Point() { clear();}
	Point(const Vec2& P) { set(P.x,P.y);}
	Point(const Point& P) { set(P.x,P.y);}
	Point(double X, double Y) { set(X,Y);}
	
	void clear()			{ x=0.0; y=0.0;}
	void set(double X, double Y)	{ x=X;   y=Y;}
	
	Vec2 vec() {
		Vec2 V;
		V.x = x; V.y = y;
		return V;
	}
	
	//attributes
	double length() const
	{
		return sqrt(x*x+y*y);
	}
	double slope() const
	{
		return y/x;
	}
	static double signed_area(const Point& P1, const Point& P2, const Point& P3)
	{
		return (P2.x-P1.x)*(P3.y-P1.y) - (P3.x-P1.x)*(P2.y-P1.y);
	}
	
	//vector operators	
	Point operator+(const Point &b) const
	{
		return Point( x+b.x, y+b.y);
	}
	Point operator-() const
	{
		return Point( -x, -y);
	}
	Point operator-(const Point &b) const
	{
		return Point( x-b.x, y-b.y);
	}
	Point operator*(double k) const
	{
		return Point( x*k, y*k);
	}
	
	Point& operator=(const Point& b) {
		x = b.x; y = b.y;
		return *this;
	}
	Point& operator+=(const Point& b)
	{
		x += b.x; y += b.y;
		return *this;
	}
	Point& operator-=(const Point& b)
	{
		x -= b.x; y -= b.y;
		return *this;
	}
	Point& operator*=(const double k)
	{
		x *= k; y *= k;
		return *this;
	}
	Point& operator/=(const double k)
	{
		x /= k; y /= k;
		return *this;
	}
	
	static void dot( const Point& a, const Point& b, Point& o) //dot product: o = a dot b
	{
		o.x = a.x * b.x;
		o.y = a.y * b.y;
	}
	Point dot_prod( const Point& b) const //return dot product
	{
		return Point( x*b.x, y*b.y);
	}
	
	//self operations
	void opposite()
	{
		x = -x;
		y = -y;
	}
	void opposite_of( const Point& a)
	{
		x = -a.x;
		y = -a.y;
	}
	double normalize()
	{
		double L = length();
		if ( L > vaser_min_alw)
		{
			x /= L; y /= L;
		}
		return L;
	}
	void perpen() //perpendicular: anti-clockwise 90 degrees
	{
		double y_value=y;
		y=x;
		x=-y_value;
	}
	void follow_signs( const Point& a)
	{
		if ( (x>0) != (a.x>0))	x = -x;
		if ( (y>0) != (a.y>0))	y = -y;
	}
	void follow_magnitude( const Point& a);
	void follow_direction( const Point& a);
	
	//judgements
	static inline bool negligible( double M)
	{
		return -vaser_min_alw < M && M < vaser_min_alw;
	}
	bool negligible() const
	{
		return Point::negligible(x) && Point::negligible(y);
	}
	bool non_negligible() const
	{
		return !negligible();
	}
	bool is_zero() const
	{
		return x==0.0 && y==0.0;
	}
	bool non_zero() const
	{
		return !is_zero();
	}
	static bool intersecting( const Point& A, const Point& B,
		const Point& C, const Point& D)
	{	//return true if AB intersects CD
		return signed_area(A,B,C)>0 != signed_area(A,B,D)>0;
	}
	
	//operations require 2 input points
	static double distance_squared( const Point& A, const Point& B)
	{
		double dx=A.x-B.x;
		double dy=A.y-B.y;
		return (dx*dx+dy*dy);
	}
	static inline double distance( const Point& A, const Point& B)
	{
		return sqrt( distance_squared(A,B));
	}
	static Point midpoint( const Point& A, const Point& B)
	{
		return (A+B)*0.5;
	}
	static bool opposite_quadrant( const Point& P1, const Point& P2)
	{
		char P1x = P1.x>0? 1:(P1.x<0?-1:0);
		char P1y = P1.y>0? 1:(P1.y<0?-1:0);
		char P2x = P2.x>0? 1:(P2.x<0?-1:0);
		char P2y = P2.y>0? 1:(P2.y<0?-1:0);
		
		if ( P1x!=P2x) {
			if ( P1y!=P2y)
				return true;
			if ( P1y==0 || P2y==0)
				return true;
		}
		if ( P1y!=P2y) {
			if ( P1x==0 || P2x==0)
				return true;
		}
		return false;
	}
	
	//operations of 3 points
	static inline bool anchor_outward_D( Point& V, const Point& b, const Point& c)
	{
		return (b.x*V.x - c.x*V.x + b.y*V.y - c.y*V.y) > 0;
	}
	static bool anchor_outward( Point& V, const Point& b, const Point& c, bool reverse=false)
	{ //put the correct outward vector at V, with V placed on b, comparing distances from c
		bool determinant = anchor_outward_D ( V,b,c);
		if ( determinant == (!reverse)) { //when reverse==true, it means inward
			//positive V is the outward vector
			return false;
		} else {
			//negative V is the outward vector
			V.x=-V.x;
			V.y=-V.y;
			return true; //return whether V is changed
		}
	}
	static void anchor_inward( Point& V, const Point& b, const Point& c)
	{
		anchor_outward( V,b,c,true);
	}
	
	//operations of 4 points
	static char intersect( const Point& P1, const Point& P2,  //line 1
			const Point& P3, const Point& P4, //line 2
			Point& Pout,			  //the output point
			double* ua_out=0, double* ub_out=0)
	{ //Determine the intersection point of two line segments
		double mua,mub;
		double denom,numera,numerb;

		denom  = (P4.y-P3.y) * (P2.x-P1.x) - (P4.x-P3.x) * (P2.y-P1.y);
		numera = (P4.x-P3.x) * (P1.y-P3.y) - (P4.y-P3.y) * (P1.x-P3.x);
		numerb = (P2.x-P1.x) * (P1.y-P3.y) - (P2.y-P1.y) * (P1.x-P3.x);

		if( negligible(numera) &&
			negligible(numerb) &&
			negligible(denom)) {
		Pout.x = (P1.x + P2.x) * 0.5;
		Pout.y = (P1.y + P2.y) * 0.5;
		return 2; //meaning the lines coincide
		}

		if ( negligible(denom)) {
			Pout.x = 0;
			Pout.y = 0;
			return 0; //meaning lines are parallel
		}

		mua = numera / denom;
		mub = numerb / denom;
		if ( ua_out) *ua_out = mua;
		if ( ub_out) *ub_out = mub;

		Pout.x = P1.x + mua * (P2.x - P1.x);
		Pout.y = P1.y + mua * (P2.y - P1.y);
		
		bool out1 = mua < 0 || mua > 1;
		bool out2 = mub < 0 || mub > 1;
		
		if ( out1 & out2) {
			return 5; //the intersection lies outside both segments
		} else if ( out1) {
			return 3; //the intersection lies outside segment 1
		} else if ( out2) {
			return 4; //the intersection lies outside segment 2
		} else {
			return 1; //great
		}
	//http://paulbourke.net/geometry/lineline2d/
	}
}; //end of class Point

/* after all,
 * sizeof(Vec2)=16  sizeof(Point)=16
 * Point is not heavier, just more powerful :)
*/


================================================
FILE: cpp/vaser/polyline.cpp
================================================
namespace VASErin
{	//VASEr internal namespace

/*visual testes:
 * A. points (geometry test)
 *  1. arbitrary polyline of only 2 point
 *  2. polylines of 3 points, making arbitrary included angle
 *  3. arbitrary polyline of 4 or more points
 * B. colors
 *  1. different colors on each point
 * C. weight
 *  1. varying weight
 * D. other drawing options
 *  1. feathering
 *  2. different joint types
 *  3. different cap types
 * E. memory test
 *  1. drawing a polyline of 1000 points
 */

/*known visual bugs: ( ",," simply means "go wild" as it is too hard to describe)
 * 1.  [solved]when 2 segments are exactly at 90 degrees, the succeeding line segment is reflexed.
 * 1.1 [solved]when 2 segments are exactly at 180 degrees,,
 * 2.  [solved]when polyline is dragged, caps seem to have pseudo-podia.
 * 3.  [solved]when 2 segments are exactly horizontal/ vertical, both segments are reflexed.
 * 3.1 [solved]when a segment is exactly horizontal/ vertical, the cap disappears
 * 4.  [solved]when 2 segments make < 5 degrees,,
 * 4.1 [solved]when 2 segments make exactly 0 degree,,
 * 5.  when a segment is shorter than its own width,,
 */

/* const double vaser_actual_PPI = 96.0;
	const double vaser_standard_PPI = 111.94; //the PPI I used for calibration
 */

//critical weight to do approximation rather than real joint processing
const double cri_segment_approx=1.6;

void determine_t_r ( double w, double& t, double& R)
{
	//efficiency: can cache one set of w,t,R values
	// i.e. when a polyline is of uniform thickness, the same w is passed in repeatedly
	double f=w-static_cast<int>(w);
	
	/*   */if ( w>=0.0 && w<1.0) {
		t=0.05; R=0.768;//R=0.48+0.32*f;
	} else if ( w>=1.0 && w<2.0) {
		t=0.05+f*0.33; R=0.768+0.312*f;
	} else if ( w>=2.0 && w<3.0){
		t=0.38+f*0.58; R=1.08;
	} else if ( w>=3.0 && w<4.0){
		t=0.96+f*0.48; R=1.08;
	} else if ( w>=4.0 && w<5.0){
		t=1.44+f*0.46; R=1.08;
	} else if ( w>=5.0 && w<6.0){
		t=1.9+f*0.6; R=1.08;
	} else if ( w>=6.0){
		double ff=w-6.0;
		t=2.5+ff*0.50; R=1.08;
	}
	
	/* //PPI correction
	double PPI_correction = vaser_standard_PPI / vaser_actual_PPI;
	const double up_bound = 1.6; //max value of w to receive correction
	const double start_falloff = 1.0;
	if ( w>0.0 && w<up_bound)
	{	//here we gracefully apply the correction
		// so that the effect of correction diminishes starting from w=start_falloff
		//   and completely disappears when w=up_bound
		double correction = 1.0 + (PPI_correction-1.0)*(up_bound-w)/(up_bound-start_falloff);
		t *= PPI_correction;
		R *= PPI_correction;
	} */
}
float get_PLJ_round_dangle(float t, float r)
{
	float dangle;
	float sum = t+r;
	if ( sum <= 1.44f+1.08f) //w<=4.0, feathering=1.0
		dangle = 0.6f/(t+r);
	else if ( sum <= 3.25f+1.08f) //w<=6.5, feathering=1.0
		dangle = 2.8f/(t+r);
	else
		dangle = 4.2f/(t+r);
	return dangle;
}

void make_T_R_C( Point& P1, Point& P2, Point* T, Point* R, Point* C,
				double w, const polyline_opt& opt,
				double* rr, double* tt, float* dist,
				bool seg_mode=false)
{
	double t=1.0,r=0.0;
	Point DP=P2-P1;
	
	//calculate t,r
	determine_t_r( w,t,r);
	
	if ( opt.feather && !opt.no_feather_at_core && opt.feathering != 1.0)
		r *= opt.feathering;
	else if ( seg_mode)
	{
		//TODO: handle correctly for hori/vert segments in a polyline
		if ( Point::negligible(DP.x) && P1.x==(int)P1.x) {
			if ( w>0.0 && w<=1.0) {
				t=0.5; r=0.0;
				P2.x = P1.x = (int)P1.x+0.5;
			}
		} else if ( Point::negligible(DP.y) && P1.y==(int)P1.y) {
			if ( w>0.0 && w<=1.0) {
				t=0.5; r=0.0;
				P2.y = P1.y = (int)P1.y+0.5;
			}
		}
	}
	
	//output t,r
	if (tt) *tt = t;
	if (rr) *rr = r;
	
	//calculate T,R,C
	double len = DP.normalize();
	if (dist) *dist = (float)len;
	if (C) *C = DP;
	DP.perpen();
	
	if (T) *T = DP*t;
	if (R) *R = DP*r;
}

void same_side_of_line( Point& V, const Point& ref, const Point& a, const Point& b)
{
	double sign1 = Point::signed_area( a+ref,a,b);
	double sign2 = Point::signed_area( a+V,  a,b);
	if ( (sign1>=0) != (sign2>=0))
	{
		V.opposite();
	}
}

struct st_polyline
//the struct to hold info for anchor_late() to perform triangluation
{
	//for all joints
	Point vP; //vector to intersection point
	Point vR; //fading vector at sharp end
		//all vP,vR are outward
	
	//for djoint==PLJ_bevel
	Point T; //core thickness of a line
	Point R; //fading edge of a line
	Point bR; //out stepping vector, same direction as cap
	Point T1,R1; //alternate vectors, same direction as T21
		//all T,R,T1,R1 are outward
	
	//for djoint==PLJ_round
	float t,r;
	
	//for degeneration case
	bool degenT; //core degenerated
	bool degenR; //fade degenerated
	bool pre_full; //draw the preceding segment in full
	Point PT,PR;
	float pt; //parameter at intersection
	bool R_full_degen;
	
	char djoint; //determined joint
			// e.g. originally a joint is PLJ_miter. but it is smaller than critical angle, should then set djoint to PLJ_bevel
};

struct st_anchor
//the struct to hold memory for the working of anchor()
{
	Point P[3]; //point
	Color C[3]; //color
	double W[3];//weight
	
	Point cap_start, cap_end;
	st_polyline SL[3];
	vertex_array_holder vah;
};

void inner_arc( vertex_array_holder& hold, const Point& P,
		const Color& C, const Color& C2,
		float dangle, float angle1, float angle2,
		float r, float r2, bool ignor_ends,
		Point* apparent_P)	//(apparent center) center of fan
//draw the inner arc between angle1 and angle2 with dangle at each step.
// -the arc has thickness, r is the outer radius and r2 is the inner radius,
//    with color C and C2 respectively.
//    in case when inner radius r2=0.0f, it gives a pie.
// -when ignor_ends=false, the two edges of the arc lie exactly on angle1
//    and angle2. when ignor_ends=true, the two edges of the arc do not touch
//    angle1 or angle2.
// -P is the mathematical center of the arc.
// -when apparent_P points to a valid Point (apparent_P != 0), r2 is ignored,
//    apparent_P is then the apparent origin of the pie.
// -the result is pushed to hold, in form of a triangle strip
// -an inner arc is an arc which is always shorter than or equal to a half circumference
{
	const double& m_pi = vaser_pi;
	
	bool incremental=true;
	
	if ( angle2 > angle1)
	{
		if ( angle2-angle1>m_pi)
		{
			angle2=angle2-2*m_pi;
		}
	}
	else
	{
		if ( angle1-angle2>m_pi)
		{
			angle1=angle1-2*m_pi;
		}
	}
	if ( angle1>angle2)
	{
		incremental = false; //means decremental
	}
	
	if ( incremental)
	{
		if ( ignor_ends)
		{
			int i=0;
			for ( float a=angle1+dangle; a<angle2; a+=dangle, i++)
			{
				float x=cos(a);
				float y=sin(a);
				
				#define INNER_ARC_PUSH \
					hold.push( Point(P.x+x*r,P.y-y*r), C);\
					if ( !apparent_P)\
						hold.push( Point(P.x+x*r2,P.y-y*r2), C2);\
					else\
						hold.push( *apparent_P, C2);
				
				INNER_ARC_PUSH
				
				if ( i>100) {
					DEBUG("trapped in loop: inc,ig_end angle1=%.2f, angle2=%.2f, dangle=%.2f\n", angle1, angle2, dangle);
					break;
				}
			}
			//DEBUG( "steps=%d ",i); fflush(stdout);
		}
		else
		{
			int i=0;
			for ( float a=angle1; ; a+=dangle, i++)
			{
				if ( a>angle2)
					a=angle2;
				
				float x=cos(a);
				float y=sin(a);
				
				INNER_ARC_PUSH
				
				if ( a>=angle2)
					break;
				
				if ( i>100) {
					DEBUG("trapped in loop: inc,end angle1=%.2f, angle2=%.2f, dangle=%.2f\n", angle1, angle2, dangle);
					break;
				}
			}
		}
	}
	else //decremental
	{
		if ( ignor_ends)
		{
			int i=0;
			for ( float a=angle1-dangle; a>angle2; a-=dangle, i++)
			{
				float x=cos(a);
				float y=sin(a);
				
				INNER_ARC_PUSH
				
				if ( i>100) {
					DEBUG("trapped in loop: dec,ig_end angle1=%.2f, angle2=%.2f, dangle=%.2f\n", angle1, angle2, dangle);
					break;
				}
			}
		}
		else
		{
			int i=0;
			for ( float a=angle1; ; a-=dangle, i++)
			{
				if ( a<angle2)
					a=angle2;
				
				float x=cos(a);
				float y=sin(a);
				
				INNER_ARC_PUSH
				#undef INNER_ARC_PUSH
				
				if ( a<=angle2)
					break;
				
				if ( i>100) {
					DEBUG("trapped in loop: dec,end angle1=%.2f, angle2=%.2f, dangle=%.2f\n", angle1, angle2, dangle);
					break;
				}
			}
		}
	}
}
void vectors_to_arc( vertex_array_holder& hold, const Point& P,
		const Color& C, const Color& C2,
		Point A, Point B, float dangle, float r, float r2, bool ignor_ends,
		Point* apparent_P)
//triangulate an inner arc between vectors A and B,
//  A and B are position vectors relative to P
{
	const double& m_pi = vaser_pi;
	A *= 1/r;
	B *= 1/r;
	if ( A.x > 1.0-vaser_min_alw) A.x = 1.0-vaser_min_alw;
	if ( A.x <-1.0+vaser_min_alw) A.x =-1.0+vaser_min_alw;
	if ( B.x > 1.0-vaser_min_alw) B.x = 1.0-vaser_min_alw;
	if ( B.x <-1.0+vaser_min_alw) B.x =-1.0+vaser_min_alw;
	
	float angle1 = acos(A.x);
	float angle2 = acos(B.x);
	if ( A.y>0){ angle1=2*m_pi-angle1;}
	if ( B.y>0){ angle2=2*m_pi-angle2;}
	//printf( "steps=%d ",int((angle2-angle1)/den*r));
	
	inner_arc( hold, P, C,C2, dangle,angle1,angle2, r,r2, ignor_ends, apparent_P);
}

#ifdef VASER_DEBUG
void annotate( const Point& P, Color cc, int I=-1)
{
	static int i=0;
	if ( I != -1) i=I;
	
	glBegin(GL_LINES);
		glColor3f(1,0,0);
		glVertex2f(P.x-4,P.y-4);
		glVertex2f(P.x+4,P.y+4);
		glVertex2f(P.x-4,P.y+4);
		glVertex2f(P.x+4,P.y-4);
	glEnd();
	
	char str[10];
	sprintf(str,"%d",i);
	gl_font( FL_HELVETICA, 8);
	gl_draw( str,float(P.x+2),float(P.y));
	i++;
}
void annotate( const Point& P)
{
	Color cc;
	annotate(P,cc);
}
void draw_vector( const Point& P, const Point& V, const char* name)
{
	Point P2 = P+V;
	glBegin(GL_LINES);
		glColor3f(1,0,0);
		glVertex2f(P.x,P.y);
		glColor3f(1,0.9,0.9);
		glVertex2f(P2.x,P2.y);
	glEnd();
	if ( name)
	{
		glColor3f(0,0,0);
		gl_font( FL_HELVETICA, 8);
		gl_draw( name,float(P2.x+2),float(P2.y));
	}
}
void printpoint( const Point& P, const char* name)
{
	printf("%s(%.4f,%.4f) ",name,P.x,P.y);
	fflush(stdout);
}
#endif
/*
Point plus_minus( const Point& a, const Point& b, bool plus)
{
	if (plus) return a+b;
	else return a-b;
}
Point plus_minus( const Point& a, bool plus)
{
	if (plus) return a;
	else return -a;
}
bool quad_is_reflexed( const Point& P0, const Point& P1, const Point& P2, const Point& P3)
{
	//points:
	//   1------3
	//  /      /
	// 0------2
	// vector 01 parallel to 23
	
	return Point::distance_squared(P1,P3) + Point::distance_squared(P0,P2)
		> Point::distance_squared(P0,P3) + Point::distance_squared(P1,P2);
}
void push_quad_safe( vertex_array_holder& core,
		const Point& P2, const Color& cc2, bool transparent2,
		const Point& P3, const Color& cc3, bool transparent3)
{
	//push 2 points to form a quad safely(without reflex)
	Point P0 = core.get_relative_end(-2);
	Point P1 = core.get_relative_end(-1);
	
	if ( !quad_is_reflexed(P0,P1,P2,P3))
	{
		core.push(P2,cc2,transparent2);
		core.push(P3,cc3,transparent3);
	}
	else
	{
		core.push(P3,cc3,transparent3);
		core.push(P2,cc2,transparent2);
	}
}*/

#define push_quad(A0,A1,A2,A3,A4,A5,A6,A7,A8) push_quad_(__LINE__,A0,A1,A2,A3,A4,A5,A6,A7,A8)
#define push_quadf(A0,A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,A11,A12) push_quadf_(__LINE__,A0,A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,A11,A12)

void push_quad_( short line, vertex_array_holder& core,
		const Point& P0, const Point& P1, const Point& P2, const Point& P3,
		const Color& c0, const Color& c1, const Color& c2, const Color& c3)
{
	if( P0.is_zero()) DEBUG("pushed P0 (0,0) at %d\n",line);
	if( P1.is_zero()) DEBUG("pushed P1 (0,0) at %d\n",line);
	if( P2.is_zero()) DEBUG("pushed P2 (0,0) at %d\n",line);
	if( P3.is_zero()) DEBUG("pushed P3 (0,0) at %d\n",line);
	//interpret P0 to P3 as triangle strip
	core.push3( P0, P1, P2,
		c0, c1, c2);
	core.push3( P1, P2, P3,
		c1, c2, c3);
}
void push_quadf_( short line, vertex_array_holder& core,
		const Point& P0, const Point& P1, const Point& P2, const Point& P3,
		const Color& c0, const Color& c1, const Color& c2, const Color& c3,
		bool trans0, bool trans1, bool trans2, bool trans3)
{
	if( P0.is_zero()) DEBUG("pushed P0 (0,0) at %d\n",line);
	if( P1.is_zero()) DEBUG("pushed P1 (0,0) at %d\n",line);
	if( P2.is_zero()) DEBUG("pushed P2 (0,0) at %d\n",line);
	if( P3.is_zero()) DEBUG("pushed P3 (0,0) at %d\n",line);
	//interpret P0 to P3 as triangle strip
	core.push3( P0, P1, P2,
		c0, c1, c2,
		trans0, trans1, trans2);
	core.push3( P1, P2, P3,
		c1, c2, c3,
		trans1, trans2, trans3);
}

struct st_knife_cut
{
	Point T1[4]; //retained polygon, also serves as input triangle
	Color C1[4]; //
	
	Point T2[4]; //cut away polygon
	Color C2[4]; //
	
	int T1c, T2c; //count of T1 & T2
		//must be 0,3 or 4
};
int triangle_knife_cut( const Point& kn1, const Point& kn2, const Point& kn_out, //knife
			       const Color* kC0, const Color* kC1, //color of knife
		st_knife_cut& ST)//will modify for output
//see knife_cut_test for more info
{	//return number of points cut away
	int points_cut_away = 0;
	
	bool kn_colored = kC0 && kC1; //if true, use the colors of knife instead
	bool std_sign = Point::signed_area( kn1,kn2,kn_out) > 0;
	bool s1 = Point::signed_area( kn1,kn2,ST.T1[0])>0 == std_sign; //true means this point should be cut
	bool s2 = Point::signed_area( kn1,kn2,ST.T1[1])>0 == std_sign;
	bool s3 = Point::signed_area( kn1,kn2,ST.T1[2])>0 == std_sign;
	int sums = int(s1)+int(s2)+int(s3);
	
	if ( sums == 0)
	{	//all 3 points are retained
		ST.T1c = 3;
		ST.T2c = 0;
		
		points_cut_away = 0;
	}
	else if ( sums == 3)
	{	//all 3 are cut away
		ST.T1c = 0;
		ST.T2c = 3;
		
		ST.T2[0] = ST.T1[0];
		ST.T2[1] = ST.T1[1];
		ST.T2[2] = ST.T1[2];
			ST.C2[0] = ST.C1[0];
			ST.C2[1] = ST.C1[1];
			ST.C2[2] = ST.C1[2];
		
		points_cut_away = 3;
	}
	else
	{
		if ( sums == 2) {
			s1 = !s1; 
			s2 = !s2;
			s3 = !s3;
		}
		//
		Point ip1,ip2, outp;
		Color iC1,iC2, outC;
		if ( s1) { //here assume one point is cut away
				// thus only one of s1,s2,s3 is true
			outp= ST.T1[0];  outC= ST.C1[0];
			ip1 = ST.T1[1];  iC1 = ST.C1[1];
			ip2 = ST.T1[2];  iC2 = ST.C1[2];
		} else if ( s2) {
			outp= ST.T1[1];  outC= ST.C1[1];
			ip1 = ST.T1[0];  iC1 = ST.C1[0];
			ip2 = ST.T1[2];  iC2 = ST.C1[2];
		} else if ( s3) {
			outp= ST.T1[2];  outC= ST.C1[2];
			ip1 = ST.T1[0];  iC1 = ST.C1[0];
			ip2 = ST.T1[1];  iC2 = ST.C1[1];
		}
		
		Point interP1,interP2;
		Color interC1,interC2;
		double ble1,kne1, ble2,kne2;
		Point::intersect( kn1,kn2, ip1,outp, interP1, &kne1,&ble1);
		Point::intersect( kn1,kn2, ip2,outp, interP2, &kne2,&ble2);
		
		{	if ( kn_colored && Color_valid_range(kne1))
				interC1 = Color_between( *kC0, *kC1, kne1);
			else
				interC1 = Color_between( iC1, outC, ble1);
		}
		
		{	if ( kn_colored && Color_valid_range(kne2))
				interC2 = Color_between( *kC0, *kC1, kne2);
			else
				interC2 = Color_between( iC2, outC, ble2);
		}
		
		//ip2 first gives a polygon
		//ip1 first gives a triangle strip
		
		if ( sums == 1) {
			//one point is cut away
			ST.T1[0] = ip1;      ST.C1[0] = iC1;
			ST.T1[1] = ip2;      ST.C1[1] = iC2;
			ST.T1[2] = interP1;  ST.C1[2] = interC1;
			ST.T1[3] = interP2;  ST.C1[3] = interC2;
			ST.T1c = 4;
			
			ST.T2[0] = outp;     ST.C2[0] = outC;
			ST.T2[1] = interP1;  ST.C2[1] = interC1;
			ST.T2[2] = interP2;  ST.C2[2] = interC2;
			ST.T2c = 3;
			
			points_cut_away = 1;
		} else if ( sums == 2) {
			//two points are cut away
			ST.T2[0] = ip1;      ST.C2[0] = iC1;
			ST.T2[1] = ip2;      ST.C2[1] = iC2;
			ST.T2[2] = interP1;  ST.C2[2] = interC1;
			ST.T2[3] = interP2;  ST.C2[3] = interC2;
			ST.T2c = 4;
			
			ST.T1[0] = outp;     ST.C1[0] = outC;
			ST.T1[1] = interP1;  ST.C1[1] = interC1;
			ST.T1[2] = interP2;  ST.C1[2] = interC2;
			ST.T1c = 3;
			
			points_cut_away = 2;
		}
		
		/*if ( (0.0-vaser_min_alw < kne1 && kne1 < 1.0+vaser_min_alw) ||
		     (0.0-vaser_min_alw < kne2 && kne2 < 1.0+vaser_min_alw) )
		{	//highlight the wound
			glBegin(GL_LINE_STRIP);
				glColor3f(1,0,0);
				glVertex2f(ST.T1[0].x,ST.T1[0].y);
				glVertex2f(ST.T1[1].x,ST.T1[1].y);
				glVertex2f(ST.T1[2].x,ST.T1[2].y);
				glVertex2f(ST.T1[0].x,ST.T1[0].y);
			glEnd();
			
			if ( ST.T1c > 3)
			glBegin(GL_LINE_STRIP);
				glVertex2f(ST.T1[1].x,ST.T1[1].y);
				glVertex2f(ST.T1[2].x,ST.T1[2].y);
				glVertex2f(ST.T1[3].x,ST.T1[3].y);
				glVertex2f(ST.T1[1].x,ST.T1[1].y);
			glEnd();
		}*/
	}
	
	return points_cut_away;
}
void vah_knife_cut( vertex_array_holder& core, //serves as both input and output
		const Point& kn1, const Point& kn2, const Point& kn_out)
//perform knife cut on all triangles (GL_TRIANGLES) in core
{
	st_knife_cut ST;
	for ( int i=0; i<core.count; i+=3)
	{
		ST.T1[0] = core.get(i);
		ST.T1[1] = core.get(i+1);
		ST.T1[2] = core.get(i+2);
		ST.C1[0] = core.get_color(i);
		ST.C1[1] = core.get_color(i+1);
		ST.C1[2] = core.get_color(i+2);
		ST.T1c = 3; //will be ignored anyway
		
		int result = triangle_knife_cut( kn1,kn2,kn_out,0,0, ST);
		
		switch (result)
		{
		case 0:
			//do nothing
		break;
		
		case 3:	//degenerate the triangle
			core.move(i+1,i); //move i into i+1
			core.move(i+2,i);
		break;
		
		case 1:
		case 2:
			core.replace(i,  ST.T1[0],ST.C1[0]);
			core.replace(i+1,ST.T1[1],ST.C1[1]);
			core.replace(i+2,ST.T1[2],ST.C1[2]);
			
			if ( result==1)
			{	//create a new triangle
				Point dump_P;
				Color dump_C;
				int a1,a2,a3;
				a1 = core.push( dump_P, dump_C);
				a2 = core.push( dump_P, dump_C);
				a3 = core.push( dump_P, dump_C);
				
				//copy the original points
				core.move( a1, i+1);
				core.move( a2, i+2);
				core.move( a3, i+2);
				
				//make the new point
				core.replace( a3, ST.T1[3],ST.C1[3]);
			}
		break;
		
		}
	}
}
void vah_N_knife_cut( vertex_array_holder& in, vertex_array_holder& out,
		const Point* kn0, const Point* kn1, const Point* kn2,
		const Color* kC0, const Color* kC1,
		int N)
{	//an iterative implementation
	const int MAX_ST = 10;
	st_knife_cut ST[MAX_ST];
	
	bool kn_colored = kC0 && kC1;
	
	if ( N > MAX_ST)
	{
		DEBUG("vah_N_knife_cut: max N for current build is %d\n", MAX_ST);
		N = MAX_ST;
	}
	
	for ( int i=0; i<in.count; i+=3) //each input triangle
	{
		int ST_count = 1;
		ST[0].T1[0] = in.get(i);
		ST[0].T1[1] = in.get(i+1);
		ST[0].T1[2] = in.get(i+2);
			ST[0].C1[0] = in.get_color(i);
			ST[0].C1[1] = in.get_color(i+1);
			ST[0].C1[2] = in.get_color(i+2);
		ST[0].T1c = 3;
		
		for ( int k=0; k<N; k++) //each knife
		{
			int cur_count = ST_count;
			for ( int p=0; p<cur_count; p++) //each triangle to be cut
			{
				//perform cut
				if ( ST[p].T1c > 0)
					if ( kn_colored)
					triangle_knife_cut( kn0[k], kn1[k], kn2[k],
							   &kC0[k],&kC1[k],
								ST[p]);
					else
					triangle_knife_cut( kn0[k],kn1[k],kn2[k],
							    0,0,ST[p]);
				
				//push retaining part
				if ( ST[p].T1c > 0) {
					out.push( ST[p].T1[0], ST[p].C1[0]);
					out.push( ST[p].T1[1], ST[p].C1[1]);
					out.push( ST[p].T1[2], ST[p].C1[2]);
					if ( ST[p].T1c > 3) {
						out.push( ST[p].T1[1], ST[p].C1[1]);
						out.push( ST[p].T1[2], ST[p].C1[2]);
						out.push( ST[p].T1[3], ST[p].C1[3]);
					}
				}
				
				//store cut away part to be cut again
				if ( ST[p].T2c > 0)
				{
					ST[p].T1[0] = ST[p].T2[0];
					ST[p].T1[1] = ST[p].T2[1];
					ST[p].T1[2] = ST[p].T2[2];
						ST[p].C1[0] = ST[p].C2[0];
						ST[p].C1[1] = ST[p].C2[1];
						ST[p].C1[2] = ST[p].C2[2];
					ST[p].T1c = 3;
					
					if ( ST[p].T2c > 3)
					{
						ST[ST_count].T1[0] = ST[p].T2[1];
						ST[ST_count].T1[1] = ST[p].T2[2];
						ST[ST_count].T1[2] = ST[p].T2[3];
							ST[ST_count].C1[0] = ST[p].C2[1];
							ST[ST_count].C1[1] = ST[p].C2[2];
							ST[ST_count].C1[2] = ST[p].C2[3];
						ST[ST_count].T1c = 3;
						ST_count++;
					}
				}
				else
				{
					ST[p].T1c = 0;
				}
			}
		}
	}
}

const float cri_core_adapt = 0.0001f;
void anchor_late( const Vec2* P, const Color* C, st_polyline* SL,
		vertex_array_holder& tris,
		Point cap1, Point cap2)
{	const int size_of_P = 3;

	tris.set_gl_draw_mode(GL_TRIANGLES);
	
	Point P_0, P_1, P_2;
	P_0 = Point(P[0]);
	P_1 = Point(P[1]);
	P_2 = Point(P[2]);
	if ( SL[0].djoint==PLC_butt || SL[0].djoint==PLC_square)
		P_0 -= cap1;
	if ( SL[2].djoint==PLC_butt || SL[2].djoint==PLC_square)
		P_2 -= cap2;
	
	Point P0, P1, P2, P3, P4, P5, P6, P7;
	Point P0r,P1r,P2r,P3r,P4r,P5r,P6r,P7r; //fade
	
	P0 = P_1 + SL[1].vP;
		P0r = P0 + SL[1].vR;
	P1 = P_1 - SL[1].vP;
		P1r = P1 - SL[1].vR;
	
	P2 = P_1 + SL[1].T1;
		P2r = P2 + SL[1].R1 + SL[0].bR;
	P3 = P_0 + SL[0].T;
		P3r = P3 + SL[0].R;
	P4 = P_0 - SL[0].T;
		P4r = P4 - SL[0].R;
	
	P5 = P_1 + SL[1].T;
		P5r = P5 + SL[1].R - SL[1].bR;
	P6 = P_2 + SL[2].T;
		P6r = P6 + SL[2].R;
	P7 = P_2 - SL[2].T;
		P7r = P7 - SL[2].R;
		/* annotate( P0,C[0],0);
		annotate( P1);
		annotate( P2);
		annotate( P3);
		annotate( P4);
		annotate( P5);
		annotate( P6);
		annotate( P7); */

	int normal_line_core_joint = 1; //0:dont draw, 1:draw, 2:outer only

	//consider these as inline child functions
	#define normal_first_segment \
			tris.push3( P3,  P2,  P1, \
				  C[0],C[1],C[1]);\
			tris.push3( P1,  P3,  P4, \
				  C[1],C[0],C[0])
	
	#define normal_last_segment \
			tris.push3( P1,  P5,  P6, \
				  C[1],C[1],C[2]);\
			tris.push3( P1,  P6,  P7, \
				  C[1],C[2],C[2])
	
	Color Cpt; //color at PT
	if ( SL[1].degenT || SL[1].degenR)
	{
		float pt = sqrt(SL[1].pt);
		if ( SL[1].pre_full)
			Cpt = Color_between(C[0],C[1], pt);
		else
			Cpt = Color_between(C[1],C[2], 1-pt);
	}
	
	if ( SL[1].degenT)
	{	//degen line core
		P1 = SL[1].PT;
			if( SL[1].degenR)
				P1r = SL[1].PR;
		
		tris.push3( P3,  P2,  P1,
			  C[0],C[1],C[1]); //fir seg
		tris.push3( P1,  P5,  P6,
			  C[1],C[1],C[2]); //las seg
		
		if ( SL[1].pre_full)
		{	tris.push3( P1,  P3,  P4,
				  C[1],C[0],C[0]);
		}
		else
		{	tris.push3( P1,  P6,  P7,
				  C[1],C[2],C[2]);
		}
	}
	else if ( SL[1].degenR && SL[1].pt > cri_core_adapt) //&& ! SL[1].degenT
	{	//line core adapted for degenR
		if ( SL[1].pre_full)
		{
			normal_last_segment;

			//special first segment
			Point P9 = SL[1].PT;
			tris.push3( P3,  P2,  P1,
				  C[0],C[1],C[1]);
			tris.push3( P3,  P9,  P1,
				  C[0], Cpt,C[1]);
			tris.push3( P3,  P9,  P4,
				  C[0], Cpt,C[0]);
		}
		else
		{
			normal_first_segment;
			
			//special last segment
			Point P9 = SL[1].PT;
			push_quad( tris,
				  P5,  P1,  P6,  P9,
				C[1],C[1],C[2], Cpt);
			tris.push3( P7,  P9,  P6,
				  C[2], Cpt,C[2]);
				/*annotate(P1,C[1],1);
				annotate(P5,C[1],5);
				annotate(P6,C[1],6);
				annotate(P7,C[1],7);
				annotate(P9,C[1],9);*/
		}
	}
	else
	{
		normal_first_segment;
		normal_last_segment;
	#undef normal_first_segment
	#undef normal_last_segment
	}
	
	if (normal_line_core_joint)
	{
		switch( SL[1].djoint)
		{
			case PLJ_miter:
				tris.push3( P2,  P5,  P0,
					  C[1],C[1],C[1]);
			case PLJ_bevel:
				if ( normal_line_core_joint==1)
				tris.push3( P2,  P5,  P1,
					  C[1],C[1],C[1]);
			break;
			
			case PLJ_round: {
				vertex_array_holder strip;
				strip.set_gl_draw_mode(GL_TRIANGLE_STRIP);
				
			if ( normal_line_core_joint==1)
				vectors_to_arc( strip, P_1, C[1], C[1],
				SL[1].T1, SL[1].T,
				get_PLJ_round_dangle(SL[1].t,SL[1].r),
				SL[1].t, 0.0f, false, &P1);
			else if ( normal_line_core_joint==2)
				vectors_to_arc( strip, P_1, C[1], C[1],
				SL[1].T1, SL[1].T,
				get_PLJ_round_dangle(SL[1].t,SL[1].r),
				SL[1].t, 0.0f, false, &P5);
				
				tris.push(strip);
			} break;
		}
	}
	
	if ( SL[1].degenR)
	{	//degen inner fade
		Point P9 = SL[1].PT;
			Point P9r = SL[1].PR;
		//annotate(P9,C[0],9);
		//annotate(P9r);

		Color ccpt=Cpt;
		if ( SL[1].degenT)
			ccpt = C[1];
		
		if ( SL[1].pre_full)
		{	push_quadf( tris,
				    P9,  P4, P9r, P4r,
				  ccpt,C[0],C[1],C[0],
				     0,   0,   1,   1); //fir seg

			if ( !SL[1].degenT)
			{
				Point mid = Point::midpoint(P9,P7);
				tris.push3( P1,  P9, mid,
					  C[1], Cpt,C[1],
					     0,   0,   1);
				tris.push3( P1,  P7, mid,
					  C[1],C[2],C[1],
					     0,   0,   1);
			}
		}
		else
		{	push_quadf( tris,
				    P9,  P7, P9r, P7r,
				  ccpt,C[2],C[1],C[2],
				     0,   0,   1,   1); //las seg
			
			if ( !SL[1].degenT)
			{
				Point mid = Point::midpoint(P9,P4);
				tris.push3( P1,  P9, mid,
					  C[1], Cpt,C[1],
					     0,   0,   1);
				tris.push3( P1,  P4, mid,
					  C[1],C[0],C[1],
					     0,   0,   1);
			}
		}
	}
	else
	{	//normal inner fade
		push_quadf( tris,
			    P1,  P4, P1r, P4r,
			  C[1],C[0],C[1],C[0],
			     0,   0,   1,   1); //fir seg
		push_quadf( tris,
			    P1,  P7, P1r, P7r,
			  C[1],C[2],C[1],C[2],
			     0,   0,   1,   1); //las seg
	}
	
	{	//outer fade, whether degen or normal
		push_quadf( tris,
			    P2,  P3, P2r, P3r,
			  C[1],C[0],C[1],C[0],
			     0,   0,   1,   1); //fir seg
		push_quadf( tris,
			    P5,  P6, P5r, P6r,
			  C[1],C[2],C[1],C[2],
			     0,   0,   1,   1); //las seg
		switch( SL[1].djoint)
		{	//line fade joint
			case PLJ_miter:
				push_quadf( tris,
					    P0,  P5, P0r, P5r,
					  C[1],C[1],C[1],C[1],
					     0,   0,   1,   1);
				push_quadf( tris,
					    P0,  P2, P0r, P2r,
					  C[1],C[1],C[1],C[1],
					     0,   0,   1,   1);
			break;
			case PLJ_bevel:
				push_quadf( tris,
					    P2,  P5, P2r, P5r,
					  C[1],C[1],C[1],C[1],
					     0,   0,   1,   1);
			break;
			
			case PLJ_round: {
				vertex_array_holder strip;
				strip.set_gl_draw_mode(GL_TRIANGLE_STRIP);
				Color C2 = C[1]; C2.a = 0.0f;
				vectors_to_arc( strip, P_1, C[1], C2,
				SL[1].T1, SL[1].T,
				get_PLJ_round_dangle(SL[1].t,SL[1].r),
				SL[1].t, SL[1].t+SL[1].r, false, 0);
				
				tris.push(strip);
			} break;
		}
	}
} //anchor_late

void anchor_cap( const Vec2* P, const Color* C, st_polyline* SL,
		vertex_array_holder& tris,
		Point cap1, Point cap2)
{
	Point P4 = Point(P[0]) - SL[0].T;
	Point P7 = Point(P[2]) - SL[2].T;
	for ( int i=0,k=0; k<=1; i=2, k++)
	{
		vertex_array_holder cap;
		Point& cur_cap = i==0? cap1:cap2;
		if ( cur_cap.non_zero())
		{
			cap.set_gl_draw_mode(GL_TRIANGLES);
			bool perform_cut = ( SL[1].degenR && SL[1].R_full_degen) &&
					((k==0 && !SL[1].pre_full) ||
					 (k==1 &&  SL[1].pre_full) );
			
			Point P3 = Point(P[i])-SL[i].T*2-SL[i].R+cur_cap;
			
			if ( SL[i].djoint == PLC_round)
			{	//round caps
				{	vertex_array_holder strip;
					strip.set_gl_draw_mode(GL_TRIANGLE_STRIP);
					
					Color C2 = C[i]; C2.a = 0.0f;
					Point O  = Point(P[i]);
					Point app_P = O+SL[i].T;
					Point bR = SL[i].bR;
					bR.follow_signs(cur_cap);
					float dangle = get_PLJ_round_dangle(SL[i].t,SL[i].r);
					
					vectors_to_arc( strip, O, C[i], C[i],
					SL[i].T+bR, -SL[i].T+bR,
					dangle,
					SL[i].t, 0.0f, false, &app_P);
						strip.push( O-SL[i].T,C[i]);
						strip.push( app_P,C[i]);

					strip.jump();

					Point a1 = O+SL[i].T;
					Point a2 = O+SL[i].T*(1/SL[i].t)*(SL[i].t+SL[i].r);
					Point b1 = O-SL[i].T;
					Point b2 = O-SL[i].T*(1/SL[i].t)*(SL[i].t+SL[i].r);
					
						strip.push( a1,C[i]);
						strip.push( a2,C2);
					vectors_to_arc( strip, O, C[i], C2,
					SL[i].T+bR, -SL[i].T+bR,
					dangle,
					SL[i].t, SL[i].t+SL[i].r, false, 0);						
						strip.push( b1,C[i]);
						strip.push( b2,C2);
					cap.push(strip);
				}
				if ( perform_cut)
				{
					Point P4k;
					if ( !SL[1].pre_full)
						P4k = P7; //or P7r ?
					else
						P4k = P4;
					
					vah_knife_cut( cap, SL[1].PT, P4k, P3);
					/*annotate(SL[1].PT,C[i],0);
					annotate(P3,C[i],3);
					annotate(P4k,C[i],4);*/
				}
			}
			else //if ( SL[i].djoint == PLC_butt | SL[i].cap == PLC_square | SL[i].cap == PLC_rect)
			{	//rectangle caps
				Point P_cur = P[i];
				bool degen_nxt=0, degen_las=0;
				if ( k == 0)
					if ( SL[0].djoint==PLC_butt || SL[0].djoint==PLC_square)
						P_cur -= cap1;
				if ( k == 1)
					if ( SL[2].djoint==PLC_butt || SL[2].djoint==PLC_square)
						P_cur -= cap2;
				
				Point P0,P1,P2,P3,P4,P5,P6;
				
				P0 = P_cur+SL[i].T+SL[i].R;
				P1 = P0+cur_cap;
				P2 = P_cur+SL[i].T;
				P4 = P_cur-SL[i].T;
				P3 = P4-SL[i].R+cur_cap;
				P5 = P4-SL[i].R;
				
				cap.push( P0, C[i],true);
				cap.push( P1, C[i],true);
				cap.push( P2, C[i]);
				
						cap.push( P1, C[i],true);
					cap.push( P2, C[i]);
				cap.push( P3, C[i],true);
				
						cap.push( P2, C[i]);
					cap.push( P3, C[i],true);
				cap.push( P4, C[i]);
				
						cap.push( P3, C[i],true);
					cap.push( P4, C[i]);
				cap.push( P5, C[i],true);
				//say if you want to use triangle strip,
				//  just push P0~ P5 in sequence
				if ( perform_cut)
				{
					vah_knife_cut( cap, SL[1].PT, SL[1].PR, P3);
					/*annotate(SL[1].PT,C[i],0);
					annotate(SL[1].PR);
					annotate(P3);
					annotate(P4);*/
				}
			}
		}
		tris.push(cap);
	}
} //anchor_cap

void segment_late( const Vec2* P, const Color* C, st_polyline* SL,
		vertex_array_holder& tris,
		Point cap1, Point cap2)
{
	tris.set_gl_draw_mode(GL_TRIANGLES);
	
	Point P_0, P_1, P_2;
	P_0 = Point(P[0]);
	P_1 = Point(P[1]);
	if ( SL[0].djoint==PLC_butt || SL[0].djoint==PLC_square)
		P_0 -= cap1;
	if ( SL[1].djoint==PLC_butt || SL[1].djoint==PLC_square)
		P_1 -= cap2;
	
	Point P1, P2, P3, P4;  //core
	Point P1c,P2c,P3c,P4c; //cap
	Point P1r,P2r,P3r,P4r; //fade

	P1 = P_0 + SL[0].T;
		P1r = P1 + SL[0].R;
		P1c = P1r + cap1;
	P2 = P_0 - SL[0].T;
		P2r = P2 - SL[0].R;
		P2c = P2r + cap1;
	P3 = P_1 + SL[1].T;
		P3r = P3 + SL[1].R;
		P3c = P3r + cap2;
	P4 = P_1 - SL[1].T;
		P4r = P4 - SL[1].R;
		P4c = P4r + cap2;
	//core
	push_quad( tris,
		  P1,  P2,  P3,  P4,
		C[0],C[0],C[1],C[1] );
	//fade
	push_quadf( tris,
		  P1, P1r,  P3, P3r,
		C[0],C[0],C[1],C[1],
		   0,   1,   0,   1 );
	push_quadf( tris,
		  P2, P2r,  P4, P4r,
		C[0],C[0],C[1],C[1],
		   0,   1,   0,   1 );
	//caps
	for ( int j=0; j<2; j++)
	{
		vertex_array_holder cap;
		cap.set_gl_draw_mode(GL_TRIANGLE_STRIP);
		Point &cur_cap = j==0?cap1:cap2;
		if( cur_cap.is_zero())
			continue;
		
		if ( SL[j].djoint == PLC_round)
		{	//round cap
			Color C2 = C[j]; C2.a = 0.0f;
			Point O  = Point(P[j]);
			Point app_P = O+SL[j].T;
			Point bR = SL[j].bR;
			bR.follow_signs( j==0?cap1:cap2);
			float dangle = get_PLJ_round_dangle(SL[j].t,SL[j].r);
			
			vectors_to_arc( cap, O, C[j], C[j],
			SL[j].T+bR, -SL[j].T+bR,
			dangle,
			SL[j].t, 0.0f, false, &app_P);
				cap.push( O-SL[j].T,C[j]);
				cap.push( app_P,C[j]);
			
			cap.jump();
			
			{	//fade
				Point a1 = O+SL[j].T;
				Point a2 = O+SL[j].T*(1/SL[j].t)*(SL[j].t+SL[j].r);
				Point b1 = O-SL[j].T;
				Point b2 = O-SL[j].T*(1/SL[j].t)*(SL[j].t+SL[j].r);
				
					cap.push( a1,C[j]);
					cap.push( a2,C2);
				vectors_to_arc( cap, O, C[j], C2,
				SL[j].T+bR, -SL[j].T+bR,
				dangle,
				SL[j].t, SL[j].t+SL[j].r, false, 0);						
					cap.push( b1,C[j]);
					cap.push( b2,C2);
			}
		}
		else //if ( SL[j].djoint == PLC_butt | SL[j].cap == PLC_square | SL[j].cap == PLC_rect)
		{	//rectangle cap
			Point Pj,Pjr,Pjc, Pk,Pkr,Pkc;
			if ( j==0)
			{
				Pj = P1;
				Pjr= P1r;
				Pjc= P1c;
				
				Pk = P2;
				Pkr= P2r;
				Pkc= P2c;
			}
			else
			{
				Pj = P3;
				Pjr= P3r;
				Pjc= P3c;
				
				Pk = P4;
				Pkr= P4r;
				Pkc= P4c;
			}
			
			cap.push( Pkr, C[j], 1);
			cap.push( Pkc, C[j], 1);
			cap.push( Pk , C[j], 0);
			cap.push( Pjc, C[j], 1);
			cap.push( Pj , C[j], 0);
			cap.push( Pjr, C[j], 1);
		}
		tris.push(cap);
	}
	
	/*annotate(P1,C[0],1);
	annotate(P2,C[0],2);
	annotate(P3,C[0],3);
	annotate(P4,C[0],4);
		annotate(P1c,C[0],11);
		annotate(P2c,C[0],21);
		annotate(P3c,C[0],31);
		annotate(P4c,C[0],41);
		
		annotate(P1r,C[0],12);
		annotate(P2r,C[0],22);
		annotate(P3r,C[0],32);
		annotate(P4r,C[0],42);
	*/
}

void segment( st_anchor& SA, const polyline_opt* options,  bool cap_first, bool cap_last, char last_cap_type=-1)
{
	double* weight = SA.W;
	if ( !SA.P || !SA.C || !weight) return;
	
	Point P[2]; P[0]=SA.P[0]; P[1]=SA.P[1];
	Color C[2]; C[0]=SA.C[0]; C[1]=SA.C[1];
	
	polyline_opt opt={0};
	if ( options)
		opt = (*options);
	
	Point T1,T2;
	Point R1,R2;
	Point bR;
	double t,r;
	
	bool varying_weight = !(weight[0]==weight[1]);
	
	Point cap_start, cap_end;
	st_polyline SL[2];
	
	for ( int i=0; i<2; i++)
	{
		if ( weight[i]>=0.0 && weight[i]<1.0)
		{
			double f=weight[i]-static_cast<int>(weight[i]);
			C[i].a *=f;
		}
	}
	
	{	int i=0;
		make_T_R_C( P[i], P[i+1], &T2,&R2,&bR, weight[i],opt, &r,&t,0, true);
		
		if ( cap_first)
		{
			if ( opt.cap==PLC_square)
			{
				P[0] = Point(P[0]) - bR * (t+r);
			}
			cap_start = bR;
			cap_start.opposite(); if ( opt.feather && !opt.no_feather_at_cap)
			cap_start*=opt.feathering;
		}
		
		SL[i].djoint=opt.cap;
		SL[i].t=t;
		SL[i].r=r;
		SL[i].T=T2;
		SL[i].R=R2;
		SL[i].bR=bR*0.01;
		SL[i].degenT = false;
		SL[i].degenR = false;
	}
	
	{	int i=1;
		if ( varying_weight)
			make_T_R_C( P[i-1], P[i], &T2,&R2,&bR,weight[i],opt, &r,&t,0, true);
		
		last_cap_type = last_cap_type==-1 ? opt.cap:last_cap_type;
		
		if ( cap_last)
		{
			if ( last_cap_type==PLC_square)
			{
				P[1] = Point(P[1]) + bR * (t+r);
			}
			cap_end = bR;
			if ( opt.feather && !opt.no_feather_at_cap)
				cap_end*=opt.feathering;
		}
		
		SL[i].djoint = last_cap_type;
		SL[i].t=t;
		SL[i].r=r;
		SL[i].T=T2;
		SL[i].R=R2;
		SL[i].bR=bR*0.01;
		SL[i].degenT = false;
		SL[i].degenR = false;
	}
	
	segment_late( P,C,SL,SA.vah, cap_start,cap_end);
}

int anchor( st_anchor& SA, const polyline_opt* options, bool cap_first, bool cap_last)
{
	polyline_opt opt={0};
	if ( options)
		opt = (*options);
	
	Point* P = SA.P;
	Color* C = SA.C;
	double* weight = SA.W;

	{	st_polyline emptySL;
		SA.SL[0]=emptySL; SA.SL[1]=emptySL; SA.SL[2]=emptySL;
	}
	st_polyline* SL = SA.SL;
	SA.vah.set_gl_draw_mode(GL_TRIANGLES);
	SA.cap_start = Point();
	SA.cap_end = Point();
	
	//const double critical_angle=11.6538;
	//	critical angle in degrees where a miter is force into bevel
	//	it is _similar_ to cairo_set_miter_limit () but cairo works with ratio while VASEr works with included angle
	const double cos_cri_angle=0.979386; //cos(critical_angle)
	
	bool varying_weight = !(weight[0]==weight[1] & weight[1]==weight[2]);
	
	double combined_weight=weight[1]+(opt.feather?opt.feathering:0.0);
	if ( combined_weight < cri_segment_approx)
	{
		segment( SA, &opt, cap_first,false, opt.joint==PLJ_round?PLC_round:PLC_butt);
		char ori_cap = opt.cap;
		opt.cap = opt.joint==PLJ_round?PLC_round:PLC_butt;
		SA.P[0]=SA.P[1]; SA.P[1]=SA.P[2];
		SA.C[0]=SA.C[1]; SA.C[1]=SA.C[2];
		SA.W[0]=SA.W[1]; SA.W[1]=SA.W[2];
		segment( SA, &opt, false,cap_last, ori_cap);
		return 0;
	}
	
	Point T1,T2,T21,T31;		//]these are for calculations in early stage
	Point R1,R2,R21,R31;		//]
	
	for ( int i=0; i<3; i++)
	{	//lower the transparency for weight < 1.0
		if ( weight[i]>=0.0 && weight[i]<1.0)
		{
			double f=weight[i];
			C[i].a *=f;
		}
	}
	
	{	int i=0;
	
		Point cap1;
		double r,t;		
		make_T_R_C( P[i], P[i+1], &T2,&R2,&cap1, weight[i],opt, &r,&t,0);
		if ( varying_weight) {
		make_T_R_C( P[i], P[i+1], &T31,&R31,0, weight[i+1],opt, 0,0,0);
		} else {
			T31 = T2;
			R31 = R2;
		}
		Point::anchor_outward(R2, P[i+1],P[i+2] /*,inward_first->value()*/);
			T2.follow_signs(R2);
		
		SL[i].bR=cap1;
		
		if ( cap_first)
		{
			if ( opt.cap==PLC_square)
			{
				P[0] = Point(P[0]) - cap1 * (t+r);
			}
			cap1.opposite(); if ( opt.feather && !opt.no_feather_at_cap)
			cap1*=opt.feathering;
			SA.cap_start = cap1;
		}
		
		SL[i].djoint=opt.cap;
		SL[i].T=T2;
		SL[i].R=R2;
		SL[i].t=(float)t;
		SL[i].r=(float)r;
		SL[i].degenT = false;
		SL[i].degenR = false;
		
		SL[i+1].T1=T31;
		SL[i+1].R1=R31;
	}
	
	if ( cap_last)
	{	int i=2;

		Point cap2;
		double t,r;
		make_T_R_C( P[i-1],P[i], 0,0,&cap2,weight[i],opt, &r,&t,0);
		if ( opt.cap==PLC_square)
		{
			P[2] = Point(P[2]) + cap2 * (t+r);
		}
		
		SL[i].bR=cap2;
		
		if ( opt.feather && !opt.no_feather_at_cap)
			cap2*=opt.feathering;
		SA.cap_end = cap2;
	}
	
	{	int i=1;
	
		double r,t;
		Point P_cur = P[i]; //current point //to avoid calling constructor repeatedly
		Point P_nxt = P[i+1]; //next point
		Point P_las = P[i-1]; //last point
		if ( opt.cap==PLC_butt || opt.cap==PLC_square)
		{
			P_nxt -= SA.cap_end;
			P_las -= SA.cap_start;
		}
		
		{
		Point bR; float length_cur, length_nxt;
		make_T_R_C( P_las, P_cur,  &T1,&R1, 0, weight[i-1],opt,0,0, &length_cur);
		if ( varying_weight) {
		make_T_R_C( P_las, P_cur, &T21,&R21,0, weight[i],opt,  0,0,0);
		} else {
			T21 = T1;
			R21 = R1;
		}
		
		make_T_R_C( P_cur, P_nxt,  &T2,&R2,&bR, weight[i],opt, &r,&t, &length_nxt);
		if ( varying_weight) {
		make_T_R_C( P_cur, P_nxt, &T31,&R31,0, weight[i+1],opt, 0,0,0);
		} else {
			T31 = T2;
			R31 = R2;
		}
		
		SL[i].T=T2;
		SL[i].R=R2;
		SL[i].bR=bR;
		SL[i].t=(float)t;
		SL[i].r=(float)r;
		SL[i].degenT = false;
		SL[i].degenR = false;
		
		SL[i+1].T1=T31;
		SL[i+1].R1=R31;
		}
		
		{	//2nd to 2nd last point
			
			//find the angle between the 2 line segments
			Point ln1,ln2, V;
			ln1 = P_cur - P_las;
			ln2 = P_nxt - P_cur;
			ln1.normalize();
			ln2.normalize();
			Point::dot(ln1,ln2, V);
			double cos_tho=-V.x-V.y;
			bool zero_degree = Point::negligible(cos_tho-1);
			bool d180_degree = cos_tho < -1+0.0001;
			bool smaller_than_30_degree = cos_tho > 0.8660254;
			char result3 = 1;
			
			if ( (cos_tho < 0 && opt.joint==PLJ_bevel) ||
			     (opt.joint!=PLJ_bevel && opt.cap==PLC_round) ||
			     (opt.joint==PLJ_round)
			   )
			{	//when greater than 90 degrees
				SL[i-1].bR *= 0.01;
				SL[i]  .bR *= 0.01;
				SL[i+1].bR *= 0.01;
				//to solve an overdraw in bevel and round joint
			}
			
			Point::anchor_outward( T1, P_cur,P_nxt);
				R1.follow_signs(T1);
			Point::anchor_outward( T21, P_cur,P_nxt);
				R21.follow_signs(T21);
				SL[i].T1.follow_signs(T21);
				SL[i].R1.follow_signs(T21);
			Point::anchor_outward( T2, P_cur,P_las);
				R2.follow_signs(T2);
				SL[i].T.follow_signs(T2);
				SL[i].R.follow_signs(T2);
			Point::anchor_outward( T31, P_cur,P_las);
				R31.follow_signs(T31);
			
			{ //must do intersection
				Point interP, vP;
				result3 = Point::intersect( P_las+T1, P_cur+T21,
							P_nxt+T31, P_cur+T2,
							interP);
				
				if ( result3) {
					vP = interP - P_cur;
					SL[i].vP=vP;
					SL[i].vR=vP*(r/t);
				} else {
					SL[i].vP=SL[i].T;
					SL[i].vR=SL[i].R;
					DEBUG( "intersection failed: cos(angle)=%.4f, angle=%.4f(degree)\n", cos_tho, acos(cos_tho)*180/3.14159);
				}
			}
			
			T1.opposite();		//]inward
				R1.opposite();
			T21.opposite();
				R21.opposite();
			T2.opposite();
				R2.opposite();
			T31.opposite();
				R31.opposite();
			
			//make intersections
			Point PR1,PR2, PT1,PT2;
			double pt1,pt2;
			
			char result1r = Point::intersect( P_nxt-T31-R31, P_nxt+T31+R31,
						P_las+T1+R1, P_cur+T21+R21, //knife1
						PR1); //fade
			char result2r = Point::intersect( P_las-T1-R1, P_las+T1+R1,
						P_nxt+T31+R31, P_cur+T2+R2, //knife2
						PR2);
			bool is_result1r = result1r == 1;
			bool is_result2r = result2r == 1;
			//
			char result1t = Point::intersect( P_nxt-T31, P_nxt+T31,
						P_las+T1, P_cur+T21, //knife1_a
						PT1, 0,&pt1); //core
			char result2t = Point::intersect( P_las-T1, P_las+T1,
						P_nxt+T31, P_cur+T2, //knife2_a
						PT2, 0,&pt2);
			bool is_result1t = result1t == 1;
			bool is_result2t = result2t == 1;
			//
			bool inner_sec = Point::intersecting( P_las+T1+R1, P_cur+T21+R21,
						P_nxt+T31+R31, P_cur+T2+R2);
			//
			if ( zero_degree)
			{
				bool pre_full = is_result1t;
				opt.no_feather_at_cap=true;
				if ( pre_full)
				{
					segment( SA, &opt, true,cap_last, opt.joint==PLJ_round?PLC_round:PLC_butt);
				}
				else
				{
					char ori_cap = opt.cap;
					opt.cap = opt.joint==PLJ_round?PLC_round:PLC_butt;
					SA.P[0]=SA.P[1]; SA.P[1]=SA.P[2];
					SA.C[0]=SA.C[1]; SA.C[1]=SA.C[2];
					SA.W[0]=SA.W[1]; SA.W[1]=SA.W[2];
					segment( SA, &opt, true,cap_last, ori_cap);
				}
				return 0;
			}
			
			if ( (is_result1r | is_result2r) && !inner_sec)
			{	//fade degeneration
				SL[i].degenR=true;
				SL[i].PT = is_result1r? PT1:PT2; //this is is_result1r!!
				SL[i].PR = is_result1r? PR1:PR2;
				SL[i].pt = float(is_result1r? pt1:pt2);
					if ( SL[i].pt < 0)
						SL[i].pt = cri_core_adapt;
				SL[i].pre_full = is_result1r;
				SL[i].R_full_degen = false;
				
				Point P_nxt = P[i+1]; //override that in the parent scope
				Point P_las = P[i-1];
				Point PR;
				if ( opt.cap==PLC_rect || opt.cap==PLC_round)
				{
					P_nxt += SA.cap_end;
					P_las += SA.cap_start;
				}
				char result2;
				if ( is_result1r)
				{
					result2 = Point::intersect( P_nxt-T31-R31, P_nxt+T31,
						P_las+T1+R1, P_cur+T21+R21, //knife1
						PR); 	//fade
				}
				else
				{
					result2 = Point::intersect( P_las-T1-R1, P_las+T1,
						P_nxt+T31+R31, P_cur+T2+R2, //knife2
						PR);
				}
				if ( result2 == 1)
				{
					SL[i].R_full_degen = true;
					SL[i].PR = PR;
				}
			}
			
			if ( is_result1t | is_result2t)
			{	//core degeneration
				SL[i].degenT=true;
				SL[i].pre_full=is_result1t;
				SL[i].PT = is_result1t? PT1:PT2;
				SL[i].pt = float(is_result1t? pt1:pt2);
			}
			
			//make joint
			SL[i].djoint = opt.joint;
			if ( opt.joint == PLJ_miter)
				if ( cos_tho >= cos_cri_angle)
					SL[i].djoint=PLJ_bevel;
			
			/*if ( varying_weight && smaller_than_30_degree)
			{	//not sure why, but it appears to solve a visual bug for varing weight
				Point interR,vR;
				char result3 = Point::intersect( P_las-T1-R1, P_cur-T21-R21,
							P_nxt-T31-R31, P_cur-T2-R2,
							interR);
				SL[i].vR = P_cur-interR-SL[i].vP;
				annotate(interR,C[i],9);
				draw_vector(P_las-T1-R1, P_cur-T21-R21 - P_las+T1+R1,"1");
				draw_vector(P_nxt-T31-R31, P_cur-T2-R2 - P_nxt+T31+R31,"2");
			}*/
			
			if ( d180_degree | !result3)
			{	//to solve visual bugs 3 and 1.1
				//efficiency: if color and weight is same as previous and next point
				// ,do not generate vertices
				same_side_of_line( SL[i].R, SL[i-1].R, P_cur,P_las);
					SL[i].T.follow_signs(SL[i].R);
				SL[i].vP=SL[i].T;
				SL[i].T1.follow_signs(SL[i].T);
				SL[i].R1.follow_signs(SL[i].T);
				SL[i].vR=SL[i].R;
				SL[i].djoint=PLJ_miter;
			}
		} //2nd to 2nd last point
	}
	
	{	int i=2;

		double r,t;
		make_T_R_C( P[i-1],P[i], &T2,&R2,0,weight[i],opt,  &r,&t,0);
			same_side_of_line( R2, SL[i-1].R, P[i-1],P[i]);
				T2.follow_signs(R2);
		
		SL[i].djoint=opt.cap;
		SL[i].T=T2;
		SL[i].R=R2;
		SL[i].t=(float)t;
		SL[i].r=(float)r;
		SL[i].degenT = false;
		SL[i].degenR = false;
	}
	
	if( cap_first || cap_last)
		anchor_cap( SA.P,SA.C, SA.SL,SA.vah, SA.cap_start,SA.cap_end);
	anchor_late( SA.P,SA.C, SA.SL,SA.vah, SA.cap_start,SA.cap_end);
	return 1;
} //anchor

#ifdef VASE_RENDERER_EXPER
template <typename T>
class circular_array
{
	const int size;
	int cur; //current
	T* array;
public:
	circular_array(int size_) : size(size_)
	{
		array = new T[size];
		cur = 0;
	}
	
	~circular_array()
	{
		delete[] array;
	}
	
	void push( T obj)
	{
		array[cur] = obj;
		move(1);
	}
	
	int get_size() const
		{ return size;}
	
	int get_i( int i) const //get valid index relative to current
	{
		int des = cur + i%size;
		if ( des > size-1)
		{
			des -= size;
		}
		if ( des < 0)
		{
			des = size+i;
		}
		return des;
	}
	
	void move( int i) //move current relatively
	{
		cur = get_i(i);
	}
	
	T& operator[] (int i) //get element at relative position
	{
		return array[get_i(i)];
	}
};
#endif //VASE_RENDERER_EXPER

struct polyline_inopt
{
	bool const_color;
	bool const_weight;
	bool no_cap_first;
	bool no_cap_last;
	bool join_first;
	bool join_last;
	double* segment_length; //array of length of each segment
};

void poly_point_inter( const Point* P, const Color* C, const double* W, const polyline_inopt* inopt,
		Point& p, Color& c, double& w,
		int at, double t)
{
	#define color(I)  C[inopt&&inopt->const_color?0: I]
	#define weight(I) W[inopt&&inopt->const_weight?0: I]
	if( t==0.0)
	{
		p = P[at];
		c = color(at);
		w = weight(at);
	}
	else if( t==1.0)
	{
		p = P[at+1];
		c = color(at+1);
		w = weight(at+1);
	}
	else
	{
		p = (P[at]+P[at+1]) * t;
		c = Color_between(color(at),color(at+1), t);
		w = (weight(at)+weight(at+1)) * t;
	}
	#undef color
	#undef weight
}

void polyline_approx(
	const Vec2* points,
	const Color* C,
	const double* W,
	int length,
	const polyline_opt* opt,
	const polyline_inopt* inopt)
{
	const Point* P=(Point*)points;
	bool cap_first= inopt? !inopt->no_cap_first :true;
	bool cap_last=  inopt? !inopt->no_cap_last  :true;
	double* seg_len=inopt? inopt->segment_length: 0;

	st_anchor SA1,SA2;
	vertex_array_holder vcore;  //curve core
	vertex_array_holder vfadeo; //outer fade
	vertex_array_holder vfadei; //inner fade
	vcore.set_gl_draw_mode(GL_TRIANGLE_STRIP);
	vfadeo.set_gl_draw_mode(GL_TRIANGLE_STRIP);
	vfadei.set_gl_draw_mode(GL_TRIANGLE_STRIP);

	if( length<2)
		return;

	#define color(I)  C[inopt&&inopt->const_color?0: I]
	#define weight(I) W[inopt&&inopt->const_weight?0: I]

	for( int i=1; i<length-1; i++)
	{
		double t,r;
		determine_t_r(weight(i),t,r);
		if ( opt && opt->feather && !opt->no_feather_at_core)
			r*=opt->feathering;
		Point V=P[i]-P[i-1];
		V.perpen();
		V.normalize();
		Point F=V*r;
		V*=t;
		vcore.push( P[i]+V,  color(i));
		vcore.push( P[i]-V,  color(i));
		vfadeo.push( P[i]+V, color(i));
		vfadeo.push( P[i]+V+F, color(i), 1);
		vfadei.push( P[i]-V,   color(i));
		vfadei.push( P[i]-V-F, color(i), 1);
	}
	Point P_las,P_fir;
	Color C_las,C_fir;
	double W_las,W_fir;
	poly_point_inter( P,C,W,inopt, P_las,C_las,W_las, length-2, 0.5);
	{
		double t,r;
		determine_t_r(W_las,t,r);
		if ( opt && opt->feather && !opt->no_feather_at_core)
			r*=opt->feathering;
		Point V=P[length-1]-P[length-2];
		V.perpen();
		V.normalize();
		Point F=V*r;
		V*=t;
		vcore.push( P_las+V, C_las);
		vcore.push( P_las-V, C_las);
		vfadeo.push( P_las+V, C_las);
		vfadeo.push( P_las+V+F, C_las, 1);
		vfadei.push( P_las-V, C_las);
		vfadei.push( P_las-V-F, C_las, 1);
	}

	//first caps
	{
		poly_point_inter( P,C,W,inopt, P_fir,C_fir,W_fir, 0, inopt&&inopt->join_first? 0.5:0.0);
		SA1.P[0] = P_fir;
		SA1.P[1] = P[1];
		SA1.C[0] = C_fir;
		SA1.C[1] = color(1);
		SA1.W[0] = W_fir;
		SA1.W[1] = weight(1);
		segment( SA1, opt, cap_first,false);
	}
	//last cap
	if( !(inopt&&inopt->join_last))
	{
		SA2.P[0] = P_las;
		SA2.P[1] = P[length-1];
		SA2.C[0] = C_las;
		SA2.C[1] = color(length-1);
		SA2.W[0] = W_las;
		SA2.W[1] = weight(length-1);
		segment( SA2, opt, false,cap_last);
	}

	#undef color
	#undef weight

	if( opt && opt->tess && opt->tess->tessellate_only && opt->tess->holder)
	{
		vertex_array_holder& holder = *(vertex_array_holder*)opt->tess->holder;
		holder.push(vcore);
		holder.push(vfadeo);
		holder.push(vfadei);
		holder.push(SA1.vah);
		holder.push(SA2.vah);
	}
	else
	{
		vcore.draw();
		vfadeo.draw();
		vfadei.draw();
		SA1.vah.draw();
		SA2.vah.draw();
	}

	if ( opt && opt->tess && opt->tess->triangulation)
	{
		vcore.draw_triangles();
		vfadeo.draw_triangles();
		vfadei.draw_triangles();
		SA1.vah.draw_triangles();
		SA2.vah.draw_triangles();
	}
}

void polyline_exact(
	const Vec2* P,
	const Color* C,
	const double* W,
	int size_of_P,
	const polyline_opt* opt,
	const polyline_inopt* inopt)
{
	bool cap_first= inopt? !inopt->no_cap_first :true;
	bool cap_last=  inopt? !inopt->no_cap_last  :true;
	bool join_first = inopt && inopt->join_first;
	bool join_last =  inopt && inopt->join_last;

	#define color(I)  C[inopt&&inopt->const_color?0: I]
	#define weight(I) W[inopt&&inopt->const_weight?0: I]

	Point mid_l, mid_n; //the last and the next mid point
	Color c_l, c_n;
	double w_l, w_n;
	{	//init for the first anchor
		poly_point_inter( (Point*)P,C,W,inopt, mid_l,c_l,w_l, 0, join_first?0.5:0);
	}

	st_anchor SA;
	if ( size_of_P == 2)
	{
		SA.P[0] = P[0];
		SA.P[1] = P[1];
		SA.C[0] = color(0);
		SA.C[1] = color(1);
		SA.W[0] = weight(0);
		SA.W[1] = weight(1);
		segment( SA, opt, cap_first, cap_last);
	}
	else
	for ( int i=1; i<size_of_P-1; i++)
	{
		if ( i==size_of_P-2 && !join_last)
			poly_point_inter( (Point*)P,C,W,inopt, mid_n,c_n,w_n, i, 1.0);
		else
			poly_point_inter( (Point*)P,C,W,inopt, mid_n,c_n,w_n, i, 0.5);

		SA.P[0]=mid_l.vec(); SA.C[0]=c_l;  SA.W[0]=w_l;
		SA.P[2]=mid_n.vec(); SA.C[2]=c_n;  SA.W[2]=w_n;

		SA.P[1]=P[i];
		SA.C[1]=color(i);
		SA.W[1]=weight(i);

		anchor( SA, opt, i==1&&cap_first, i==size_of_P-2&&cap_last);

		mid_l = mid_n;
		c_l = c_n;
		w_l = w_n;
	}
	//draw or not
	if( opt && opt->tess && opt->tess->tessellate_only && opt->tess->holder)
		(*(vertex_array_holder*)opt->tess->holder).push(SA.vah);
	else
		SA.vah.draw();
	//draw triangles
	if( opt && opt->tess && opt->tess->triangulation)
		SA.vah.draw_triangles();

	#undef color
	#undef weight
}

void polyline_range(
	const Vec2* P,
	const Color* C,
	const double* W,
	int length,
	const polyline_opt* opt,
	const polyline_inopt* in_options,
	int from, int to,
	bool approx)
{
	polyline_inopt inopt={0};
	if( in_options) inopt=*in_options;
	if( from>0) from-=1;
	inopt.join_first = from!=0;
	inopt.join_last = to!=(length-1);
	inopt.no_cap_first = inopt.no_cap_first || inopt.join_first;
	inopt.no_cap_last = inopt.no_cap_last || inopt.join_last;

	if( approx)
		polyline_approx( P+from, C+(inopt.const_color?0:from), W+(inopt.const_weight?0:from), to-from+1, opt, &inopt);
	else
		polyline_exact ( P+from, C+(inopt.const_color?0:from), W+(inopt.const_weight?0:from), to-from+1, opt, &inopt);
}

void polyline(
	const Vec2* PP,  //pointer to array of point of a polyline
	const Color* C,  //array of color
	const double* W, //array of weight
	int length, //size of the buffer P
	const polyline_opt* options, //options
	const polyline_inopt* in_options) //internal options
{
	polyline_opt   opt={0};
	polyline_inopt inopt={0};
	if( options)    opt=*options;
	if( in_options) inopt=*in_options;

	/* if( opt.fallback)
	{
		backend::polyline(PP,C[0],W[0],length,0);
		return;
	} */

	if( opt.cap >= 10)
	{
		char dec=(opt.cap/10)*10;
		if( dec==PLC_first || dec==PLC_none)
			inopt.no_cap_last=true;
		if( dec==PLC_last || dec==PLC_none)
			inopt.no_cap_first=true;
		opt.cap -= dec;
	}

	if( inopt.const_weight && W[0] < cri_segment_approx)
	{
		polyline_exact(PP,C,W,length,&opt,&inopt);
		return;
	}

	const Point* P=(Point*)PP;
	int A=0,B=0;
	bool on=false;
	for( int i=1; i<length-1; i++)
	{
		Point V1=P[i]-P[i-1];
		Point V2=P[i+1]-P[i];
		double len=0.0;
		if( inopt.segment_length)
		{
			V1 /= inopt.segment_length[i];
			V2 /= inopt.segment_length[i+1];
			len += (inopt.segment_length[i]+inopt.segment_length[i+1])*0.5;
		}
		else
		{
			len += V1.normalize()*0.5;
			len += V2.normalize()*0.5;
		}
		double costho = V1.x*V2.x+V1.y*V2.y;
		//double angle = acos(costho)*180/vaser_pi;
		const double cos_a = cos(15*vaser_pi/180);
		const double cos_b = cos(10*vaser_pi/180);
		const double cos_c = cos(25*vaser_pi/180);
		double weight = W[inopt.const_weight?0:i];
		bool approx = false;
		if( (weight<7 && costho>cos_a) ||
			(costho>cos_b) || //when the angle difference at an anchor is smaller than a critical degree, do polyline approximation
			(len<weight && costho>cos_c) ) //when vector length is smaller than weight, do approximation
			approx = true;
		if( approx && !on)
		{
			A=i; if( A==1) A=0;
			on=true;
			if( A>1)
				polyline_range(PP,C,W,length,&opt,&inopt,B,A,false);
		}
		else if( !approx && on)
		{
			B=i;
			on=false;
			polyline_range(PP,C,W,length,&opt,&inopt,A,B,true);
		}
	}
	if( on && B<length-1)
	{
		B=length-1;
		polyline_range(PP,C,W,length,&opt,&inopt,A,B,true);
	}
	else if( !on && A<length-1)
	{
		A=length-1;
		polyline_range(PP,C,W,length,&opt,&inopt,B,A,false);
	}
}

#undef push_quad
#undef push_quadf

} //sub namespace VASErin

//export implementations

void polyline( const Vec2* P, const Color* C, const double* W, int length, const polyline_opt* opt)
{
	VASErin::polyline(P,C,W,length,opt,0);
}
void polyline( const Vec2* P, Color C, double W, int length, const polyline_opt* opt) //constant color and weight
{
	VASErin::polyline_inopt inopt={0};
	inopt.const_color=true;
	inopt.const_weight=true;
	VASErin::polyline(P,&C,&W,length,opt,&inopt);
}
void polyline( const Vec2* P, const Color* C, double W, int length, const polyline_opt* opt) //constant weight
{
	VASErin::polyline_inopt inopt={0};
	inopt.const_weight=true;
	VASErin::polyline(P,C,&W,length,opt,&inopt);
}
void polyline( const Vec2* P, Color C, const double* W, int length, const polyline_opt* opt) //constant color
{
	VASErin::polyline_inopt inopt={0};
	inopt.const_color=true;
	VASErin::polyline(P,&C,W,length,opt,&inopt);
}

void segment(  Vec2 P1, Vec2 P2, Color C1, Color C2, double W1, double W2, const polyline_opt* options)
{
	Vec2   AP[2];
	Color  AC[2];
	double AW[2];
		AP[0] = P1; AC[0] = C1; AW[0] = W1;
		AP[1] = P2; AC[1] = C2; AW[1] = W2;
	polyline( AP, AC, AW, 2, options);
}
void segment(  Vec2 P1, Vec2 P2, Color C, double W, const polyline_opt* options) //constant color and weight
{
	Vec2   AP[2];
		AP[0] = P1;
		AP[1] = P2;
	polyline( AP, C, W, 2, options);
}
void segment(  Vec2 P1, Vec2 P2, Color C1, Color C2, double W, const polyline_opt* options) //constant weight
{
	Vec2   AP[2];
	Color  AC[2];
	double AW[2];
		AP[0] = P1; AC[0] = C1; AW[0] = W;
		AP[1] = P2; AC[1] = C2; AW[1] = W;
	polyline( AP, AC, AW, 2, options);
}
void segment(  Vec2 P1, Vec2 P2, Color C, double W1, double W2, const polyline_opt* options) //const color
{
	Vec2   AP[2];
	Color  AC[2];
	double AW[2];
		AP[0] = P1; AC[0] = C; AW[0] = W1;
		AP[1] = P2; AC[1] = C; AW[1] = W2;
	polyline( AP, AC, AW, 2, options);
}


================================================
FILE: cpp/vaser/vaser.cpp
================================================
#ifndef VASER_CPP
#define VASER_CPP

#include "vaser.h"

#ifdef VASER_DEBUG
	#define DEBUG printf
#else
	#define DEBUG ;//
#endif

#include <math.h>
#include <vector>
#include <stdlib.h>

namespace VASEr
{
namespace VASErin
{	//VASEr internal namespace
const double vaser_min_alw=0.00000000001; //smallest value not regarded as zero
const Color default_color = {0,0,0,1};
const double default_weight = 1.0;
#include "point.h"
#include "color.h"
class vertex_array_holder;
#include "backend.h"
#include "vertex_array_holder.h"
#include "agg_curve4.cpp"
}
#include "opengl.cpp"
#include "polyline.cpp"
#include "gradient.cpp"
#include "curve.cpp"

} //namespace VASEr

#undef DEBUG
#endif


================================================
FILE: cpp/vaser/vaser.h
================================================
#ifndef VASER_H
#define VASER_H
/* Vase Renderer first draft, version 0.3 */

/* Basic usage
* You should provide these structs before any vase_renderer include, using
struct Vec2 { double x,y;};
struct Color { float r,g,b,a;};
* or
typedef your_vec2 Vec2;
typedef your_color Color;
*/

namespace VASEr
{
const double vaser_pi=3.141592653589793;

struct gradient_stop
{
	double t; //position
	char type; //GS_xx
	union
	{
		Color color;
		double weight;
	};
};
	const char GS_none  =0;
	const char GS_rgba  =1;
	const char GS_rgb   =2; //rgb only
	const char GS_alpha =3;
	const char GS_weight=4;
struct gradient
{
	gradient_stop* stops; //array must be sorted in ascending order of t
	int length; //number of stops
	char unit; //use_GD_XX
};
	const char GD_ratio =0; //default
	const char GD_length=1;

struct Image
{
	unsigned char* buf; //must **free** buffer manually
	short width;
	short height;
};

class renderer
{
public:
	static void init();
	static void before();
	static void after();
	static Image get_image();
};

struct tessellator_opt
{
	//set the whole structure to 0 will give default options
	bool triangulation;
	char parts; //use TS_xx
	bool tessellate_only;
	void* holder; //used as (VASErin::vertex_array_holder*) if tessellate_only is true
};
	//for tessellator_opt.parts
	const char TS_core_fade =0; //default
	const char TS_core      =1;
	const char TS_outer_fade=2;
	const char TS_inner_fade=3;

struct polyline_opt
{
	//set the whole structure to 0 will give default options
	const tessellator_opt* tess;
	char joint; //use PLJ_xx
	char cap;   //use PLC_xx
	bool feather;
		double feathering;
		bool no_feather_at_cap;
		bool no_feather_at_core;
};
	//for polyline_opt.joint
	const char PLJ_miter =0; //default
	const char PLJ_bevel =1;
	const char PLJ_round =2;
	//for polyline_opt.cap
	const char PLC_butt  =0; //default
	const char PLC_round =1;
	const char PLC_square=2;
	const char PLC_rect  =3;
	const char PLC_both  =0; //default
	const char PLC_first =10;
	const char PLC_last  =20;
	const char PLC_none  =30;

void polyline( const Vec2*, const Color*, const double*, int length, const polyline_opt*);
void polyline( const Vec2*, Color, double W, int length, const polyline_opt*); //constant color and weight
void polyline( const Vec2*, const Color*, double W, int length, const polyline_opt*); //constant weight
void polyline( const Vec2*, Color, const double* W, int length, const polyline_opt*); //constant color
void segment( Vec2, Vec2, Color, Color, double W1, double W2, const polyline_opt*);
void segment( Vec2, Vec2, Color, double W, const polyline_opt*); //constant color and weight
void segment( Vec2, Vec2, Color, Color, double W, const polyline_opt*); //constant weight
void segment( Vec2, Vec2, Color, double W1, double W2, const polyline_opt*); //const color

struct polybezier_opt
{
	//set the whole structure to 0 will give default options
	const polyline_opt* poly;
};

void polybezier( const Vec2*, const gradient*, int length, const polybezier_opt*);
void polybezier( const Vec2*, Color, double W, int length, const polybezier_opt*);

} //namespace VASEr

#endif


================================================
FILE: cpp/vaser/vertex_array_holder.h
================================================
#ifndef VASER_VERTEX_ARRAY_HOLDER_H
#define VASER_VERTEX_ARRAY_HOLDER_H

class vertex_array_holder
{
public:
	int count; //counter
	int glmode; //drawing mode in opengl
	bool jumping;
	std::vector<float> vert; //because it holds 2d vectors
	std::vector<float> color; //RGBA

	vertex_array_holder()
	{
		count = 0;
		glmode = GL_TRIANGLES;
		jumping = false;
	}
	
	void set_gl_draw_mode( int gl_draw_mode)
	{
		glmode = gl_draw_mode;
	}
	
	void clear()
	{
		count = 0;
	}
	void move( int a, int b) //move b into a
	{
		vert[a*2]   = vert[b*2];
		vert[a*2+1] = vert[b*2+1];
		
		color[a*4]  = color[b*4];
		color[a*4+1]= color[b*4+1];
		color[a*4+2]= color[b*4+2];
		color[a*4+3]= color[b*4+3];
	}
	void replace( int a, Point P, Color C)
	{
		vert[a*2]   = P.x;
		vert[a*2+1] = P.y;
		
		color[a*4]  = C.r;
		color[a*4+1]= C.g;
		color[a*4+2]= C.b;
		color[a*4+3]= C.a;
	}
	
	/* int draw_and_flush()
	{
		int& i = count;
		draw();
		switch( glmode)
		{
			case GL_POINTS:
				i=0;
			break;
			
			case GL_LINES:
				if ( i%2 == 0) {
					i=0;
				} else {
					goto copy_the_last_point;
				}
			break;
			
			case GL_TRIANGLES:
				if ( i%3 == 0) {
					i=0;
				} else if ( i%3 == 1) {
					goto copy_the_last_point;
				} else {
					goto copy_the_last_2_points;
				}
			break;
			
			case GL_LINE_STRIP: case GL_LINE_LOOP:
			//for line loop it is not correct
			copy_the_last_point:
				move(0,MAX_VERT-1);
				i=1;
			break;
			
			case GL_TRIANGLE_STRIP:
			copy_the_last_2_points:
				move(0,MAX_VERT-2);
				move(1,MAX_VERT-1);
				i=2;
			break;
			
			case GL_TRIANGLE_FAN:
				//retain the first point,
				// and copy the last point
				move(1,MAX_VERT-1);
				i=2;
			break;
			
			case GL_QUAD_STRIP:
			case GL_QUADS:
			case GL_POLYGON:
			//let it be and I cannot help
				i=0;
			break;
		}
		if ( i == MAX_VERT) //as a double check
			i=0;
	}*/
	
	int push( const Point& P, const Color& cc, bool trans=false)
	{
		int cur = count;
		vert.push_back(P.x);
		vert.push_back(P.y);
		color.push_back(cc.r);
		color.push_back(cc.g);
		color.push_back(cc.b);
		color.push_back(trans?0.0f:cc.a);

		count++;
		if ( jumping)
		{
			jumping=false;
			repeat_last_push();
		}
		return cur;
	}
	
	void push3( const Point& P1, const Point& P2, const Point& P3,
			const Color& C1, const Color& C2, const Color& C3,
			bool trans1=0, bool trans2=0, bool trans3=0)
	{
		push( P1,C1,trans1);
		push( P2,C2,trans2);
		push( P3,C3,trans3);
	}
	
	void push( const vertex_array_holder& hold)
	{
		if ( glmode == hold.glmode)
		{
			count += hold.count;
			vert.insert(vert.end(), hold.vert.begin(), hold.vert.end());
			color.insert(color.end(), hold.color.begin(), hold.color.end());
		}
		else if ( glmode == GL_TRIANGLES &&
			hold.glmode == GL_TRIANGLE_STRIP)
		{		
			int& a = count;
			for (int b=2; b < hold.count; b++)
			{
				for ( int k=0; k<3; k++,a++)
				{
					int B = b-2 + k;
					vert.push_back(hold.vert[B*2]);
					vert.push_back(hold.vert[B*2+1]);
					color.push_back(hold.color[B*4]);
					color.push_back(hold.color[B*4+1]);
					color.push_back(hold.color[B*4+2]);
					color.push_back(hold.color[B*4+3]);
				}
			}
		}
		else
		{
			DEBUG( "vertex_array_holder:push: unknown type\n");
		}
	}
	
	Point get(int i)
	{
		Point P;
		P.x = vert[i*2];
		P.y = vert[i*2+1];
		return P;
	}
	Color get_color(int b)
	{
		Color C;
		C.r = color[b*4];
		C.g = color[b*4+1];
		C.b = color[b*4+2];
		C.a = color[b*4+3];
		return C;
	}
	Point get_relative_end(int di=-1)
	{	//di=-1 is the last one
		int i = count+di;
		if ( i<0) i=0;
		if ( i>=count) i=count-1;
		return get(i);
	}
	void repeat_last_push()
	{
		Point P;
		Color cc;
		
		int i = count-1;
		
		P.x = vert[i*2];
		P.y = vert[i*2+1];
		cc.r = color[i*4];
		cc.g = color[i*4+1];
		cc.b = color[i*4+2];
		cc.a = color[i*4+3];
		
		push(P,cc);
	}
	void jump() //to make a jump in triangle strip by degenerated triangles
	{
		if ( glmode == GL_TRIANGLE_STRIP)
		{
			repeat_last_push();
			jumping=true;
		}
	}
	void draw()
	{
		backend::vah_draw(*this);
	}
	void draw_triangles()
	{
		Color col={1 , 0, 0, 0.5};
		if ( glmode == GL_TRIANGLES)
		{
			for ( int i=0; i<count; i++)
			{
				Point P[4];
				P[0] = get(i); i++;
				P[1] = get(i); i++;
				P[2] = get(i);
				P[3] = P[0];
				polyline((Vec2*)P,col,1.0,4,0);
			}
		}
		else if ( glmode == GL_TRIANGLE_STRIP)
		{
			for ( int i=2; i<count; i++)
			{
				Point P[3];
				P[0] = get(i-2);
				P[1] = get(i);
				P[2] = get(i-1);
				polyline((Vec2*)P,col,1.0,3,0);
			}
		}
	}
	void swap(vertex_array_holder& B)
	{
		int hold_count=count;
		int hold_glmode=glmode;
		bool hold_jumping=jumping;
		count = B.count;
		glmode = B.glmode;
		jumping = B.jumping;
		B.count = hold_count;
		B.glmode = hold_glmode;
		B.jumping = hold_jumping;
		vert.swap(B.vert);
		color.swap(B.color);
	}
};

#endif


================================================
FILE: cpp/workbench/base.html
================================================
<body>
<script src='raphael-min.js'></script>
<script src='dragger.js'></script>
<script src='drawer.js'></script>
<link rel="stylesheet" type="text/css" href="layout.css" />
<div class='side_pane'>
	This is description.
</div>

<script>
//an application contains:
//-TP (drawer)
//-DG (dragger)
//-canvas1 (html element)
//-rl (Raphael canvas)
var app_count=0;

function demo_application1()
{
	var i=this.i=app_count;
	var parent=this;
	app_count++;
	document.write("<div class='main_canvas' id='canvas"+i+"'></div>");
	
	this.TP = new drawer();
	this.DG = new dragger(this.TP,'canvas'+i);
	this.rl = Raphael('canvas'+i);
	//
	this.TP.px=[30,30,200,200];
	this.TP.py=[100,200,100,200];
	
	this.TP.redraw=function()
	{
		var rl=parent.rl;
		var TP=parent.TP;
		rl.clear();
		rl.rect(0,0,800-1,600-1);
		
		//drawings,,,
		rl.text(120,80,"I am application "+parent.i+"!");
		for ( var i=0; i<4; i++)
		{
			TP.drawpoint(TP.px[i],TP.py[i], 4,0);
		}
		
		TP.drawpath(rl);
	}
	this.TP.redraw();
}

app1 = new demo_application1();
//app2 = new demo_application1();
</script>
</body>


================================================
FILE: cpp/workbench/dragger.js
================================================
function dragger(TP,div_id)
{
	this.drag=-1;
	this.TP=TP;

	this.onMouseDown = function(e)
	{
		if (e.token=='in') {
			this.parent=e.parent;
		} else {
			var T=this.parent;
			var TP=T.TP;

			e=e?e:event;
			T.xmouse=e.clientX-T.canx+document.body.scrollLeft;
			T.ymouse=e.clientY-T.cany+document.body.scrollTop;
			T.lastxmouse=T.xmouse;
			T.lastymouse=T.ymouse;
			//
			for ( var i=0; i<TP.px.length; i++)
			{
				if (Math.abs(T.xmouse - TP.px[i]) < 12 && Math.abs(T.ymouse - TP.py[i]) < 12)
				{
					T.drag = i;
					return 1;
				}
			}
			T.drag = -1;
		}
	}

	this.onMouseUp = function(e)
	{
		if (e.token=='in') {
			this.parent=e.parent;
		} else {
			var T=this.parent;
			var TP=T.TP;

			T.drag=-1;
		}
	}
	this.onMouseMove = function(e)
	{
		if (e.token=='in') {
			this.parent=e.parent;
		} else {
			var T=this.parent;
			var TP=T.TP;

			e=e?e:event;
			T.xmouse=e.clientX-T.canx+document.body.scrollLeft;
			T.ymouse=e.clientY-T.cany+document.body.scrollTop;
			if ( T.drag!=-1)
			{
				var i = T.drag;
				TP.px[i] = T.xmouse;
				TP.py[i] = T.ymouse;
				TP.redraw();
			}
			T.lastxmouse=T.xmouse;
			T.lastymouse=T.ymouse;
		}
	}
	this.printpoints = function(TP)
	{
		xstr = "this.TP.px=[";
		ystr = "this.TP.py=[";
		for ( var i=0; i<TP.px.length; i++)
		{
			if ( i != 0)
			{
				xstr+=",";
				ystr+=",";
			}
			xstr += TP.px[i];
			ystr += TP.py[i];
		}
		xstr += "];";
		ystr += "];";
		alert(xstr+"\n"+ystr);
	}

	tardiv = document.getElementById(div_id);
	
	function getPositionLeft(This){
		var el=This;var pL=0;
		while(el){pL+=el.offsetLeft;el=el.offsetParent;}
		return pL
	}
	function getPositionTop(This){
		var el=This;var pT=0;
		while(el){pT+=el.offsetTop;el=el.offsetParent;}
		return pT
	}
	this.canx=getPositionLeft(tardiv);
	this.cany=getPositionTop(tardiv);
	
	tardiv.onmousedown	=this.onMouseDown;
	tardiv.onmouseup	=this.onMouseUp;
	tardiv.onmousemove	=this.onMouseMove;

	tardiv.onmousedown({token:'in', parent:this});
	tardiv.onmouseup({token:'in', parent:this});
	tardiv.onmousemove({token:'in', parent:this});
}


================================================
FILE: cpp/workbench/drawer.js
================================================
function drawer()
{
	var T=this;
	T.canx=0; T.cany=0;
	T.linestring=["","","","",""];
	T.linecolor=["#000","#F00","#0F0","#00B","#AAA"];
	T.moveTo=function( x,y,C)
	{
		if ( C==null) {C=4;}
		T.linestring[C] += " M "+x+","+y;
	}
	T.lineTo=function( x,y,C)
	{
		if ( C==null) {C=4;}
		T.linestring[C] += " L "+x+","+y;
	}
	T.drawpoint=function(x,y,s,C)
	{
		if (!s) {s=2;}
		if (C==null) {C=0;}
		T.moveTo(x-s,y-s,C);
		T.lineTo(x+s,y+s,C);
		T.moveTo(x-s,y+s,C);
		T.lineTo(x+s,y-s,C);
		T.moveTo(x,y,C);
	}
	T.drawarrow=function( ax,ay,bx,by, size,C)
	{
		if ( size != null)
		{
			var vx=ay-by;
			var vy=bx-ax;
			var nsize=Math.sqrt(vx*vx+vy*vy);
			var cx=vy*size/nsize;
			var cy=vx*size/nsize;
			var bx=ax+cx;
			var by=ay-cy;
		}
		T.moveTo(ax,ay, C);
		T.lineTo(bx,by, C);
		//
		var R=0.9; var K=0.04;
		var vx=ay-by;
		var vy=bx-ax;
		var acx=vy*R+ax;
		var acy=-vx*R+ay;
		//
		T.moveTo(acx+vx*K,acy+vy*K, C)
		T.lineTo(bx,by, C);
		T.lineTo(acx-vx*K,acy-vy*K, C);
	}
	T.drawpath=function(rl)
	{
		for ( var i=0; i<5; i++)
			rl.path( T.linestring[i]).attr( {stroke: T.linecolor[i], "stroke-width": 0.5});
		T.linestring=["","","","",""];
	}
	T.fillpath=function(rl,i)
	{
		rl.path( T.linestring[i]).attr( {fill: T.linecolor[i]});
		T.linestring[i]="";
	}
}


================================================
FILE: cpp/workbench/gradient_along_path.html
================================================
<!DOCTYPE html>
<meta charset="utf-8">
<body>
<script src="http://d3js.org/d3.v3.min.js"></script>
<script>
//code comes from https://gist.github.com/mbostock/4163057

var points = [
  [86, 388],
  [788, 40],
  [805, 447],
  [93, 72]
];
 
var width = 960,
    height = 500;
 
var color = d3.interpolateLab("#008000", "#c83a22");
 
var svg = d3.select("body").append("svg")
    .attr("width", width)
    .attr("height", height);
 
var line = d3.svg.line()
    .interpolate("basis");
 
svg.selectAll("path")
    .data(quad(sample(line(points), 8)))
  .enter().append("path")
    .style("fill", function(d) { return color(d.t); })
    .style("stroke", function(d) { return color(d.t); })
    .attr("d", function(d) { return lineJoin(d[0], d[1], d[2], d[3], 32); });
 
// Sample the SVG path string "d" uniformly with the specified precision.
function sample(d, precision) {
  var path = document.createElementNS(d3.ns.prefix.svg, "path");
  path.setAttribute("d", d);
 
  var n = path.getTotalLength(), t = [0], i = 0, dt = precision;
  while ((i += dt) < n) t.push(i);
  t.push(n);
 
  return t.map(function(t) {
    var p = path.getPointAtLength(t), a = [p.x, p.y];
    a.t = t / n;
    return a;
  });
}
 
// Compute quads of adjacent points [p0, p1, p2, p3].
function quad(points) {
  return d3.range(points.length - 1).map(function(i) {
    var a = [points[i - 1], points[i], points[i + 1], points[i + 2]];
    a.t = (points[i].t + points[i + 1].t) / 2;
    return a;
  });
}
 
// Compute stroke outline for segment p12.
function lineJoin(p0, p1, p2, p3, width) {
  var u12 = perp(p1, p2),
      r = width / 2,
      a = [p1[0] + u12[0] * r, p1[1] + u12[1] * r],
      b = [p2[0] + u12[0] * r, p2[1] + u12[1] * r],
      c = [p2[0] - u12[0] * r, p2[1] - u12[1] * r],
      d = [p1[0] - u12[0] * r, p1[1] - u12[1] * r];
 
  if (p0) { // clip ad and dc using average of u01 and u12
    var u01 = perp(p0, p1), e = [p1[0] + u01[0] + u12[0], p1[1] + u01[1] + u12[1]];
    a = lineIntersect(p1, e, a, b);
    d = lineIntersect(p1, e, d, c);
  }
 
  if (p3) { // clip ab and dc using average of u12 and u23
    var u23 = perp(p2, p3), e = [p2[0] + u23[0] + u12[0], p2[1] + u23[1] + u12[1]];
    b = lineIntersect(p2, e, a, b);
    c = lineIntersect(p2, e, d, c);
  }
 
  return "M" + a + "L" + b + " " + c + " " + d + "Z";
}
 
// Compute intersection of two infinite lines ab and cd.
function lineIntersect(a, b, c, d) {
  var x1 = c[0], x3 = a[0], x21 = d[0] - x1, x43 = b[0] - x3,
      y1 = c[1], y3 = a[1], y21 = d[1] - y1, y43 = b[1] - y3,
      ua = (x43 * (y1 - y3) - y43 * (x1 - x3)) / (y43 * x21 - x43 * y21);
  return [x1 + ua * x21, y1 + ua * y21];
}
 
// Compute unit vector perpendicular to p01.
function perp(p0, p1) {
  var u01x = p0[1] - p1[1], u01y = p1[0] - p0[0],
      u01d = Math.sqrt(u01x * u01x + u01y * u01y);
  return [u01x / u01d, u01y / u01d];
}
 
</script>


================================================
FILE: cpp/workbench/knife_cut_test.cpp
================================================
/*config.h is generated by fltk in your system
 * this file is used with fltk 1.3 with gl enabled.
 * compile by: fltk-config --use-gl --compile knife_cut_test.cpp
 * or something like: g++ -lX11 -lGL 'test1_drag.cpp' -o 'test1_drag'
*/
#include <math.h>
#include <stdio.h>

#include "../samples/config.h" //config.h must always be placed before any Fl header
#include <FL/gl.h>
#include <FL/Fl_Box.H>
#include <FL/Fl_Value_Slider.H>
#include <FL/Fl_Window.H>
#include <FL/Fl_Radio_Light_Button.H>

namespace VASEr
{
struct Vec2 { double x,y;};
struct Color { float r,g,b,a;};
}
#include "../vaser/vaser.cpp"
using namespace VASEr;

void test_draw();
#include "../samples/test1_base.cpp"

const int buf_size=20;

Vec2 AP[buf_size];
Color AC[buf_size];
int size_of_AP = 0;

Fl_Window* main_wnd;
Gl_Window* gl_wnd;
Fl_Box* text;
Fl_Button *nk1, *nk2, *nk3;

using namespace VASEr;
using namespace VASErin;

//application
void line_update()
{
	Color cc[3];
	{ Color col={1 , 0, 0, 1}; cc[0]=col;}
	{ Color col={.8,.8, 0, 1}; cc[1]=col;}
	{ Color col={ 0, 0, 1, 1}; cc[2]=col;}
	Color grey={.5,.5,.5, 1};
	
	for ( int i=0; i<size_of_AP; i++)
	{
		if ( i<3) {
			AC[i] = cc[i%3];
			AC[i].a = 0.5f;
		} else {
			AC[i] = grey;
			AC[i].a = 0.2f;
		}
	}
}
void line_init( int)
{
	AP[0].x=300; AP[0].y=30;
	AP[1].x=120; AP[1].y=250;
	AP[2].x=480; AP[2].y=250;
	
	AP[3].x=240; AP[3].y=130;
	AP[4].x=360; AP[4].y=130;
	AP[5].x=300; AP[5].y=220;
	size_of_AP = 6;
	
	line_update();
	gl_wnd->set_drag_target( AP, size_of_AP); 
}
void drag_cb(Fl_Widget* W, void*)
{
	gl_wnd->redraw();
}
void nk_cb(Fl_Widget* W, void*)
{
	gl_wnd->redraw();
}
int N_knife()
{
	if ( nk1->value())
		return 1;
	else if ( nk2->value())
		return 2;
	else if ( nk3->value())
		return 3;
}
void make_form()
{
	text = new Fl_Box(FL_FRAME_BOX,0,300,600,80,
	"This is the test of general knife cut. "
	"The grey triangle define the knifes, which cut the colored "
	"triangle into parts. By using the 3 sides of a triangle as knives, "
	"you can obtain the result of triangle A minus triangle B. "
	"Note that the knife cut method takes care also the interpolation "
	"of colors. \n"
	"Drag the points of the triangles to play."
	);
	text->align( FL_ALIGN_TOP | FL_ALIGN_LEFT | FL_ALIGN_INSIDE | FL_ALIGN_WRAP);
	
	{	Fl_Group* o = new Fl_Group(0,380,600,20);
		new Fl_Box(0,380,30,20,"N =");
		nk1 = new Fl_Radio_Light_Button(30,380,80,20,"1 knife");
		nk2 = new Fl_Radio_Light_Button(110,380,30,20,"2");
		nk3 = new Fl_Radio_Light_Button(140,380,30,20,"3");
		
		nk1->callback(nk_cb);
		nk2->callback(nk_cb);
		nk3->callback(nk_cb);
		
		nk1->value(1);
		o->end();
	}
}
void draw_triangles_outline( vertex_array_holder& tris)
{
	for ( int i=0; i<tris.count; i++)
	{
		Point P1 = tris.get(i); i++;
		Point P2 = tris.get(i); i++;
		Point P3 = tris.get(i);
		
		glBegin(GL_LINE_STRIP);
			glColor3f(1,0,0);
			glVertex2f( P1.x,P1.y);
			glVertex2f( P2.x,P2.y);
			glVertex2f( P3.x,P3.y);
			glVertex2f( P1.x,P1.y);
		glEnd();
	}
}
void test_draw()
{
	renderer::before();
	
	{	vertex_array_holder tri_in,tri_out;
		tri_in .set_gl_draw_mode(GL_TRIANGLES);
		tri_out.set_gl_draw_mode(GL_TRIANGLES);
		
		for ( int i=0; i<3; i++)
		{
			tri_in.push( AP[i], AC[i]);
		}
		
		Point kn0[3]={AP[3],AP[4],AP[5]};
		Point kn1[3]={AP[4],AP[5],AP[3]};
		Point kn2[3]={AP[5],AP[3],AP[4]};
		
		vah_N_knife_cut( tri_in, tri_out, kn0,kn1,kn2, 0,0,N_knife());
		tri_out.draw();
		draw_triangles_outline( tri_out);
	}
	
	{	vertex_array_holder kn;
		kn.set_gl_draw_mode(GL_TRIANGLES);
		for ( int i=3; i<6; i++)
		{
			kn.push( AP[i],AC[i]);
		}
		kn.draw();
	}
	
	renderer::after();
}

int main(int argc, char **argv)
{
	main_wnd = new Fl_Window( 600,400,"knife cut test (fltk-opengl)");
		make_form(); //initialize
		gl_wnd = new Gl_Window( 0,0,600,300);  gl_wnd->end(); //create gl window
		line_init(3);
	main_wnd->end();
	main_wnd->show();
	main_wnd->redraw();
	
	return Fl::run();
}


================================================
FILE: cpp/workbench/layout.css
================================================
.main_canvas
{
	width:800px; height:600px;
}

.side_pane
{
	position:absolute;
	left:810px; top:10px;
}


================================================
FILE: cpp/workbench/outward_vector.html
================================================
<body>
<script src='raphael-min.js'></script>
<script src='dragger.js'></script>
<script src='drawer.js'></script>
<link rel="stylesheet" type="text/css" href="layout.css" />

<div class='main_canvas' id='canvas1'></div>
<div class='side_pane'>
Blue vectors are outward perpendicular vectors.<br />
Red ones are outward bisecting vectors.<br />
This method only works for these 2 special case: outward perpendicular
and outward bisecting vectors.
Drag control points to observe.
</div>

<script>
TP = new drawer();
DG = new dragger(TP,'canvas1');
TP.px=[300,300,500,500]; //feel free to expand these arrays
TP.py=[400,200,200,400];

TP.redraw=function()
{
	rl.clear();
	rl.rect(0,0,800-1,600-1);

	TP.moveTo( TP.px[0],TP.py[0],0);
	for ( var i=0; i<TP.px.length; i++)
	{
		TP.lineTo( TP.px[i],TP.py[i],0);
		TP.drawpoint( TP.px[i],TP.py[i],4,0);
	}
	make_perpen_vector( TP.px,TP.py);
	make_outward_vector( TP.px,TP.py);

	TP.drawpath(rl);
}

function distance( ax,ay,bx,by)
{
	return Math.sqrt( (bx-ax)*(bx-ax) + (by-ay)*(by-ay));
}
function normalize( V)
{
	L= Math.sqrt(V.x*V.x+V.y*V.y);
	return { x:V.x/L, y:V.y/L};
}
function choose_outward(V, b,c)
{
	/* //the brute force way to calculate determinant:
	var determinant = distance(b.x+V.x,b.y+V.y,c.x,c.y) - 
			distance(b.x-V.x,b.y-V.y,c.x,c.y);*/
	//a simplified way:
	var determinant = b.x*V.x - V.x*c.x + b.y*V.y - V.y*c.y;
	
	if ( determinant>0)
	{
		//positive V is the outward vector
	} else {
		//negative V is the outward vector
		V.x=-V.x;
		V.y=-V.y;
	}
	return V;
}
function signed_area(p1,p2,p3)
{
	var D = (p2.x-p1.x)*(p3.y-p1.y)-(p3.x-p1.x)*(p2.y-p1.y);
	return D;
}

function make_perpen_vector( px,py)
{
	var L={x:0,y:0};
	var V={x:0,y:0};
	for ( var i=0; i<px.length; i++)
	{
		var j1,j0;
		if ( i==0) {
			j1=1; j0=0;
		} else if ( i==px.length-1) {
			j1=px.length-2; j0=px.length-1;
		} else {
			j0=i; j1=i-1;
		}

		L.x=px[j1]-px[j0]; //line vector
		L.y=py[j1]-py[j0];
		V.x=-L.y; //perpendicular vector
		V.y=L.x;
		
		V=normalize(V);
		V.x*=30; //make it longer for observation
		V.y*=30;
		if ( i==0) {
			V=choose_outward( V,{x:px[j1],y:py[j1]},{x:px[j1+1],y:py[j1+1]} );	
		} else if ( i==px.length-1) {
			V=choose_outward( V,{x:px[j1],y:py[j1]},{x:px[j1-1],y:py[j1-1]} );
		} else {
			V=choose_outward( V,{x:px[j0],y:py[j0]},{x:px[j0+1],y:py[j0+1]} );
		}
		
		TP.drawarrow( px[j0],py[j0],px[j0]+V.x,py[j0]+V.y,null,3);
	}
}
function make_outward_vector( px,py)
{
	var L1={x:0,y:0};
	var L2={x:0,y:0};
	var V={x:0,y:0};
	for ( var i=1; i<px.length-1; i++)
	{
		L1.x=px[i]-px[i-1];
		L1.y=py[i]-py[i-1];
		L2.x=px[i+1]-px[i];
		L2.y=py[i+1]-py[i];
		L1=normalize(L1);
		L2=normalize(L2);

		V.x=L1.x-L2.x; //average vector
		V.y=L1.y-L2.y;
		V=normalize(V);
		V.x*=30; //make it longer for observation
		V.y*=30;
		V=choose_outward( V,{x:px[i],y:py[i]},{x:px[i+1],y:py[i+1]} );		

		TP.drawarrow( px[i],py[i],px[i]+V.x,py[i]+V.y,null,1);
	}
}

rl = Raphael('canvas1');
TP.redraw();
</script>
</body>


================================================
FILE: cpp/workbench/quad_reflex.html
================================================
<body>
<script src='raphael-min.js'></script>
<script src='dragger.js'></script>
<script src='drawer.js'></script>
<link rel="stylesheet" type="text/css" href="layout.css" />
<div class='side_pane'>
	Note that we always draw the 2 blue lines correctly, even when
	the quad is reflexed.<br />
	This is especially useful when drawing quad by triangle strip
	to ensure there is no reflex.<br />
	<button onclick="app1.DG.printpoints(app1.TP)">print points</button>
</div>

<script>
var app_count=0;

function distance_squared(x1,y1,x2,y2)
{
	dx = x2-x1;
	dy = y2-y1;
	return (dx*dx+dy*dy);
}

function quad_is_reflexed(px,py)
{
	//points:
	//   1------3
	//  /      /
	// 0------2
	// vector 01 parallel to 23
	
	return distance_squared(px[1],py[1],px[3],py[3]) + distance_squared(px[0],py[0],px[2],py[2])
		> distance_squared(px[0],py[0],px[3],py[3]) + distance_squared(px[1],py[1],px[2],py[2]);
	
	//when dist(1,3)+dist(0,2) > dist(0,3)+dist(1,2),
	//  then the quad is reflexed
}

function demo_application1()
{
	var i=this.i=app_count;
	var parent=this;
	app_count++;
	document.write("<div class='main_canvas' id='canvas"+i+"'></div>");
	
	this.TP = new drawer();
	this.DG = new dragger(this.TP,'canvas'+i);
	this.rl = Raphael('canvas'+i);
	//
	this.TP.px=[219,248,441,540];
	this.TP.py=[335,223,338,231];
	
	this.TP.redraw=function()
	{
		var rl=parent.rl;
		var TP=parent.TP;
		rl.clear();
		rl.rect(0,0,800-1,600-1);
		
		TP.drawarrow( TP.px[0],TP.py[0], TP.px[1],TP.py[1], null, 0);
		TP.drawarrow( TP.px[2],TP.py[2], TP.px[3],TP.py[3], null, 0);
		
		if ( !quad_is_reflexed(TP.px,TP.py))
		{
			TP.moveTo( TP.px[0],TP.py[0],3);
			TP.lineTo( TP.px[2],TP.py[2],3);
			
			TP.moveTo( TP.px[1],TP.py[1],3);
			TP.lineTo( TP.px[3],TP.py[3],3);
		}
		else
		{
			TP.moveTo( TP.px[0],TP.py[0],3);
			TP.lineTo( TP.px[3],TP.py[3],3);
			
			TP.moveTo( TP.px[1],TP.py[1],3);
			TP.lineTo( TP.px[2],TP.py[2],3);
		}
		
		TP.drawpath(rl);
	}
	this.TP.redraw();
}

app1 = new demo_application1();
</script>
</body>


================================================
FILE: cpp/workbench/raphael-min.js
================================================
/*
 * Raphael 1.5.2 - JavaScript Vector Library
 *
 * Copyright (c) 2010 Dmitry Baranovskiy (http://raphaeljs.com)
 * Licensed under the MIT (http://raphaeljs.com/license.html) license.
 */
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================================================
FILE: cpp/workbench/readme.txt
================================================
this folder is for holding experiments related to development. you can safely ignor them.


================================================
FILE: cpp/workbench/triangle_knife_cut.js
================================================
function triangle_knife_cut(p1,p2,p3,kn1,kn2,kn3)
{
	var poly = []; //the retained polygon
	var poly_cut = []; //the cut away polygon

	var std_sign = signed_area( kn1,kn2,kn3);
	var s1 = signed_area( kn1,kn2,p1)>0 == std_sign>0; //true means this point should be cut
	var s2 = signed_area( kn1,kn2,p2)>0 == std_sign>0;
	var s3 = signed_area( kn1,kn2,p3)>0 == std_sign>0;
	var sums = s1+s2+s3;
	
	if ( sums == 0)
	{	//all 3 points are retained
		poly.push(p1);
		poly.push(p2);
		poly.push(p3);
		return { poly:poly, poly_cut:poly_cut};
	}
	else if ( sums == 3)
	{	//all 3 are cut away
		poly_cut.push(p1);
		poly_cut.push(p2);
		poly_cut.push(p3);
		return { poly:poly, poly_cut:poly_cut};
	}
	else
	{
		if ( sums == 2) {
			s1 = !s1;
			s2 = !s2;
			s3 = !s3;
		}
		//
		var ip1,ip2, outp;
		if ( s1) { //here assume one point is cut away
			outp= p1;
			ip1 = p2;
			ip2 = p3;
		} else if ( s2) {
			outp= p2;
			ip1 = p1;
			ip2 = p3;
		} else if ( s3) {
			outp= p3;
			ip1 = p1;
			ip2 = p2;
		}
		
		var interP1 = intersect( kn1,kn2, ip2,outp);
		var interP2 = intersect( kn1,kn2, ip1,outp);
		//ip2 first gives a polygon
		//ip1 first gives a triangle strip
		
		poly.push(ip1);
		poly.push(ip2);
		poly.push(interP1);
		poly.push(interP2);
		
		poly_cut.push(outp);
		poly_cut.push(interP1);
		poly_cut.push(interP2);
		
		if ( sums == 1) {
			return { poly:poly, poly_cut:poly_cut};
		} else if ( sums == 2) {
			return { poly:poly_cut, poly_cut:poly};
			//^ we swap the result!
		}
	}
}
function signed_area(p1,p2,p3)
{
	var D = (p2.x-p1.x)*(p3.y-p1.y)-(p3.x-p1.x)*(p2.y-p1.y);
	return D;
}
function intersect( P1,P2,  //line 1
			P3,P4) //line 2
{ //Determine the intersection point of two line segments
	var mua,mub;
	var denom,numera,numerb;

	denom  = (P4.y-P3.y) * (P2.x-P1.x) - (P4.x-P3.x) * (P2.y-P1.y);
	numera = (P4.x-P3.x) * (P1.y-P3.y) - (P4.y-P3.y) * (P1.x-P3.x);
	numerb = (P2.x-P1.x) * (P1.y-P3.y) - (P2.y-P1.y) * (P1.x-P3.x);
	
	function negligible(M)
	{
		return -0.00000001 < M && M < 0.00000001;
	}
	
	if ( negligible(numera) && negligible(numerb) && negligible(denom)) {
		//meaning the lines coincide
		return { x: (P1.x + P2.x) * 0.5,
			y:  (P1.y + P2.y) * 0.5 };
	}

	if ( negligible(denom)) {
		//meaning lines are parallel
		return { x:0, y:0};
	}

	mua = numera / denom;
	mub = numerb / denom;

	return { x: P1.x + mua * (P2.x - P1.x),
		y:  P1.y + mua * (P2.y - P1.y) };
//http://paulbourke.net/geometry/lineline2d/
}


================================================
FILE: cpp/workbench/triangles_dual_knife_cut.html
================================================
<body>
<script src='raphael-min.js'></script>
<script src='dragger.js'></script>
<script src='drawer.js'></script>
<script src='triangle_knife_cut.js'></script>
<link rel="stylesheet" type="text/css" href="layout.css" />
<div class='side_pane'>
This is the "dual knife cut" method of a triangle.<br />
The green points define the sides to be cut away.<br />
It can operate on multiple triangles.<br />
The cut away part is shown in red and retained part in blue.<br />
The 2 parts are given offsets (depend on the green points) so they look separated, just for fun.<br />
Drag the anchors to play. You can also drag the tips of the triangles.<br />
</div>

<script>
//math are in 'triangle_knife_cut.js'

//demo application
var app_count=0;

function make_polygon(TP,P,color, dP)
{
	if ( P.length>0)
	{
		TP.moveTo(P[0].x+dP.x,P[0].y+dP.y,color);
		for ( var i=0; i<P.length; i++)
		{
			TP.lineTo(P[i].x+dP.x,P[i].y+dP.y,color);
		}
		TP.lineTo(P[0].x+dP.x,P[0].y+dP.y,color);
	}
}
function demo_application1()
{
	var i=this.i=app_count;
	var parent=this;
	app_count++;
	document.write("<div class='main_canvas' id='canvas"+i+"'></div>");
	
	this.TP = new drawer();
	this.DG = new dragger(this.TP,'canvas'+i);
	this.rl = Raphael('canvas'+i);
	//
	this.TP.px=[650,400,400, 350,450,250, 350,450,550];
	this.TP.py=[300,300,550, 200,400,400, 200,400,200];

	this.TP.redraw=function()
	{
		var rl=parent.rl;
		var TP=parent.TP;
		rl.clear();
		rl.rect(0,0,800-1,600-1);
		
		function Point(i)
		{
			return {x:TP.px[i],y:TP.py[i]};
		}
		var kn1=0, kn2=1; kn3=2; //points that define a knife
		
		//draw knife
		TP.drawpoint(TP.px[kn1],TP.py[kn1], 6,2); //points
		TP.drawpoint(TP.px[kn2],TP.py[kn2], 6,0);
		TP.drawpoint(TP.px[kn3],TP.py[kn3], 6,2);
		
		TP.moveTo(TP.px[kn1],TP.py[kn1], 0); //lines
		TP.lineTo(TP.px[kn2],TP.py[kn2], 0);
		TP.moveTo(TP.px[kn2],TP.py[kn2], 0);
		TP.lineTo(TP.px[kn3],TP.py[kn3], 0);
		TP.drawpath(rl);
		
		//draw triangles
		for ( var i=3; i<TP.px.length; i+=3)
		{	//lines
			var result1 = triangle_knife_cut( Point(i), Point(i+1), Point(i+2),
					Point(kn1), Point(kn2), Point(kn3));
			var result2 = triangle_knife_cut(
				result1.poly_cut[0], result1.poly_cut[1], result1.poly_cut[2],
					Point(kn3), Point(kn2), Point(kn1));
			var result3 = 0;
			if ( result1.poly_cut.length > 3)
			{
			result3 = triangle_knife_cut(
				result1.poly_cut[0], result1.poly_cut[2], result1.poly_cut[3],
					Point(kn3), Point(kn2), Point(kn1));
			}
			
			var offset = { x: 0, y: 0};
			{	var Va = { x: TP.px[kn1]-TP.px[kn2],
					y: TP.py[kn1]-TP.py[kn2] };
				var Vb = { x: TP.px[kn3]-TP.px[kn2],
					y: TP.py[kn3]-TP.py[kn2] };
				var La = Math.sqrt(Va.x*Va.x + Va.y*Va.y);
				var Lb = Math.sqrt(Vb.x*Vb.x + Vb.y*Vb.y);
				Va.x /= La;  Va.y /= La;
				Vb.x /= Lb;  Vb.y /= Lb;
				
				var Vs = { x: Va.x+Vb.x, y: Va.y+Vb.y};
				offset.x = Vs.x*10;
				offset.y = Vs.y*10;
			}
			
			make_polygon(TP,result1.poly,    3, {x:-offset.x, y:-offset.y} );
			make_polygon(TP,result2.poly,    3, {x:-offset.x, y:-offset.y} );
			make_polygon(TP,result2.poly_cut,1, offset);
			if ( result3)
			{
			make_polygon(TP,result3.poly,    3, {x:-offset.x, y:-offset.y} );
			make_polygon(TP,result3.poly_cut,1, offset);
			}
			
			TP.fillpath(rl,3);
			TP.fillpath(rl,1);
		}
	}
	this.TP.redraw();
}
app1 = new demo_application1();
</script>
</body>


================================================
FILE: cpp/workbench/triangles_knife_cut.html
================================================
<body>
<script src='raphael-min.js'></script>
<script src='dragger.js'></script>
<script src='drawer.js'></script>
<script src='triangle_knife_cut.js'></script>
<link rel="stylesheet" type="text/css" href="layout.css" />
<div class='side_pane'>
This is the "knife cut" method of a triangle.<br />
The 2 black anchored points define the knife, while the green point define
the side to be cut away.<br />
The cut away part is shown in red and retained part in blue.<br />
The 2 parts are given offsets (depend on the green point) so they look separated, just for fun.<br />
It can operate on multiple triangles.<br />
Drag the anchors to play. You can also drag the tips of the triangles.<br />
</div>

<script>
//math are in 'triangle_knife_cut.js'

//demo application
var app_count=0;

function make_polygon(TP,P,color, dP)
{
	if ( P.length>0)
	{
		TP.moveTo(P[0].x+dP.x,P[0].y+dP.y,color);
		for ( var i=0; i<P.length; i++)
		{
			TP.lineTo(P[i].x+dP.x,P[i].y+dP.y,color);
		}
		TP.lineTo(P[0].x+dP.x,P[0].y+dP.y,color);
	}
}
function demo_application1()
{
	var i=this.i=app_count;
	var parent=this;
	app_count++;
	document.write("<div class='main_canvas' id='canvas"+i+"'></div>");
	
	this.TP = new drawer();
	this.DG = new dragger(this.TP,'canvas'+i);
	this.rl = Raphael('canvas'+i);
	//
	this.TP.px=[700,100,100, 350,450,250, 350,450,550];
	this.TP.py=[300,300,350, 200,400,400, 200,400,200];

	this.TP.redraw=function()
	{
		var rl=parent.rl;
		var TP=parent.TP;
		rl.clear();
		rl.rect(0,0,800-1,600-1);
		
		function Point(i)
		{
			return {x:TP.px[i],y:TP.py[i]};
		}
		var kn1=0, kn2=1; kn3=2; //points that define a knife
		
		//draw knife
		TP.drawpoint(TP.px[kn1],TP.py[kn1], 6,0); //points
		TP.drawpoint(TP.px[kn2],TP.py[kn2], 6,0);
		TP.drawpoint(TP.px[kn3],TP.py[kn3], 4,2);
		
		TP.moveTo(TP.px[kn1],TP.py[kn1], 0); //lines
		TP.lineTo(TP.px[kn2],TP.py[kn2], 0);
		TP.moveTo(TP.px[kn2],TP.py[kn2], 4);
		TP.lineTo(TP.px[kn3],TP.py[kn3], 4);
		TP.drawpath(rl);
		
		//draw triangles
		for ( var i=3; i<TP.px.length; i+=3)
		{	//lines			
			var result = triangle_knife_cut( Point(i),Point(i+1),Point(i+2),
					Point(kn1),Point(kn2),Point(kn3));
			var offset = { x: (TP.px[kn3]-TP.px[kn2]) * 0.1,
				y: (TP.py[kn3]-TP.py[kn2]) * 0.1 };
			
			make_polygon(TP,result.poly,3, {x:-offset.x, y:-offset.y} );
			make_polygon(TP,result.poly_cut,1, offset);
			TP.fillpath(rl,3);
			TP.fillpath(rl,1);
		}
	}
	this.TP.redraw();
}
app1 = new demo_application1();
</script>
</body>


================================================
FILE: cpp/workbench/vector_arc.html
================================================
<body>
<script src='raphael-min.js'></script>
<script src='dragger.js'></script>
<script src='drawer.js'></script>
<link rel="stylesheet" type="text/css" href="layout.css" />

<div class='main_canvas' id='canvas1'></div>
<div class='side_pane'>
<button onclick='tooglebasic()'>toogle basic</button><br />
<textarea id='txt'></textarea><br />
Note that we always draw the arc from red to blue.<br />
Drag control points to observe.<br />
Source code in contained in this HTML file.
</div>

<script>
TP = new drawer();
DG = new dragger(TP,'canvas1');
TP.px=[400,400-34.2,400+86.6];
TP.py=[300,300-94.0,300-50.0];

var basic=0;
function tooglebasic()
{
	basic = basic==0?1:0;
	TP.redraw();
}
window.onload = function()
{
	var location = window.location.href;
	if (location.match(/basic=1/))
	{
		basic=1;
		TP.redraw();
	}
}

TP.redraw=function()
{
	rl.clear();
	rl.rect(0,0,800-1,600-1);
	var P={x:TP.px[0],y:TP.py[0]};
	var A={x:TP.px[1]-TP.px[0], y:TP.py[1]-TP.py[0]};
	var B={x:TP.px[2]-TP.px[0], y:TP.py[2]-TP.py[0]};
	if ( basic==0)
		vectors_to_arc( P,A,B);
	else
		basic_vectors_arc( P,A,B,60);
	TP.drawpath(rl);
}
function roundc( c, d)
{
	c*=Math.pow(10,d);
	c =Math.round(c);
	c/=Math.pow(10,d);
	return c;
}

function vectors_to_arc( P, A,B)
{	//proper inner arc
	TP.drawarrow( P.x,P.y,P.x+A.x,P.y+A.y, null,1);
	TP.drawarrow( P.x,P.y,P.x+B.x,P.y+B.y, null,3);
	TP.drawpoint( P.x+A.x,P.y+A.y, 4,0);
	TP.drawpoint( P.x+B.x,P.y+B.y, 4,0);
	rl.text(P.x+50,P.y,'proper inner arc');
	
	var AL=Math.sqrt(A.x*A.x+A.y*A.y);
	var BL=Math.sqrt(B.x*B.x+B.y*B.y);
	A.x/=AL;
	B.x/=BL;
	var angle1=Math.acos(A.x);
	var angle2=Math.acos(B.x);
	if ( A.y>0){angle1=2*Math.PI-angle1;}
	if ( B.y>0){angle2=2*Math.PI-angle2;}

	inner_arc( P,(AL+BL)/2,Math.PI/18, angle1,angle2);
}
function inner_arc( P,r,dangle, angle1,angle2)
{	//proper inner arc
	var incremental=true;
	
	if ( angle2 > angle1)
	{
		if ( angle2-angle1>Math.PI)
		{
			angle2=angle2-2*Math.PI;
		}
	}
	else
	{
		if ( angle1-angle2>Math.PI)
		{
			angle1=angle1-2*Math.PI;
		}
	}
	if ( angle1>angle2)
	{
		incremental = false; //means decremental
	}

	TXT = document.getElementById('txt');
	TXT.value="angle1: "+roundc(angle1,2)+"\nangle2: "+roundc(angle2,2);

	if ( incremental)
	{
		for ( var a=angle1; a<angle2; a+=dangle)
		{
			var x=Math.cos(a);
			var y=Math.sin(a);
			TP.drawpoint( P.x+x*r,P.y-y*r, 2,0);
		}
		TP.drawarrow( P.x+Math.cos(angle1)*r, P.y-Math.sin(angle1)*r,
				P.x+Math.cos(angle2)*r, P.y-Math.sin(angle2)*r,
				null,4);
	}
	else
	{
		for ( var a=angle1; a>angle2; a-=dangle)
		{
			var x=Math.cos(a);
			var y=Math.sin(a);
			TP.drawpoint( P.x+x*r,P.y-y*r, 2,0);
		}
		TP.drawarrow( P.x+Math.cos(angle1)*r, P.y-Math.sin(angle1)*r,
				P.x+Math.cos(angle2)*r, P.y-Math.sin(angle2)*r,
				null,4);
	}
}

function basic_vectors_arc( P, //origin
         A, B,
         r) //radius
{	//this is the demo of failed code
	TP.drawarrow( P.x,P.y,P.x+A.x,P.y+A.y, null,1);
	TP.drawarrow( P.x,P.y,P.x+B.x,P.y+B.y, null,3);
	TP.drawpoint( P.x+A.x,P.y+A.y, 4,0);
	TP.drawpoint( P.x+B.x,P.y+B.y, 4,0);
	rl.text(P.x+30,P.y,'basic');
	
	var AL=Math.sqrt(A.x*A.x+A.y*A.y);
	var BL=Math.sqrt(B.x*B.x+B.y*B.y);
	A.x/=AL;
	B.x/=BL;
	
	var angle1=Math.acos(A.x);    var angle2=Math.acos(B.x);

	basic_arc( P,r,Math.PI/18, angle1,angle2);
}
function basic_arc( P, //origin
         r,      //radius
         dangle, //angle for each step
         angle1, angle2)
{	//this is the demo of failed code
	var incremental=true;
	if ( angle1>angle2) {
		incremental = false; //means decremental
	}
	
	if ( incremental) {
		for ( var a=angle1; a < angle2; a+=dangle)
		{
			var x=Math.cos(a);    var y=Math.sin(a);
			TP.drawpoint( P.x+x*r,P.y-y*r); //the current point on anchor
		}
	} else {
		for ( var a=angle1; a > angle2; a-=dangle)
		{
			var x=Math.cos(a);    var y=Math.sin(a);
			TP.drawpoint( P.x+x*r,P.y-y*r);
		}
	}
}


rl = Raphael('canvas1');
TP.redraw();
</script>
</body>


================================================
FILE: csharp/Assets/Demo/Demo.cs
================================================
using Vaser;
using UnityEngine;
using System.Collections.Generic;

public class Demo : MonoBehaviour {

    private int mode = 1;
    private Polyline polyline = null;
    private Polyline.Opt opt = new Polyline.Opt();
    private GameObject myGameObject = null;

    private void Start() {

        opt.feather = false;
        opt.feathering = 15f;
        opt.joint = Polyline.Opt.PLJround;
        opt.cap = Polyline.Opt.PLCround;
        opt.triangulation = false;
        {
            Camera cam = Camera.main;
            Vector3 a = cam.WorldToScreenPoint(new Vector3(0,0,0));
            Vector3 b = cam.WorldToScreenPoint(new Vector3(1,1,0));
            opt.worldToScreenRatio = Vector3.Distance(a,b) / new Vector3(1,1,0).magnitude;
        }

        VertexArrayHolder holder = null;
        if (mode == 0) {
            holder = new VertexArrayHolder();
            holder.Push3(
                new Vector2(-2, 0.5f),
                new Vector2(-1, 0.5f),
                new Vector2(-2, -0.5f),
                Color.red,
                Color.green,
                Color.blue,
                5, 0, 5
            );
            holder.Push3(
                new Vector2(-2, -0.5f),
                new Vector2(-1, -0.5f),
                new Vector2(-2, -0.75f),
                Color.red,
                Color.green,
                Color.blue,
                1.25f, 0, 5
            );
            holder.Push3(
                new Vector2(-0.6f, 0.5f),
                new Vector2(-0.1f, 0.5f),
                new Vector2(-0.6f, -0.5f),
                Color.red,
                Color.green,
                Color.blue,
                5, 0, 2.5f
            );
            holder.Push3(
                new Vector2(-0.6f, -0.5f),
                new Vector2(-0.1f, -0.5f),
                new Vector2(-0.6f, -0.75f),
                Color.red,
                Color.green,
                Color.blue,
                1.25f, 0, 2.5f
            );
            holder.Push3(
                new Vector2(0.25f, 0.5f),
                new Vector2(2.25f, 0.5f),
                new Vector2(0.25f, -0.5f),
                Color.red,
                Color.green,
                Color.blue,
                5, 0, 10
            );
            holder.Push3(
                new Vector2(0.25f, -0.5f),
                new Vector2(2f, -0.5f),
                new Vector2(0.25f, -0.75f),
                Color.red,
                Color.green,
                Color.blue,
                1.25f, 0, 10
            );
        } else if (mode == 1) {
            polyline = new Polyline(
                new List<Vector2> {
                    new Vector2(0, .75f),
                    new Vector2(-.75f, -.1f),
                    new Vector2(.75f, .1f),
                    new Vector2(0, -.75f),
                },
                new List<Color> {
                    Color.red,
                    Color.green,
                    Color.blue,
                    Color.red,
                },
                new List<float> {
                    0.05f, 0.15f, 0.15f, 0.05f,
                },
                opt
            );
        } else if (mode == 2) {
            Polybezier polybezier = new Polybezier(
                new List<Vector2> {
                    new Vector2(0, .75f),
                    new Vector2(-.75f, -.1f),
                    new Vector2(.75f, .1f),
                    new Vector2(0, -.75f),
                },
                new Vaser.Gradient (
                    new List<Vaser.Gradient.Stop> {
                        new Vaser.Gradient.Stop(0.0f,  Color.red),
                        new Vaser.Gradient.Stop(0.0f,  0.01f),
                        new Vaser.Gradient.Stop(0.25f, Color.green),
                        new Vaser.Gradient.Stop(0.25f, 0.15f),
                        new Vaser.Gradient.Stop(0.5f,  Color.blue),
                        new Vaser.Gradient.Stop(0.5f,  0.15f),
                        new Vaser.Gradient.Stop(1.0f,  Color.red),
                        new Vaser.Gradient.Stop(1.0f,  0.01f),
                    }
                ),
                new Polybezier.Opt {
                    worldToScreenRatio = opt.worldToScreenRatio
                }
            );
            polyline = polybezier.Render(opt);
        }

        myGameObject = new GameObject("Mesh", typeof(MeshFilter), typeof(MeshRenderer));
        myGameObject.transform.localScale = new Vector3(1,1,1);
        myGameObject.GetComponent<MeshRenderer>().material = Resources.Load<Material>("Vaser/Fade");

        if (polyline != null) {
            Mesh mesh = polyline.GetMesh();
            myGameObject.GetComponent<MeshFilter>().mesh = mesh;
        }

        if (mode == 0) {
            Mesh mesh = new Mesh();
            mesh.SetVertices(holder.GetVertices());
            mesh.SetUVs(0, holder.GetUVs());
            mesh.SetColors(holder.GetColors());
            mesh.SetTriangles(holder.GetTriangles(), 0);
            myGameObject.GetComponent<MeshFilter>().mesh = mesh;
        }
    }

    void Update()
    {
        float time = Time.fixedTime;
        if (mode == 3) {
            polyline = new Polyline();
            polyline.holder.Push4(
                new Vector2(-2.3f,  1),
                new Vector2( 2.3f,  1),
                new Vector2(-2.3f, -1),
                new Vector2( 2.3f, -1),
                new Color(0.365f, 0.808f, 0.910f, 1),
                new Color(0.769f, 0.380f, 0.639f, 1),
                new Color(0.365f, 0.808f, 0.910f, 1),
                new Color(0.5f, 0.305f, 0.773f, 1),
                0, 0, 0, 0
            );
            // pink new Color(0.769f, 0.380f, 0.639f, 1)
            // cyan new Color(0.180f, 0.5f, 0.941f, 1)
            for (int k=0; k<10; k++)
            {
                Polybezier.Buffer buffer = new Polybezier.Buffer();
                buffer.AddPoints(ComputeSineCurve(time, 0.5f+0.035f*k));
                buffer.Gradient(
                    new Vaser.Gradient (
                        new List<Vaser.Gradient.Stop> {
                            new Vaser.Gradient.Stop(0.0f,  new Color(0.365f, 0.808f, 0.910f, 1)),
                            new Vaser.Gradient.Stop(0.5f,  new Color(0.914f, 0.914f, 0.369f, 1)),
                            new Vaser.Gradient.Stop(1.0f,  new Color(0.5f, 0.305f, 0.773f, 1)),
                            new Vaser.Gradient.Stop(0.0f,  0.01f),
                            new Vaser.Gradient.Stop(1.0f,  0.01f),
                        }
                    )
                );
                polyline.Append(buffer.Render(opt));
            }
            Mesh mesh = polyline.GetMesh();
            myGameObject.GetComponent<MeshFilter>().mesh = mesh;
        }
    }

    private List<Vector2> ComputeSineCurve(float time, float amplitude)
    {
        List<Vector2> curve = new List<Vector2> ();
        for (float t=-1; t<1; t+=0.02f) {
            float value = 0;
            List<float> harmonics = new List<float> { 0.5f, 0.25f, 0.25f };
            for (int j=0; j<harmonics.Count; j++) {
                value += harmonics[j] * (float) System.Math.Sin(time - System.Math.PI * t * (j+1));
            }
            curve.Add(new Vector2(2.3f * t, -t + amplitude * value));
        }
        return curve;
    }
}

================================================
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================================================
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FILE: csharp/Assets/Demo/demo.unity
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================================================
FILE: csharp/Assets/Resources/Vaser/Fade.shader
================================================
Shader "Fade" {

    SubShader {
        Tags { "Queue"="Transparent" "RenderType"="Transparent" "IgnoreProjector"="True" }

        Pass
        {
            ZWrite On
            Blend SrcAlpha OneMinusSrcAlpha

            CGPROGRAM
            #pragma vertex vert
            #pragma fragment frag

            #include "UnityCG.cginc"

            struct appdata {
                float4 vertex : POSITION;
                float4 uv : TEXCOORD0;
                fixed4 color : COLOR;
            };

            struct v2f {
                float4 uv : TEXCOORD0;
                float4 vertex : SV_POSITION;
                fixed4 color : COLOR;
            };

            v2f vert (appdata v) {
                v2f o;
                o.vertex = UnityObjectToClipPos(v.vertex);
                o.uv = v.uv;
                o.color = v.color;
                return o;
            }

            fixed4 frag (v2f i) : SV_Target {
                fixed4 col = i.color;
                float factx = min((1 - abs(i.uv.x)) * i.uv.z, 1);
                float facty = min((1 - abs(i.uv.y)) * i.uv.w, 1);
                col.a *= min(factx, facty);
                return col;
            }
            ENDCG
        }
    }
}

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================================================
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FILE: csharp/Assets/Resources/Vaser.meta
================================================
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================================================
FILE: csharp/Assets/Vaser/Gradient.cs
================================================
using UnityEngine;
using System.Collections.Generic;

namespace Vaser
{
    public class Gradient
    {
        public char unit = GD_ratio;
        public List<Stop> stops; //array must be sorted in ascending order of t

        public const char GD_ratio  = (char) 0;
        public const char GD_length = (char) 1;

        public const char GS_none   = (char) 0;
        public const char GS_rgba   = (char) 1;
        public const char GS_rgb    = (char) 2;
        public const char GS_alpha  = (char) 3;
        public const char GS_weight = (char) 4;

        public Gradient()
        {
            stops = new List<Stop> ();
        }

        public Gradient(List<Stop> stopss)
        {
            stops = stopss;
        }

        public Gradient(Color cc, float ww)
        {
            stops = new List<Stop> ();
            stops.Add(new Stop(0, cc));
            stops.Add(new Stop(0, ww));
        }

        public struct Stop
        {
            public float t; //position
            public char type;
            public Color color;
            public float weight;

            public Stop(float tt, Color cc)
            {
                t = tt;
                type = GS_rgba;
                color = cc;
                weight = 0;
            }

            public Stop(float tt, float ww)
            {
                t = tt;
                type = GS_weight;
                color = new Color(0,0,0,0);
                weight = ww;
            }
        }

        public void Apply(List<Color> C, List<float> W, List<float> L, int limit, float pathLength)
        {
            if (stops.Count == 0) {
                return;
            }

            //current stops
            int las_c = 0, las_a = 0, las_w = 0, //last
                cur_c = 0, cur_a = 0, cur_w = 0, //current
                nex_c = 0, nex_a = 0, nex_w = 0; //next

            float lengthAlong = 0.0f;

            if (stops.Count <= 1) {
                return;
            }
            for (int i = 0; i < limit; i += 1) {
                lengthAlong += L[i];
                float p = 0.0f;
                if (unit == GD_ratio) {
                    p = lengthAlong / pathLength;
                } else if (unit == GD_length) {
                    p = lengthAlong;
                } else {
                    break;
                }

                //lookup for cur
                for (nex_w = cur_w; nex_w < stops.Count; nex_w += 1) {
                    if (stops[nex_w].type == GS_weight && p <= stops[nex_w].t) {
                        cur_w = nex_w;
                        break;
                    }
                }
                for (nex_c = cur_c; nex_c < stops.Count; nex_c += 1) {
                    if ((stops[nex_c].type == GS_rgba || stops[nex_c].type == GS_rgb) && p <= stops[nex_c].t) {
                        cur_c = nex_c;
                        break;
                    }
                }
                for (nex_a = cur_a; nex_a < stops.Count; nex_a += 1) {
                    if ((stops[nex_a].type == GS_rgba || stops[nex_a].type == GS_alpha) && p <= stops[nex_a].t) {
                        cur_a = nex_a;
                        break;
                    }
                }
                //look for las
                for (nex_w = cur_w; nex_w >= 0; nex_w -= 1) {
                    if (stops[nex_w].type == GS_weight && p >= stops[nex_w].t) {
                        las_w = nex_w;
                        break;
                    }
                }
                for (nex_c = cur_c; nex_c >= 0; nex_c -= 1) {
                    if ((stops[nex_c].type == GS_rgba || stops[nex_c].type == GS_rgb) && p >= stops[nex_c].t) {
                        las_c = nex_c;
                        break;
                    }
                }
                for (nex_a = cur_a; nex_a >= 0; nex_a -= 1) {
                    if ((stops[nex_a].type == GS_rgba || stops[nex_a].type == GS_alpha) && p >= stops[nex_a].t) {
                        las_a = nex_a;
                        break;
                    }
                }

                if (cur_c == las_c) {
                    C[i] = Sc(cur_c);
                } else {
                    C[i] = ColorBetween(Sc(las_c), Sc(cur_c), (p - St(las_c)) / (St(cur_c) - St(las_c)));
                }
                if (cur_w == las_w) {
                    W[i] = Sw(cur_w);
                } else {
                    W[i] = GetStep(Sw(las_w), Sw(cur_w), p - St(las_w), St(cur_w) - St(las_w));
                }
                if (cur_a == las_a) {
                    C[i] = SaC(i, cur_a);
                } else {
                    C[i] = GetStepColor(i, Sa(las_a), Sa(cur_a), p - St(las_a), St(cur_a) - St(las_a));
                }
            }

            Color Sc(int x) {
                return stops[x].color;
            }
            float Sw(int x) {
                return stops[x].weight;
            }
            float Sa(int x) {
                return stops[x].color.a;
            }
            float St(int x) {
                return stops[x].t;
            }
            Color SaC(int i, int x) {
                Color c = new Color(C[i].r, C[i].g, C[i].b, C[i].a);
                c.a = stops[x].color.a;
                return c;
            }
            float GetStep(float A, float B, float t, float T) {
                return ((T - t) * A + t * B) / T;
            }
            Color GetStepColor(int i, float A, float B, float t, float T) {
                Color c = new Color(C[i].r, C[i].g, C[i].b, C[i].a);
                c.a = GetStep(A, B, t, T);
                return c;
            }
        }

        public static Color ColorBetween(Color A, Color B, float t)
        {
            if (t < 0.0f) t = 0.0f;
            if (t > 1.0f) t = 1.0f;

            float kt = 1.0f - t;
            return new Color(
                A.r * kt + B.r * t,
                A.g * kt + B.g * t,
                A.b * kt + B.b * t,
                A.a * kt + B.a * t
            );
        }
    }
}

================================================
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================================================
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================================================
FILE: csharp/Assets/Vaser/Polybezier.cs
================================================
using UnityEngine;
using System.Collections.Generic;

namespace Vaser
{
    public class Polybezier
    {
        private Buffer buffer;

        public class Opt
        {
            public float worldToScreenRatio = 1.0f;
        }

        public Polybezier(List<Vector2> P, Color cc, float ww, Opt opt)
            : this(P, new Gradient(cc, ww), opt)
        {
            // empty
        }

        public Polybezier(List<Vector2> P, Gradient grad, Opt opt)
        {
            buffer = new Buffer();
            if (opt == null) {
                opt = new Opt();
            }

            double default_approximation_scale = (grad.stops.Count > 2 ? 2 : 1) * opt.worldToScreenRatio;
            const double default_angle_tolerance = (15 / 180 * System.Math.PI);
            const double default_cusp_limit = 5.0;

            for (int i=0; i<P.Count-3; i+=3) {
                Curve4Div(
                    P[i+0].x,P[i+0].y,
                    P[i+1].x,P[i+1].y,
                    P[i+2].x,P[i+2].y,
                    P[i+3].x,P[i+3].y,
                    default_approximation_scale,
                    default_angle_tolerance,
                    default_cusp_limit,
                    buffer);
            }
            if (grad != null) {
                buffer.Gradient(grad);
            }
        }

        public Polyline Render(Polyline.Opt opt)
        {
            return buffer.Render(opt);
        }

        public class Buffer
        {
            public List<Vector2> P;
            public List<Color> C;
            public List<float> W;
            public List<float> L; //length along polyline
            public float pathLength; //total segment length

            public Buffer()
            {
                P = new List<Vector2>();
                C = new List<Color>();
                W = new List<float>();
                L = new List<float>();
                pathLength = 0.0f;
                L.Add(0.0f);
            }

            public void Gradient(Gradient grad)
            {
                grad.Apply(C, W, L, C.Count, pathLength);
            }

            public Polyline Render(Polyline.Opt opt)
            {
                if (P.Count == 0) {
                    return new Polyline();
                }
                Polyline.Inopt inopt = new Polyline.Inopt();
                inopt.segmentLength = L;
                return new Polyline(P, C, W, opt, inopt);
            }

            public void AddPoint(float x, float y)
            {
                AddPoint(new Vector2(x, y));
            }

            public void AddPoint(double x, double y)
            {
                AddPoint(new Vector2((float) x, (float) y));
            }

            public void AddPoint(Vector2 V)
            {
                AddVertex(V, new Color(0,0,0,1), 1);
            }

            public void AddPoints(List<Vector2> points)
            {
                for (int i=0; i<points.Count; i++)
                {
                    AddPoint(points[i]);
                }
            }

            private bool AddVertex(Vector2 V, Color cc, float ww)
            {
                int N = P.Count;
                if (N > 0 && P[N-1].x == V.x && P[N-1].y == V.y) {
                    return false; //duplicate
                } else {
                    //point
                    P.Add(V);
                    if (N > 0) {
                        float len = (V - P[N-1]).Length();
                        pathLength += len;
                        L.Add(len);
                    }
                    C.Add(cc);
                    W.Add(ww);
                    return true;
                }
            }
        }

        //-----------------------------------------------------------------------
        // The Anti-Grain Geometry Project
        // A high quality rendering engine for C++
        // http://antigrain.com
        // 
        // Anti-Grain Geometry has dual licensing model. The Modified BSD 
        // License was first added in version v2.4 just for convenience.
        // It is a simple, permissive non-copyleft free software license, 
        // compatible with the GNU GPL. It's well proven and recognizable.
        // See http://www.fsf.org/licensing/licenses/index_html#ModifiedBSD
        // for details.
        // 
        // Note that the Modified BSD license DOES NOT restrict your rights 
        // if you choose the Anti-Grain Geometry Public License.
        // 
        // Anti-Grain Geometry Public License
        // ====================================================
        // 
        // Anti-Grain Geometry - Version 2.4 
        // Copyright (C) 2002-2005 Maxim Shemanarev (McSeem) 
        // 
        // Permission to copy, use, modify, sell and distribute this software 
        // is granted provided this copyright notice appears in all copies. 
        // This software is provided "as is" without express or implied
        // warranty, and with no claim as to its suitability for any purpose.
        // 
        // 
        // 
        // Modified BSD License
        // ====================================================
        // Anti-Grain Geometry - Version 2.4 
        // Copyright (C) 2002-2005 Maxim Shemanarev (McSeem) 
        // 
        // Redistribution and use in source and binary forms, with or without 
        // modification, are permitted provided that the following conditions 
        // are met:
        // 
        //   1. Redistributions of source code must retain the above copyright 
        //      notice, this list of conditions and the following disclaimer. 
        // 
        //   2. Redistributions in binary form must reproduce the above copyright
        //      notice, this list of conditions and the following disclaimer in 
        //      the documentation and/or other materials provided with the 
        //      distribution. 
        // 
        //   3. The name of the author may not be used to endorse or promote 
        //      products derived from this software without specific prior 
        //      written permission. 
        // 
        // THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 
        // IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 
        // WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
        // ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, 
        // INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 
        // (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR 
        // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 
        // HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 
        // STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING 
        // IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
        // POSSIBILITY OF SUCH DAMAGE.
        //
        //-----------------------------------------------------------------------
        // Contact: mcseem@antigrain.com
        //          mcseemagg@yahoo.com
        //          http://www.antigrain.com
        //-----------------------------------------------------------------------

        private void RecursiveBezier(
            double x1, double y1, 
            double x2, double y2, 
            double x3, double y3, 
            double x4, double y4,
            int level,
            double m_angle_tolerance,
            double m_cusp_limit,
            double m_distance_tolerance_square,
            Buffer obj)
        {
            const double M_PI = System.Math.PI;
            //const double curve_distance_epsilon                  = 1e-30;
            const double curve_collinearity_epsilon              = 1e-30;
            const double curve_angle_tolerance_epsilon           = 0.01;
            const int curve_recursion_limit = 32;

            if (level > curve_recursion_limit) {
                return;
            }

            // Calculate all the mid-points of the line segments
            //----------------------
            double x12   = (x1 + x2) / 2;
            double y12   = (y1 + y2) / 2;
            double x23   = (x2 + x3) / 2;
            double y23   = (y2 + y3) / 2;
            double x34   = (x3 + x4) / 2;
            double y34   = (y3 + y4) / 2;
            double x123  = (x12 + x23) / 2;
            double y123  = (y12 + y23) / 2;
            double x234  = (x23 + x34) / 2;
            double y234  = (y23 + y34) / 2;
            double x1234 = (x123 + x234) / 2;
            double y1234 = (y123 + y234) / 2;

            // Try to approximate the full cubic curve by a single straight line
            //------------------
            double dx = x4-x1;
            double dy = y4-y1;

            double d2 = System.Math.Abs(((x2 - x4) * dy - (y2 - y4) * dx));
            double d3 = System.Math.Abs(((x3 - x4) * dy - (y3 - y4) * dx));
            double da1, da2, k;

            switch (((d2 > curve_collinearity_epsilon ? 1 : 0) << 1) + (d3 > curve_collinearity_epsilon ? 1 : 0))
            {
                case 0:
                    // All collinear OR p1==p4
                    //----------------------
                    k = dx*dx + dy*dy;
                    if (k == 0) {
                        d2 = calc_sq_distance(x1, y1, x2, y2);
                        d3 = calc_sq_distance(x4, y4, x3, y3);
                    } else {
                        k   = 1 / k;
                        da1 = x2 - x1;
                        da2 = y2 - y1;
                        d2  = k * (da1*dx + da2*dy);
                        da1 = x3 - x1;
                        da2 = y3 - y1;
                        d3  = k * (da1*dx + da2*dy);

                        if (d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1) {
                            // Simple collinear case, 1---2---3---4
                            // We can leave just two endpoints
                            return;
                        }
                        if (d2 <= 0) {
                            d2 = calc_sq_distance(x2, y2, x1, y1);
                        } else if (d2 >= 1) {
                            d2 = calc_sq_distance(x2, y2, x4, y4);
                        } else {
                            d2 = calc_sq_distance(x2, y2, x1 + d2*dx, y1 + d2*dy);
                        }
                        if (d3 <= 0) {
                            d3 = calc_sq_distance(x3, y3, x1, y1);
                        } else if(d3 >= 1) {
                            d3 = calc_sq_distance(x3, y3, x4, y4);
                        } else {
                            d3 = calc_sq_distance(x3, y3, x1 + d3*dx, y1 + d3*dy);
                        }
                    }
                    if (d2 > d3) {
                        if (d2 < m_distance_tolerance_square) {
                            obj.AddPoint(x2, y2);
                            return;
                        }
                    } else {
                        if (d3 < m_distance_tolerance_square) {
                            obj.AddPoint(x3, y3);
                            return;
                        }
                    }
                break;

                case 1:
                    // p1,p2,p4 are collinear, p3 is significant
                    //----------------------
                    if (d3 * d3 <= m_distance_tolerance_square * (dx*dx + dy*dy)) {
                        if (m_angle_tolerance < curve_angle_tolerance_epsilon) {
                            obj.AddPoint(x23, y23);
                            return;
                        }

                        // Angle Condition
                        //----------------------
                        da1 = System.Math.Abs(System.Math.Atan2(y4 - y3, x4 - x3) - System.Math.Atan2(y3 - y2, x3 - x2));
                        if (da1 >= M_PI) da1 = 2*M_PI - da1;

                        if (da1 < m_angle_tolerance) {
                            obj.AddPoint(x2, y2);
                            obj.AddPoint(x3, y3);
                            return;
                        }

                        if (m_cusp_limit != 0.0) {
                            if (da1 > m_cusp_limit) {
                                obj.AddPoint(x3, y3);
                                return;
                            }
                        }
                    }
                break;

                case 2:
                    // p1,p3,p4 are collinear, p2 is significant
                    //----------------------
                    if (d2 * d2 <= m_distance_tolerance_square * (dx*dx + dy*dy)) {
                        if (m_angle_tolerance < curve_angle_tolerance_epsilon) {
                            obj.AddPoint(x23, y23);
                            return;
                        }

                        // Angle Condition
                        //----------------------
                        da1 = System.Math.Abs(System.Math.Atan2(y3 - y2, x3 - x2) - System.Math.Atan2(y2 - y1, x2 - x1));
                        if (da1 >= M_PI) {
                            da1 = 2*M_PI - da1;
                        }
                        if (da1 < m_angle_tolerance) {
                            obj.AddPoint(x2, y2);
                            obj.AddPoint(x3, y3);
                            return;
                        }
                        if (m_cusp_limit != 0.0) {
                            if (da1 > m_cusp_limit) {
                                obj.AddPoint(x2, y2);
                                return;
                            }
                        }
                    }
                break;

                case 3: 
                    // Regular case
                    //-----------------
                    if ((d2 + d3)*(d2 + d3) <= m_distance_tolerance_square * (dx*dx + dy*dy)) {
                        // If the curvature doesn't exceed the distance_tolerance value
                        // we tend to finish subdivisions.
                        //----------------------
                        if (m_angle_tolerance < curve_angle_tolerance_epsilon) {
                            obj.AddPoint(x23, y23);
                            return;
                        }

                        // Angle & Cusp Condition
                        //----------------------
                        k   = System.Math.Atan2(y3 - y2, x3 - x2);
                        da1 = System.Math.Abs(k - System.Math.Atan2(y2 - y1, x2 - x1));
                        da2 = System.Math.Abs(System.Math.Atan2(y4 - y3, x4 - x3) - k);
                        if (da1 >= M_PI) da1 = 2*M_PI - da1;
                        if (da2 >= M_PI) da2 = 2*M_PI - da2;

                        if (da1 + da2 < m_angle_tolerance) {
                            // Finally we can stop the recursion
                            //----------------------
                            obj.AddPoint(x23, y23);
                            return;
                        }

                        if (m_cusp_limit != 0.0) {
                            if (da1 > m_cusp_limit) {
                                obj.AddPoint(x2, y2);
                                return;
                            }
                            if (da2 > m_cusp_limit) {
                                obj.AddPoint(x3, y3);
                                return;
                            }
                        }
                    }
                break;
            }

            // Continue subdivision
            //----------------------
            RecursiveBezier(x1, y1, x12, y12, x123, y123, x1234, y1234, level + 1,
                m_angle_tolerance, m_cusp_limit, m_distance_tolerance_square,
                obj); 
            RecursiveBezier(x1234, y1234, x234, y234, x34, y34, x4, y4, level + 1,
                m_angle_tolerance, m_cusp_limit, m_distance_tolerance_square,
                obj);

            double calc_sq_distance(double xx1, double yy1, double xx2, double yy2)
            {
                double ddx = xx2-xx1;
                double ddy = yy2-yy1;
                return ddx * ddx + ddy * ddy;
            }
        }

        private void Curve4Div(
            double x1, double y1, 
            double x2, double y2, 
            double x3, double y3,
            double x4, double y4,
            double m_approximation_scale,
            double m_angle_tolerance,
            double m_cusp_limit,
            Buffer obj)
        {
            double m_distance_tolerance_square = 0.5 / m_approximation_scale;
            m_distance_tolerance_square *= m_distance_tolerance_square;
            obj.AddPoint(x1, y1);
            RecursiveBezier(
                x1, y1, x2, y2, x3, y3, x4, y4, 0,
                m_angle_tolerance, m_cusp_limit, m_distance_tolerance_square,
                obj);
            obj.AddPoint(x4, y4);
        }
        //                             end of AGG
        //-----------------------------------------------------------------------
    }
}

================================================
FILE: csharp/Assets/Vaser/Polybezier.cs.meta
================================================
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================================================
FILE: csharp/Assets/Vaser/Polyline.cs
================================================
using UnityEngine;
using System.Collections.Generic;

namespace Vaser
{
    public class Polyline
    {
        public VertexArrayHolder holder;

        public class Opt
        {
            public char joint = PLJmiter;
            public char cap = PLCbutt;
            public bool feather = false;
            public float feathering = 0.0f;
            public bool noFeatherAtCap = false;
            public bool noFeatherAtCore = false;
            public float worldToScreenRatio = 1.0f;
            public bool triangulation = false;

            //for Opt.joint
            public const char PLJmiter = (char) 0; //default
            public const char PLJbevel = (char) 1;
            public const char PLJround = (char) 2;
            //for Opt.cap
            public const char PLCbutt   = (char) 0; //default
            public const char PLCround  = (char) 1;
            public const char PLCsquare = (char) 2;
            public const char PLCrect   = (char) 3;
            public const char PLCboth   = (char) 0; //default
            public const char PLCfirst  = (char) 10;
            public const char PLClast   = (char) 20;
            public const char PLCnone   = (char) 30;
        }

        public class Inopt
        {
            public bool constColor = false;
            public bool constWeight = false;
            public bool noCapFirst = false;
            public bool noCapLast = false;
            public bool joinFirst = false;
            public bool joinLast = false;
            public List<float> segmentLength = null; // length of each segment; optional
            public VertexArrayHolder holder = new VertexArrayHolder();

            public Inopt ShallowCopy()
            {
                return (Inopt) this.MemberwiseClone();
            }
        }

        public Polyline()
        {
            holder = new VertexArrayHolder();
        }

        public Polyline(
            List<Vector2> P, List<Color> C, List<float> W, Opt opt)
            : this(P, C, W, opt, null)
        {
            // empty
        }

        public Polyline(
            List<Vector2> P, Color C, float W, Opt opt)
            : this(P, new List<Color> { C }, new List<float> { W }, opt, new Inopt {
                constColor = true, constWeight = true,
            })
        {
            // empty
        }

        public Polyline(
            List<Vector2> P, List<Color> C, List<float> W,
            Opt opt, Inopt inopt)
        {
            int length = P.Count;
            if (opt == null) {
                opt = new Opt();
            }
            if (inopt == null) {
                inopt = new Inopt();
            }

            if (opt.cap >= 10) {
                char dec = (char)((int) opt.cap - ((int) opt.cap % 10));
                if (dec == Opt.PLCfirst || dec == Opt.PLCnone) {
                    inopt.noCapLast = true;
                }
                if (dec == Opt.PLClast || dec == Opt.PLCnone) {
                    inopt.noCapFirst = true;
                }
                opt.cap -= dec;
            }

            int A = 0, B = 0;
            bool on = false;
            for (int i = 1; i < length - 1; i++) {
                Vector2 V1 = P[i] - P[i - 1];
                Vector2 V2 = P[i + 1] - P[i];
                float len = 0;
                if (inopt.segmentLength != null) {
                    V1 *= 1 / inopt.segmentLength[i];
                    V2 *= 1 / inopt.segmentLength[i + 1];
                    len += (inopt.segmentLength[i] + inopt.segmentLength[i + 1]) * 0.5f;
                } else {
                    len += Vec2Ext.Normalize(ref V1) * 0.5f;
                    len += Vec2Ext.Normalize(ref V2) * 0.5f;
                }
                float costho = V1.x * V2.x + V1.y * V2.y;
                const float m_pi = (float) System.Math.PI;
                //float angle = acos(costho)*180/m_pi;
                float cos_a = (float) System.Math.Cos(15 * m_pi / 180);
                float cos_b = (float) System.Math.Cos(10 * m_pi / 180);
                float cos_c = (float) System.Math.Cos(25 * m_pi / 180);
                float weight = W[inopt.constWeight ? 0 : i];
                bool approx = false;
                if ((weight * opt.worldToScreenRatio < 7 && costho > cos_a) || (costho > cos_b) || //when the angle difference at an anchor is smaller than a critical degree, do polyline approximation
                    (len < weight && costho > cos_c)) { //when vector length is smaller than weight, do approximation
                    approx = true;
                }
                if (approx && !on) {
                    A = i;
                    on = true;
                    if (A == 1) {
                        A = 0;
                    }
                    if (A > 1) {
                        PolylineRange(P, C, W, opt, inopt, B, A, false);
                    }
                } else if (!approx && on) {
                    B = i;
                    on = false;
                    PolylineRange(P, C, W, opt, inopt, A, B, true);
                }
            }
            if (on && B < length - 1) {
                B = length - 1;
                PolylineRange(P, C, W, opt, inopt, A, B, true);
            } else if (!on && A < length - 1) {
                A = length - 1;
                PolylineRange(P, C, W, opt, inopt, B, A, false);
            }
            holder = inopt.holder;
            inopt.holder = null;
        }

        public Mesh GetMesh()
        {
            Mesh mesh = new Mesh();
            mesh.SetVertices(holder.GetVertices());
            mesh.SetUVs(0, holder.GetUVs());
            mesh.SetColors(holder.GetColors());
            mesh.SetTriangles(holder.GetTriangles(), 0);
            return mesh;
        }

        public void Append(Polyline polyline)
        {
            holder.Push(polyline.holder);
        }

        private struct StPolyline
        // to hold info for AnchorLate() to perform triangulation
        {
            //for all joints
            public Vector2 vP; //vector to intersection point; outward

            //for djoint==PLJbevel
            public Vector2 T; //core thickness of a line
            public Vector2 R; //fading edge of a line
            public Vector2 bR; //out stepping vector, same direction as cap
            public Vector2 T1; //alternate vectors, same direction as T21
            // all T,R,T1 are outward

            //for djoint==PLJround
            public float t,r;

            //for degeneration case
            public bool degenT; //core degenerated
            public bool degenR; //fade degenerated
            public bool preFull; //draw the preceding segment in full
            public Vector2 PT;

            public char djoint; //determined joint
            // e.g. originally a joint is PLJmiter. but it is smaller than critical angle, should then set djoint to PLJbevel
        }

        private class StAnchor
        // to hold memory for the working of anchor()
        {
            public Vector2[] P = new Vector2[3]; //point
            public Color[] C = new Color[3]; //color
            public float[] W = new float[3]; //weight

            public StPolyline[] SL = new StPolyline[3];
            public VertexArrayHolder vah = new VertexArrayHolder();
        }

        private static void PolyPointInter(
            List<Vector2> P, List<Color> C, List<float> W,
            Inopt inopt, ref Vector2 p, ref Color c, ref float w, int at, float t)
        {
            Color color(int I) {
                return C[inopt != null && inopt.constColor ? 0 : I];
            }
            float weight(int I) {
                return W[inopt != null && inopt.constWeight ? 0 : I];
            }

            if (t == 0.0) {
                p = P[at];
                c = color(at);
                w = weight(at);
            } else if (t == 1.0) {
                p = P[at + 1];
                c = color(at + 1);
                w = weight(at + 1);
            } else {
                p = (P[at] + P[at + 1]) * t;
                c = Gradient.ColorBetween(color(at), color(at + 1), t);
                w = (weight(at) + weight(at + 1)) * t;
            }
        }

        private static void PolylineApprox(
            List<Vector2> P, List<Color> C, List<float> W,
            Opt opt, Inopt inopt, int from, int to)
        {
            if (to - from + 1 < 2) {
                return;
            }
            bool capFirst = !(inopt != null && inopt.noCapFirst);
            bool capLast = !(inopt != null && inopt.noCapLast);
            bool joinFirst = inopt != null && inopt.joinFirst;
            bool joinLast = inopt != null && inopt.joinLast;

            VertexArrayHolder vcore = new VertexArrayHolder(); //curve core
            vcore.SetGlDrawMode(VertexArrayHolder.GL_TRIANGLE_STRIP);

            Color color(int I) {
                return C[inopt != null && inopt.constColor ? 0: I];
            }
            float weight(int I) {
                return W[inopt != null && inopt.constWeight ? 0: I];
            }
            void poly_step(int i, Vector2 pp, float ww, Color cc) {
                float t = 0, r = 0;
                DetermineTr(ww, ref t, ref r, opt.worldToScreenRatio);
                if (opt.feather && !opt.noFeatherAtCore) {
                    r *= opt.feathering;
                }
                float rr = (t + r) / r;
                Vector2 V = P[i] - P[i - 1];
                Vec2Ext.Perpen(ref V);
                Vec2Ext.Normalize(ref V);
                V *= (t + r);
                vcore.Push(pp - V, cc, rr);
                vcore.Push(pp + V, cc, 0);
            }

            for (int i = from + 1; i < to; i++) {
                poly_step(i, P[i], weight(i), color(i));
            }
            Vector2 P_las = new Vector2(), P_fir = new Vector2();
            Color C_las = new Color(), C_fir = new Color();
            float W_las = 0, W_fir = 0;
            PolyPointInter(P, C, W, inopt, ref P_las, ref C_las, ref W_las, to - 1, 0.5f);
            poly_step(to, P_las, W_las, C_las);

            StAnchor SA = new StAnchor();
            {
                PolyPointInter(P, C, W, inopt, ref P_fir, ref C_fir, ref W_fir, from, joinFirst ? 0.5f : 0.0f);
                SA.P[0] = P_fir;
                SA.P[1] = P[from + 1];
                SA.C[0] = C_fir;
                SA.C[1] = color(from + 1);
                SA.W[0] = W_fir;
                SA.W[1] = weight(from + 1);
                Segment(SA, opt, capFirst, false, true);
            }
            if (!joinLast) {
                SA.P[0] = P_las;
                SA.P[1] = P[to];
                SA.C[0] = C_las;
                SA.C[1] = color(to);
                SA.W[0] = W_las;
                SA.W[1] = weight(to);
                Segment(SA, opt, false, capLast, true);
            }

            inopt.holder.Push(vcore);
            inopt.holder.Push(SA.vah);

            if (opt.triangulation) {
                DrawTriangles(vcore, inopt.holder, opt.worldToScreenRatio);
                DrawTriangles(SA.vah, inopt.holder, opt.worldToScreenRatio);
            }
        }

        private static void PolylineExact(
            List<Vector2> P, List<Color> C, List<float> W,
            Opt opt, Inopt inopt, int from, int to)
        {
            bool capFirst = !(inopt != null && inopt.noCapFirst);
            bool capLast = !(inopt != null && inopt.noCapLast);
            bool joinFirst = inopt != null && inopt.joinFirst;
            bool joinLast = inopt != null && inopt.joinLast;

            Color color(int I) {
                return C[inopt != null && inopt.constColor ? 0: I];
            }
            float weight(int I) {
                return W[inopt != null && inopt.constWeight ? 0: I];
            }

            Vector2 mid_l = new Vector2(), mid_n = new Vector2(); //the last and the next mid point
            Color c_l = new Color(), c_n = new Color();
            float w_l = 0, w_n = 0;

            //init for the first anchor
            PolyPointInter(P, C, W, inopt, ref mid_l, ref c_l, ref w_l, from, joinFirst ? 0.5f : 0);

            StAnchor SA = new StAnchor();
            if (to - from + 1 == 2) {
                SA.P[0] = P[from];
                SA.P[1] = P[from + 1];
                SA.C[0] = color(from);
                SA.C[1] = color(from + 1);
                SA.W[0] = weight(from);
                SA.W[1] = weight(from + 1);
                Segment(SA, opt, capFirst, capLast, true);
            } else {
                for (int i = from + 1; i < to; i++) {
                    if (i == to - 1 && !joinLast) {
                        PolyPointInter(P, C, W, inopt, ref mid_n, ref c_n, ref w_n, i, 1.0f);
                    } else {
                        PolyPointInter(P, C, W, inopt, ref mid_n, ref c_n, ref w_n, i, 0.5f);
                    }

                    SA.P[0] = mid_l;
                    SA.C[0] = c_l;
                    SA.W[0] = w_l;
                    SA.P[2] = mid_n;
                    SA.C[2] = c_n;
                    SA.W[2] = w_n;

                    SA.P[1] = P[i];
                    SA.C[1] = color(i);
                    SA.W[1] = weight(i);

                    Anchor(SA, opt, (i == 1) && capFirst, (i == to - 1) && capLast);

                    mid_l = mid_n;
                    c_l = c_n;
                    w_l = w_n;
                }
            }

            inopt.holder.Push(SA.vah);
            if (opt.triangulation) {
                DrawTriangles(SA.vah, inopt.holder, opt.worldToScreenRatio);
            }
        }

        private static void PolylineRange(
            List<Vector2> P, List<Color> C, List<float> W,
            Opt opt, Inopt ininopt, int from, int to, bool approx)
        {
            Inopt inopt;
            if (ininopt == null) {
                inopt = new Inopt();
            } else {
                inopt = ininopt.ShallowCopy();
            }
            if (from > 0) {
                from -= 1;
            }

            inopt.joinFirst = from != 0;
            inopt.joinLast = to != (P.Count - 1);
            inopt.noCapFirst = ininopt.noCapFirst || inopt.joinFirst;
            inopt.noCapLast = ininopt.noCapLast || inopt.joinLast;

            if (approx) {
                PolylineApprox(P, C, W, opt, inopt, from, to);
            } else {
                PolylineExact(P, C, W, opt, inopt, from, to);
            }
        }

        private static void DrawTriangles(VertexArrayHolder triangles, VertexArrayHolder holder, float scale)
        {
            Opt opt = new Opt();
            opt.cap = Opt.PLCnone;
            opt.joint = Opt.PLJbevel;
            opt.worldToScreenRatio = scale;
            if (triangles.glmode == VertexArrayHolder.GL_TRIANGLES) {
                for (int i = 0; i < triangles.GetCount(); i++) {
                    List<Vector2> P = new List<Vector2> ();
                    P.Add(triangles.Get(i));
                    i += 1;
                    P.Add(triangles.Get(i));
                    i += 1;
                    P.Add(triangles.Get(i));
                    P.Add(P[0]);
                    Polyline polyline = new Polyline(P, Color.red, 1 / scale, opt);
                    holder.Push(polyline.holder);
                }
            } else if (triangles.glmode == VertexArrayHolder.GL_TRIANGLE_STRIP) {
                for (int i = 2; i < triangles.GetCount(); i++) {
                    List<Vector2> P = new List<Vector2> ();
                    P.Add(triangles.Get(i - 2));
                    P.Add(triangles.Get(i));
                    P.Add(triangles.Get(i - 1));
                    Polyline polyline = new Polyline(P, Color.red, 1 / scale, opt);
                    holder.Push(polyline.holder);
                }
            }
        }

        private static void DrawDigit(VertexArrayHolder holder, Vector2 pp, float scale, int digit)
        {
            Opt opt = new Opt();
            opt.cap = Opt.PLCnone;
            opt.joint = Opt.PLJbevel;
            opt.worldToScreenRatio = scale;
            List<Vector2> P;
            float size = 5 / scale;
            float halfSize = size / 2;
            switch (digit)
            {
                case 0:
                    P = new List<Vector2> {
                        new Vector2(halfSize, size) + pp,
                        new Vector2(halfSize, -size) + pp,
                        new Vector2(-halfSize, -size) + pp,
                        new Vector2(-halfSize, size) + pp,
                        new Vector2(halfSize, size) + pp,
                        new Vector2(-halfSize, -size) + pp,
                    };
                break;
                case 1:
                    P = new List<Vector2> {
                        new Vector2(-halfSize, 0) + pp,
                        new Vector2(0, size) + pp,
                        new Vector2(0, -size) + pp,
                    };
                break;
                case 2:
                    P = new List<Vector2> {
                        new Vector2(-halfSize, size) + pp,
                        new Vector2(halfSize, size) + pp,
                        new Vector2(halfSize, 0) + pp,
                        new Vector2(-halfSize, 0) + pp,
                        new Vector2(-halfSize, -size) + pp,
                        new Vector2(halfSize, -size) + pp,
                    };
                break;
                case 3:
                    P = new List<Vector2> {
                        new Vector2(-halfSize, size) + pp,
                        new Vector2(halfSize, size) + pp,
                        new Vector2(halfSize, 0) + pp,
                        new Vector2(-halfSize, 0) + pp,
                        new Vector2(halfSize, 0) + pp,
                        new Vector2(halfSize, -size) + pp,
                        new Vector2(-halfSize, -size) + pp,
                    };
                break;
                case 4:
                    P = new List<Vector2> {
                        new Vector2(halfSize, -size) + pp,
                        new Vector2(halfSize, size) + pp,
                        new Vector2(-halfSize, 0) + pp,
                        new Vector2(halfSize, 0) + pp,
                    };
                break;
                default: return;
            }
            Polyline polyline = new Polyline(P, Color.red, 1 / scale, opt);
            holder.Push(polyline.holder);
        }

        private static void DetermineTr(float w, ref float t, ref float R, float scale)
        {
            //efficiency: can cache one set of w,t,R values
            // i.e. when a polyline is of uniform thickness, the same w is passed in repeatedly
            w *= scale;
            float f = w - (float) System.Math.Floor(w);
            // resolution dependent
            if (w >= 0.0 && w < 1.0) {
                t = 0.05f;
                R = 0.768f;
            } else if (w >= 1.0 && w < 2.0) {
                t = 0.05f + f * 0.33f;
                R = 0.768f + 0.312f * f;
            } else if (w >= 2.0 && w < 3.0) {
                t = 0.38f + f * 0.58f;
                R = 1.08f;
            } else if (w >= 3.0 && w < 4.0) {
                t = 0.96f + f * 0.48f;
                R = 1.08f;
            } else if (w >= 4.0 && w < 5.0) {
                t = 1.44f + f * 0.46f;
                R = 1.08f;
            } else if (w >= 5.0 && w < 6.0) {
                t = 1.9f + f * 0.6f;
                R = 1.08f;
            } else if (w >= 6.0) {
                t = 2.5f + (w - 6.0f) * 0.50f;
                R = 1.08f;
            }
            t /= scale;
            R /= scale;
        }

        private static void MakeTrc(
            ref Vector2 P1, ref Vector2 P2, ref Vector2 T, ref Vector2 R, ref Vector2 C,
            float w, Opt opt, ref float rr, ref float tt, ref float dist, bool anchorMode)
        {
            float t = 1.0f, r = 0.0f;

            //calculate t,r
            DetermineTr(w, ref t, ref r, opt.worldToScreenRatio);
            if (opt.feather && !opt.noFeatherAtCore) {
                r *= opt.feathering;
            }
            if (anchorMode) {
                t += r;
            }

            //output
            tt = t;
            rr = r;
            Vector2 DP = P2 - P1;
            dist = Vec2Ext.Normalize(ref DP);
            C = DP * (1 / opt.worldToScreenRatio);
            Vec2Ext.Perpen(ref DP);
            T = DP * t;
            R = DP * r;
        }

        private static void Segment(StAnchor SA, Opt opt, bool capFirst, bool capLast, bool core)
        {
            float[] weight = SA.W;

            Vector2[] P = new Vector2[2];
            P[0] = SA.P[0];
            P[1] = SA.P[1];
            Color[] C = new Color[3];
            C[0] = SA.C[0];
            C[1] = SA.C[1];

            Vector2 T2 = new Vector2();
            Vector2 R2 = new Vector2();
            Vector2 bR = new Vector2();
            float t = 0, r = 0;

            bool varying_weight = weight[0] != weight[1];

            Vector2 capStart = new Vector2(), capEnd = new Vector2();
            StPolyline[] SL = new StPolyline[2];

            /*for (int i = 0; i < 2; i++) {
                //lower the transparency for weight < 1.0
                float actualWeight = weight[i] * opt.worldToScreenRatio;
                if (actualWeight >= 0.0 && actualWeight < 1.0) {
                    C[i].a *= actualWeight;
                }
            }*/

            {
                int i = 0;
                float dd = 0f;
                MakeTrc(ref P[i], ref P[i + 1], ref T2, ref R2, ref bR, weight[i], opt, ref r, ref t, ref dd, false);

                if (capFirst) {
                    if (opt.cap == Opt.PLCsquare) {
                        P[0] -= bR * (t + r);
                    }
                    capStart = bR;
                    Vec2Ext.Opposite(ref capStart);
                    if (opt.feather && !opt.noFeatherAtCap) {
                        capStart *= opt.feathering;
                    }
                }

                SL[i].djoint = opt.cap;
                SL[i].t = t;
                SL[i].r = r;
                SL[i].T = T2;
                SL[i].R = R2;
                SL[i].bR = bR;
                SL[i].degenT = false;
                SL[i].degenR = false;
            }

            {
                int i = 1;
                float dd = 0f;
                if (varying_weight) {
                    MakeTrc(ref P[i - 1], ref P[i], ref T2, ref R2, ref bR, weight[i], opt, ref r, ref t, ref dd, false);
                }

                if (capLast) {
                    if (opt.cap == Opt.PLCsquare) {
                        P[1] += bR * (t + r);
                    }
                    capEnd = bR;
                    if (opt.feather && !opt.noFeatherAtCap) {
                        capEnd *= opt.feathering;
                    }
                }

                SL[i].djoint = opt.cap;
                SL[i].t = t;
                SL[i].r = r;
                SL[i].T = T2;
                SL[i].R = R2;
                SL[i].bR = bR;
                SL[i].degenT = false;
                SL[i].degenR = false;
            }

            SegmentLate(opt, P, C, SL, SA.vah, capStart, capEnd, core);
        }

        private static void SegmentLate(
            Opt opt, Vector2[] P, Color[] C, StPolyline[] SL,
            VertexArrayHolder tris, Vector2 cap1, Vector2 cap2, bool core)
        {
            tris.SetGlDrawMode(VertexArrayHolder.GL_TRIANGLES);

            Vector2 P_0, P_1;
            P_0 = P[0];
            P_1 = P[1];

            Vector2 P1, P2, P3, P4; //core
            Vector2 P1c, P2c, P3c, P4c; //cap
            Vector2 P1r, P2r, P3r, P4r; //fade

            float s0 = 1, s1 = 1;
            if (SL[0].t < SL[1].t) {
                s0 = (SL[0].t + SL[0].r) / (SL[1].t + SL[1].r);
            }
            if (SL[1].t < SL[0].t) {
                s1 = (SL[1].t + SL[1].r) / (SL[0].t + SL[0].r);
            }
            P1 = P_0 + SL[0].T + SL[0].R;
            P1r = P1 - SL[0].R * s0;
            P1c = P1 + cap1 * s0;
            P2 = P_0 - SL[0].T - SL[0].R;
            P2r = P2 + SL[0].R * s0;
            P2c = P2 + cap1 * s0;
            P3 = P_1 + SL[1].T + SL[1].R;
            P3r = P3 - SL[1].R * s1;
            P3c = P3 + cap2 * s1;
            P4 = P_1 - SL[1].T - SL[1].R;
            P4r = P4 + SL[1].R * s1;
            P4c = P4 + cap2 * s1;
            float rr = System.Math.Max((SL[0].t + SL[0].r) / SL[0].r, (SL[1].t + SL[1].r) / SL[1].r);
            float rc = (P_1 - P_0).Length() / System.Math.Max(SL[0].t + SL[0].r, SL[1].t + SL[1].r);

            //core
            if (core) {
                float rc0 = 0, rc1 = 0;
                if (SL[0].djoint == Opt.PLCbutt && !cap1.IsZero()) {
                    rc0 = rc;
                }
                if (SL[1].djoint == Opt.PLCbutt && !cap2.IsZero()) {
                    rc1 = rc;
                }
                tris.Push3(P1, P3, P2, C[0], C[1], C[0], rr,  0, rc0);
                tris.Push3(P2, P3, P4, C[0], C[1], C[1], 0, rc1,  rr);
            }

            //caps
            for (int j = 0; j < 2; j++) {
                VertexArrayHolder cap = new VertexArrayHolder();
                cap.SetGlDrawMode(VertexArrayHolder.GL_TRIANGLE_STRIP);
                Vector2 cur_cap = j == 0 ? cap1 : cap2;
                if (cur_cap.IsZero()) {
                    continue;
                }

                if (SL[j].djoint == Opt.PLCround) {
                    //round cap
                    Vector2 O = P[j];
                    float dangle = GetPljRoundDangle(SL[j].t, SL[j].r, opt.worldToScreenRatio);

                    VectorsToArc(
                        cap, O, C[j], C[j], SL[j].T + SL[j].R, -SL[j].T - SL[j].R,
                        dangle, SL[j].t + SL[j].r, 0.0f, false, O, j == 0 ? cap1 : cap2, rr, false);
                    //cap.Push(O-SL[j].T-SL[j].R, C[j]);
                    //cap.Push(O, C[j]);
                    tris.Push(cap);
                } else if (SL[j].djoint == Opt.PLCrect || SL[j].djoint == Opt.PLCsquare) {
                    //rectangular cap
                    Vector2 Pj, Pjr, Pjc, Pk, Pkr, Pkc;
                    if (j == 0) {
                        Pj = P1;
                        Pjr = P1r;
                        Pjc = P1c;

                        Pk = P2;
                        Pkr = P2r;
                        Pkc = P2c;
                    }
                    else {
                        Pj = P4;
                        Pjr = P4r;
                        Pjc = P4c;

                        Pk = P3;
                        Pkr = P3r;
                        Pkc = P3c;
                    }

                    tris.PushF(Pk, C[j]);
                    tris.PushF(Pkc, C[j]);
                    tris.Push(Pkr, C[j]);
                    tris.Push(Pkr, C[j]);
                    tris.PushF(Pkc, C[j]);
                    tris.Push(Pjr, C[j]);
                    tris.Push(Pjr, C[j]);
                    tris.PushF(Pkc, C[j]);
                    tris.PushF(Pjc, C[j]);
                    tris.Push(Pjr, C[j]);
                    tris.PushF(Pjc, C[j]);
                    tris.PushF(Pj, C[j]);
                }
            }
        }

        private static void Anchor(StAnchor SA, Opt opt, bool capFirst, bool capLast)
        {
            Vector2[] P = SA.P;
            Color[] C = SA.C;
            float[] weight = SA.W;
            StPolyline[] SL = SA.SL;
            if (Vec2Ext.SignedArea(P[0], P[1], P[2]) > 0) {
                // rectify clockwise
                Vector2 P0 = P[0];
                P[0] = P[2];
                P[2] = P0;
                Color C0 = C[0];
                C[0] = C[2];
                C[2] = C0;
                float weight0 = weight[0];
                weight[0] = weight[2];
                weight[2] = weight0;
                bool capCap = capFirst;
                capFirst = capLast;
                capLast = capCap;
            }

            //const float critical_angle=11.6538;
            //  critical angle in degrees where a miter is force into bevel
            //  it is _similar_ to cairo_set_miter_limit () but cairo works with ratio while VASEr works with included angle
            const float cos_cri_angle = 0.979386f; //cos(critical_angle)

            bool varying_weight = !(weight[0] == weight[1] & weight[1] == weight[2]);

            Vector2 T1 = new Vector2(), T2 = new Vector2(), T21 = new Vector2(), T31 = new Vector2(), RR = new Vector2();

            /*for (int i = 0; i < 3; i++) {
                //lower the transparency for weight < 1.0
                float actualWeight = weight[i] * opt.worldToScreenRatio;
                if (actualWeight >= 0.0 && actualWeight < 1.0) {
                    C[i].a *= actualWeight;
                }
            }*/

            {
                int i = 0;

                Vector2 cap0 = new Vector2(), cap1 = new Vector2();
                float r = 0f, t = 0f, d = 0f;
                MakeTrc(ref P[i], ref P[i + 1], ref T2, ref RR, ref cap1, weight[i], opt, ref r, ref t, ref d, true);
                if (varying_weight) {
                    MakeTrc(ref P[i], ref P[i + 1], ref T31, ref RR, ref cap0, weight[i + 1], opt, ref d, ref d, ref d, true);
                } else {
                    T31 = T2;
                }
                SL[i].djoint = opt.cap;
                SL[i].T = T2;
                SL[i].t = t;
                SL[i].r = r;
                SL[i].degenT = false;

                SL[i + 1].T1 = T31;
            }

            {
                int i = 1;

                float r = 0f, t = 0f;
                Vector2 P_cur = P[i]; //current point
                Vector2 P_nxt = P[i + 1]; //next point
                Vector2 P_las = P[i - 1]; //last point

                {
                    Vector2 cap0 = new Vector2(), bR = new Vector2();
                    float length_cur = 0f, length_nxt = 0f, d = 0f;
                    MakeTrc(ref P_las, ref P_cur, ref T1, ref RR, ref cap0, weight[i - 1], opt, ref d, ref d, ref length_cur, true);
                    if (varying_weight) {
                        MakeTrc(ref P_las, ref P_cur, ref T21, ref RR, ref cap0, weight[i], opt, ref d, ref d, ref d, true);
                    } else {
                        T21 = T1;
                    }

                    MakeTrc(ref P_cur, ref P_nxt, ref T2, ref RR, ref bR, weight[i], opt, ref r, ref t, ref length_nxt, true);
                    if (varying_weight) {
                        MakeTrc(ref P_cur, ref P_nxt, ref T31, ref RR, ref cap0, weight[i + 1], opt, ref d, ref d, ref d, true);
                    } else {
                        T31 = T2;
                    }

                    SL[i].T = T2;
                    SL[i].bR = bR;
                    SL[i].t = t;
                    SL[i].r = r;
                    SL[i].degenT = false;

                    SL[i + 1].T1 = T31;
                }

                {   //2nd point
                    //find the angle between the 2 line segments
                    Vector2 ln1 = new Vector2(), ln2 = new Vector2(), V = new Vector2();
                    ln1 = P_cur - P_las;
                    ln2 = P_nxt - P_cur;
                    Vec2Ext.Normalize(ref ln1);
                    Vec2Ext.Normalize(ref ln2);
                    Vec2Ext.Dot(ln1, ln2, ref V);
                    float cos_tho = V.x + V.y;
                    bool zero_degree = System.Math.Abs(cos_tho - 1.0f) < 0.0000001f;
                    bool d180_degree = cos_tho < -1.0f + 0.0001f;
                    bool intersection_fail = false;
                    int result3 = 1;

                    SL[i].djoint = opt.joint;
                    if (SL[i].djoint == Opt.PLJmiter) {
                        if (System.Math.Abs(cos_tho) >= cos_cri_angle) {
                            SL[i].djoint = Opt.PLJbevel;
                        }
                    }

                    Vec2Ext.AnchorOutward(ref T1, P_cur, P_nxt);
                    Vec2Ext.AnchorOutward(ref T21, P_cur, P_nxt);
                    Vec2Ext.FollowSigns(ref SL[i].T1, T21);
                    Vec2Ext.AnchorOutward(ref T2, P_cur, P_las);
                    Vec2Ext.FollowSigns(ref SL[i].T, T2);
                    Vec2Ext.AnchorOutward(ref T31, P_cur, P_las);

                    {   //must do intersection
                        Vector2 interP = new Vector2(), vP = new Vector2();
                        float[] pts = new float[2];
                        result3 = Vec2Ext.Intersect(
                            P_las + T1, P_cur + T21, P_nxt + T31, P_cur + T2, ref interP, pts);

                        if (result3 != 0) {
                            vP = interP - P_cur;
                            SL[i].vP = vP;
                            if (SL[i].djoint == Opt.PLJmiter) {
                                if (pts[0] > 2 || pts[1] > 2 || vP.Length() > 2 * SL[i].t) {
                                    SL[i].djoint = Opt.PLJbevel;
                                }
                            }
                        } else {
                            intersection_fail = true;
                            //Debug.Log(System.String.Format("intersection failed: cos(angle)={0}, angle={1} (degree)", cos_tho, System.Math.Acos(cos_tho) * 180 / 3.14159));
                        }
                    }

                    if (zero_degree || intersection_fail) {
                        Segment(SA, opt, capFirst, false, true);
                        SA.P[0] = SA.P[1];
                        SA.P[1] = SA.P[2];
                        SA.C[0] = SA.C[1];
                        SA.C[1] = SA.C[2];
                        SA.W[0] = SA.W[1];
                        SA.W[1] = SA.W[2];
                        Segment(SA, opt, false, capLast, true);
                        return;
                    }

                    Vec2Ext.Opposite(ref T1);
                    Vec2Ext.Opposite(ref T21);
                    Vec2Ext.Opposite(ref T2);
                    Vec2Ext.Opposite(ref T31);

                    //make intersections
                    Vector2 PT1 = new Vector2(), PT2 = new Vector2();
                    int result1t, result2t;
                    {
                        result1t = Vec2Ext.Intersect(
                            P_nxt - T31, P_nxt + T31, P_las + T1, P_cur + T21, //knife1_a
                            ref PT1); //core
                        result2t = Vec2Ext.Intersect(
                            P_las - T1, P_las + T1, P_nxt + T31, P_cur + T2, //knife2_a
                            ref PT2);
                    }
                    bool is_result1t = result1t == 1;
                    bool is_result2t = result2t == 1;

                    if (is_result1t | is_result2t) { //core degeneration
                        SL[i].degenT = true;
                        SL[i].preFull = is_result1t;
                        SL[i].PT = is_result1t ? PT1: PT2;
                    } else {
                        int result4;
                        result4 = Vec2Ext.Intersect(
                            P_nxt - T31, P_nxt + T31, P_las, P_cur,
                            ref PT1);
                        if (result4 == 1) {
                            SL[i].degenT = true;
                            SL[i].preFull = true;
                            SL[i].PT = PT1;
                        } else {
                            result4 = Vec2Ext.Intersect(
                                P_las - T1, P_las + T1, P_cur, P_nxt,
                                ref PT2);
                            if (result4 == 1) {
                                SL[i].degenT = true;
                                SL[i].preFull = false;
                                SL[i].PT = PT2;
                            }
                        }
                    }

                    if (d180_degree | result3 == 0) { //to solve visual bugs 3 and 1.1
                        SL[i].vP = SL[i].T;
                        Vec2Ext.FollowSigns(ref SL[i].T1, SL[i].T);
                        SL[i].djoint = Opt.PLJmiter;
                    }
                }
            }

            {
                int i = 2;

                Vector2 cap0 = new Vector2();
                float r = 0f, t = 0f, d = 0f;
                MakeTrc(ref P[i - 1], ref P[i], ref T2, ref RR, ref cap0, weight[i], opt, ref r, ref t, ref d, true);

                SL[i].djoint = opt.cap;
                SL[i].T = T2;
                SL[i].t = t;
                SL[i].r = r;
                SL[i].degenT = false;
            }

            AnchorLate(opt, P, C, SA.SL, SA.vah, capFirst, capLast);
            if (capFirst && SL[0].djoint != Opt.PLCbutt && SL[0].djoint != Opt.PLCnone) {
                Segment(SA, opt, true, false, false);
            }
            if (capLast && SL[1].djoint != Opt.PLCbutt && SL[1].djoint != Opt.PLCnone) {
                SA.P[0] = SA.P[1];
                SA.P[1] = SA.P[2];
                SA.C[0] = SA.C[1];
                SA.C[1] = SA.C[2];
                SA.W[0] = SA.W[1];
                SA.W[1] = SA.W[2];
                Segment(SA, opt, false, true, false);
            }
        } //Anchor

        private static void AnchorLate(
            Opt opt, Vector2[] P, Color[] C, StPolyline[] SL,
            VertexArrayHolder tris, bool capFirst, bool capLast)
        {
            Vector2 P_0 = P[0], P_1 = P[1], P_2 = P[2];
            Vector2 P0, P1, P2, P3, P4, P5, P6, P7;

            P0 = P_1 + SL[1].vP;
            P1 = P_1 - SL[1].vP;

            P2 = P_1 + SL[1].T1;
            P3 = P_0 + SL[0].T;
            P4 = P_0 - SL[0].T;

            P5 = P_1 + SL[1].T;
            P6 = P_2 + SL[2].T;
            P7 = P_2 - SL[2].T;

            int normal_line_core_joint = 1; //0:dont draw, 1:draw, 2:outer only
            float rr = SL[1].t / SL[1].r;
            float rc1 = 0, rc2 = 0;
            if (capFirst && SL[0].djoint == Opt.PLCbutt) {
                rc1 = (P_1 - P_0).Length() / (SL[0].r) / 2;
            }
            if (capLast && SL[2].djoint == Opt.PLCbutt) {
                rc2 = (P_2 - P_1).Length() / (SL[2].r) / 2;
            }

            if (SL[1].degenT) {
                P1 = SL[1].PT;
                tris.Push3(P1, P3, P2, C[1], C[0], C[1], 0, rr, 0); //fir seg
                tris.Push3(P1, P5, P6, C[1], C[1], C[2], 0, rr, 0); //las seg

                if (SL[1].preFull) {
                    tris.Push3(P3, P1, P4, C[0], C[1], C[0], 0, rr, 0);
                } else {
                    tris.Push3(P1, P6, P7, C[1], C[2], C[2], 0, 0, rr);
                }
            } else {
                // normal first segment
                tris.Push3(P2, P4, P3, C[1], C[0], C[0], 0, rc1, rr);
                tris.Push3(P4, P2, P1, C[0], C[1], C[1], 0, 0, rr);
                // normal last segment
                tris.Push3(P5, P7, P1, C[1], C[2], C[1], 0, rr, 0);
                tris.Push3(P7, P5, P6, C[2], C[1], C[2], 0, rr, rc2);
            }

            if (normal_line_core_joint != 0) {
                switch (SL[1].djoint) {
                case Opt.PLJmiter:
                    tris.Push3(P2, P0, P1, C[1], C[1], C[1], rr, 0, 0);
                    tris.Push3(P1, P0, P5, C[1], C[1], C[1], 0, rr, 0);
                    break;

                case Opt.PLJbevel:
                    if (normal_line_core_joint == 1) tris.Push3(P2, P5, P1, C[1], C[1], C[1], rr, 0, 0);
                    break;

                case Opt.PLJround:
                    {
                        VertexArrayHolder strip = new VertexArrayHolder();
                        strip.SetGlDrawMode(VertexArrayHolder.GL_TRIANGLE_STRIP);

                        if (normal_line_core_joint == 1) {
                            VectorsToArc(strip, P_1, C[1], C[1], SL[1].T1, SL[1].T, GetPljRoundDangle(SL[1].t, SL[1].r, opt.worldToScreenRatio), SL[1].t, 0.0f, false, P1, new Vector2(), rr, true);
                        } else if (normal_line_core_joint == 2) {
                            VectorsToArc(strip, P_1, C[1], C[1], SL[1].T1, SL[1].T, GetPljRoundDangle(SL[1].t, SL[1].r, opt.worldToScreenRatio), SL[1].t, 0.0f, false, P5, new Vector2(), rr, true);
                        }
                        tris.Push(strip);
                    }
                    break;
                }
            }
        } //AnchorLate

        private static void VectorsToArc(
            VertexArrayHolder hold, Vector2 P, Color C, Color C2,
            Vector2 PA, Vector2 PB, float dangle, float r, float r2,
            bool ignorEnds, Vector2 apparentP, Vector2 hint, float rr, bool innerFade)
        {
            // triangulate an inner arc between vectors A and B,
            // A and B are position vectors relative to P
            const float m_pi = (float) System.Math.PI;
            Vector2 A = PA * (1 / r);
            Vector2 B = PB * (1 / r);
            float rrr;
            if (innerFade) {
                rrr = 0;
            } else {
                rrr = -1;
            }

            float angle1 = (float) System.Math.Acos(A.x);
            float angle2 = (float) System.Math.Acos(B.x);
            if (A.y > 0) {
                angle1 = 2 * m_pi - angle1;
            }
            if (B.y > 0) {
                angle2 = 2 * m_pi - angle2;
            }
            if (!hint.IsZero()) {
                // special case when angle1 == angle2,
                //   have to determine which side by hint
                if (hint.x > 0 && hint.y == 0) {
                    angle1 -= (angle1 < angle2 ? 1 : -1) * 0.00001f;
                } else if (hint.x == 0 && hint.y > 0) {
                    angle1 -= (angle1 < angle2 ? 1 : -1) * 0.00001f;
                } else if (hint.x > 0 && hint.y > 0) {
                    angle1 -= (angle1 < angle2 ? 1 : -1) * 0.00001f;
                } else if (hint.x > 0 && hint.y < 0) {
                    angle1 -= (angle1 < angle2 ? 1 : -1) * 0.00001f;
                } else if (hint.x < 0 && hint.y > 0) {
                    angle1 += (angle1 < angle2 ? 1 : -1) * 0.00001f;
                } else if (hint.x < 0 && hint.y < 0) {
                    angle1 += (angle1 < angle2 ? 1 : -1) * 0.00001f;
                }
            }

            // (apparent center) center of fan
            //draw the inner arc between angle1 and angle2 with dangle at each step.
            // -the arc has thickness, r is the outer radius and r2 is the inner radius,
            //    with color C and C2 respectively.
            //    in case when inner radius r2=0.0f, it gives a pie.
            // -when ignorEnds=false, the two edges of the arc lie exactly on angle1
            //    and angle2. when ignorEnds=true, the two edges of the arc do not touch
            //    angle1 or angle2.
            // -P is the mathematical center of the arc.
            // -when use_apparent_P is true, r2 is ignored,
            //    apparentP is then the apparent origin of the pie.
            // -the result is pushed to hold, in form of a triangle strip
            // -an inner arc is an arc which is always shorter than or equal to a half circumference

            if (angle2 > angle1) {
                if (angle2 - angle1 > m_pi) {
                    angle2 = angle2 - 2 * m_pi;
                }
            }
            else {
                if (angle1 - angle2 > m_pi) {
                    angle1 = angle1 - 2 * m_pi;
                }
            }

            bool incremental = true;
            if (angle1 > angle2) {
                incremental = false;
            }

            if (incremental) {
                if (!ignorEnds) {
                    hold.Push(new Vector2(P.x + PB.x, P.y + PB.y), C, rr);
                    hold.Push(apparentP, C2, rrr);
                }
                for (float a = angle2 - dangle; a > angle1; a -= dangle) {
                    inner_arc_push(System.Math.Cos(a), System.Math.Sin(a));
                }
                if (!ignorEnds) {
                    hold.Push(new Vector2(P.x + PA.x, P.y + PA.y), C, rr);
                    hold.Push(apparentP, C2, rrr);
                }
            }
            else //decremental
            {
                if (!ignorEnds) {
                    hold.Push(apparentP, C2, rr);
                    hold.Push(new Vector2(P.x + PB.x, P.y + PB.y), C, rrr);
                }
                for (float a = angle2 + dangle; a < angle1; a += dangle) {
                    inner_arc_push(System.Math.Cos(a), System.Math.Sin(a), true);
                }
                if (!ignorEnds) {
                    hold.Push(apparentP, C2, rr);
                    hold.Push(new Vector2(P.x + PA.x, P.y + PA.y), C, rrr);
                }
            }

            void inner_arc_push(double x, double y, bool reverse = false) {
                Vector2 PP = new Vector2(P.x + (float) x * r, P.y - (float) y * r);
                //hold.Dot(PP, 0.05f); return;
                if (!reverse) {
                    hold.Push(PP, C, rr);
                    hold.Push(apparentP, C2, rrr);
                } else {
                    hold.Push(apparentP, C2, rr);
                    hold.Push(PP, C, rrr);
                }
            }
        }

        private static float GetPljRoundDangle(float t, float r, float scale)
        {
            float dangle;
            float sum = (t + r) * scale;
            if (sum <= 1.44f + 1.08f) { //w<=4.0, feathering=1.0
                dangle = 0.6f / sum;
            } else if (sum <= 3.25f + 1.08f) { //w<=6.5, feathering=1.0
                dangle = 2.8f / sum;
            } else {
                dangle = 4.2f / sum;
            }
            return dangle;
        }
    }
}

================================================
FILE: csharp/Assets/Vaser/Polyline.cs.meta
================================================
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================================================
FILE: csharp/Assets/Vaser/Vec2Ext.cs
================================================
using UnityEngine;

namespace Vaser
{
    public static class Vec2Ext
    {
        public static float Length(this Vector2 a)
        {
            return (float) System.Math.Sqrt(a.x*a.x+a.y*a.y);
        }
        public static float SignedArea(Vector2 P1, Vector2 P2, Vector2 P3)
        {
            return (P2.x-P1.x)*(P3.y-P1.y) - (P3.x-P1.x)*(P2.y-P1.y);
        }
        public static void Dot(Vector2 a, Vector2 b, ref Vector2 o) //dot product: o = a dot b
        {
            o.x = a.x * b.x;
            o.y = a.y * b.y;
        }
        public static void Opposite(ref Vector2 a)
        {
            a.x = -a.x;
            a.y = -a.y;
        }
        public static float Normalize(ref Vector2 a)
        {
            float L = a.Length();
            if (L > 0.0000001f)
            {
                a.x /= L;
                a.y /= L;
            }
            return L;
        }
        public static void Perpen(ref Vector2 a) //perpendicular: anti-clockwise 90 degrees
        {
            float y_value=a.y;
            a.y=a.x;
            a.x=-y_value;
        }
        public static void FollowSigns(ref Vector2 a, Vector2 b)
        {
            if ((a.x>0) != (b.x>0)) a.x = -a.x;
            if ((a.y>0) != (b.y>0)) a.y = -a.y;
        }

        //judgements
        public static bool Negligible(float M)
        {
            const float vaser_min_alw = 0.000000001f;
            return -vaser_min_alw < M && M < vaser_min_alw;
        }
        public static bool Negligible(double M)
        {
            const double vaser_min_alw = 0.0000000001;
            return -vaser_min_alw < M && M < vaser_min_alw;
        }
        public static bool Negligible(this Vector2 a)
        {
            return Negligible(a.x) && Negligible(a.y);
        }
        public static bool IsZero(this Vector2 a)
        {
            return a.x==0.0 && a.y==0.0;
        }
        public static bool Intersecting(Vector2 A, Vector2 B, Vector2 C, Vector2 D)
        {   //return true if AB intersects CD
            return SignedArea(A,B,C)>0 != SignedArea(A,B,D)>0;
        }
        public static bool OppositeQuadrant(Vector2 P1, Vector2 P2)
        {
            int P1x = P1.x>0? 1:(P1.x<0?-1:0);
            int P1y = P1.y>0? 1:(P1.y<0?-1:0);
            int P2x = P2.x>0? 1:(P2.x<0?-1:0);
            int P2y = P2.y>0? 1:(P2.y<0?-1:0);

            if (P1x != P2x) {
                if (P1y != P2y)
                    return true;
                if (P1y == 0 || P2y == 0) {
                    return true;
                }
            }
            if (P1y != P2y) {
                if (P1x == 0 || P2x == 0) {
                    return true;
                }
            }
            return false;
        }

        public static bool AnchorOutward(ref Vector2 V, Vector2 b, Vector2 c, bool reverse=false)
        {   //put the correct outward vector at V, with V placed on b, comparing distances from c
            bool determinant = (b.x*V.x - c.x*V.x + b.y*V.y - c.y*V.y) > 0;
            if (determinant == (!reverse)) {
                //when reverse==true, it means inward
                //positive V is the outward vector
                return false;
            } else {
                //negative V is the outward vector
                V.x=-V.x;
                V.y=-V.y;
                return true; //return whether V is changed
            }
        }

        public static int Intersect(
                Vector2 P1, Vector2 P2, //line 1
                Vector2 P3, Vector2 P4, //line 2
                ref Vector2 Pout,     //the output point
                float[] u_out = null)
        {   //Determine the intersection point of two line segments
            float mua, mub;
            double denom, numera, numerb;

            denom  = (P4.y-P3.y) * (P2.x-P1.x) - (P4.x-P3.x) * (P2.y-P1.y);
            numera = (P4.x-P3.x) * (P1.y-P3.y) - (P4.y-P3.y) * (P1.x-P3.x);
            numerb = (P2.x-P1.x) * (P1.y-P3.y) - (P2.y-P1.y) * (P1.x-P3.x);

            if (Negligible(numera) &&
                Negligible(numerb) &&
                Negligible(denom)) {
                Pout.x = (P1.x + P2.x) * 0.5f;
                Pout.y = (P1.y + P2.y) * 0.5f;
                return 2; //meaning the lines coincide
            }

            if (Negligible(denom)) {
                Pout.x = 0;
                Pout.y = 0;
                return 0; //meaning lines are parallel
            }

            mua = (float) (numera / denom);
            mub = (float) (numerb / denom);
            if (u_out != null) {
                u_out[0] = mua;
                u_out[1] = mub;
            }

            Pout.x = P1.x + mua * (P2.x - P1.x);
            Pout.y = P1.y + mua * (P2.y - P1.y);

            bool out1 = mua < 0 || mua > 1;
            bool out2 = mub < 0 || mub > 1;

            if (out1 & out2) {
                return 5; //the intersection lies outside both segments
            } else if (out1) {
                return 3; //the intersection lies outside segment 1
            } else if (out2) {
                return 4; //the intersection lies outside segment 2
            } else {
                return 1; //great
            }
            //http://paulbourke.net/geometry/lineline2d/
        }

        public static int Octant(this Vector2 a)
        {
            if (a.x == 0 && a.y == 0) {
                return 0;
            }
            if (a.x == 0) {
                return a.y > 0 ? 3 : 7;
            }
            if (a.y == 0) {
                return a.x > 0 ? 1 : 5;
            }
            if (a.x > 0 && a.y > 0) {
                if (a.y/a.x < 0.5f) {
                    return 1;
                } else if (a.y/a.x > 2f) {
                    return 3;
                } else {
                    return 2;
                }
            } else if (a.x < 0 && a.y > 0) {
                if (a.y/a.x < -2f) {
                    return 3;
                } else if (a.y/a.x > -0.5f) {
                    return 5;
                } else {
                    return 4;
                }
            } else if (a.x < 0 && a.y < 0) {
                if (a.y/a.x < 0.5f) {
                    return 5;
                } else if (a.y/a.x > 2f) {
                    return 7;
                } else {
                    return 6;
                }
            } else if (a.x > 0 && a.y < 0) {
                if (a.y/a.x < -2f) {
                    return 7;
                } else if (a.y/a.x > -0.5f) {
                    return 1;
                } else {
                    return 8;
                }
            }
            return 0;
        }
    }
}

================================================
FILE: csharp/Assets/Vaser/Vec2Ext.cs.meta
================================================
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================================================
FILE: csharp/Assets/Vaser/VertexArrayHolder.cs
================================================
using UnityEngine;
using System.Collections.Generic;

namespace Vaser
{
    public class VertexArrayHolder
    {
        public const int GL_POINTS = 1;
        public const int GL_LINES = 2;
        public const int GL_TRIANGLES = 3;
        public const int GL_LINE_STRIP = 4;
        public const int GL_LINE_LOOP = 5;
        public const int GL_TRIANGLE_STRIP = 6;
        public const int GL_TRIANGLE_FAN = 7;

        public int glmode = GL_TRIANGLES; //drawing mode in opengl
        private bool jumping = false;
        private List<Vector3> vert = new List<Vector3>();
        private List<Color> color = new List<Color>();
        private List<float> fade = new List<float>();

        public int GetCount()
        {
            return vert.Count;
        }

        public void SetGlDrawMode(int gl_draw_mode)
        {
            glmode = gl_draw_mode;
        }

        public int Push(Vector2 P, Color cc, float fade0=0)
        {
            int cur = vert.Count;
            vert.Add(P); // A Vector2 can be implicitly converted into a Vector3. (The z is set to zero in the result).
            color.Add(cc);
            fade.Add(fade0);

            if (jumping)
            {
                jumping = false;
                RepeatLastPush();
            }
            return cur;
        }

        public int PushF(Vector2 P, Color C)
        {
            C.a = 0;
            return Push(P, C);
        }

        public void Push3(
                Vector2 P1, Vector2 P2, Vector2 P3,
                Color C1, Color C2, Color C3,
                float fade1=0, float fade2=0, float fade3=0)
        {
            Push(P1, C1, fade1);
            Push(P2, C2, fade2);
            Push(P3, C3, fade3);
        }

        public void Push4(
            Vector2 P1, Vector2 P2, Vector2 P3, Vector2 P4, 
            Color C1, Color C2, Color C3, Color C4,
            float r1, float r2, float r3, float r4)
        {
            //interpret P0 to P3 as triangle strip
            Push3(P1, P2, P3, C1, C2, C3, r1, r2, r3);
            Push3(P3, P2, P4, C3, C2, C4, r3, r2, r4);
        }

        public void Dot(Vector2 P, float size)
        {
            size /= 2;
            if (glmode == GL_TRIANGLES) {
            } else if (glmode == GL_TRIANGLE_STRIP) {
                Push(new Vector2(P.x-size, P.y), Color.red);
                Push(new Vector2(P.x, P.y+size), Color.red);
                Push(new Vector2(P.x, P.y-size), Color.red);
                Push(new Vector2(P.x+size, P.y), Color.red);
                Jump();
            }
        }

        public void Push(VertexArrayHolder hold)
        {
            if (glmode == hold.glmode)
            {
                vert.AddRange(hold.vert);
                color.AddRange(hold.color);
                fade.AddRange(hold.fade);
            }
            else if (glmode == GL_TRIANGLES &&
                hold.glmode == GL_TRIANGLE_STRIP)
            {
                for (int b=3; b < hold.vert.Count; b+=2)
                {
                    vert.Add(hold.vert[b-3]); color.Add(hold.color[b-3]); fade.Add(hold.fade[b-0]);
                    vert.Add(hold.vert[b-2]); color.Add(hold.color[b-2]); fade.Add(hold.fade[b-0]);
                    vert.Add(hold.vert[b-1]); color.Add(hold.color[b-1]); fade.Add(hold.fade[b-1]);
                    vert.Add(hold.vert[b-1]); color.Add(hold.color[b-1]); fade.Add(hold.fade[b-0]);
                    vert.Add(hold.vert[b-2]); color.Add(hold.color[b-2]); fade.Add(hold.fade[b-1]);
                    vert.Add(hold.vert[b-0]); color.Add(hold.color[b-0]); fade.Add(hold.fade[b-0]);
                }
            }
        }

        public Vector2 Get(int i)
        {
            Vector2 P = new Vector2();
            P.x = vert[i].x;
            P.y = vert[i].y;
            return P;
        }

        public Color GetColor(int b)
        {
            return color[b];
        }

        public Vector2 GetRelativeEnd(int di = -1)
        {
            //di=-1 is the last one
            int count = vert.Count;
            int i = count+di;
            if (i<0) i=0;
            if (i>=count) i=count-1;
            return Get(i);
        }

        public void RepeatLastPush()
        {
            int i = vert.Count-1;
            Push(Get(i), GetColor(i));
        }

        public void Jump() //to make a jump in triangle strip by degenerated triangles
        {
            if (glmode == GL_TRIANGLE_STRIP)
            {
                RepeatLastPush();
                jumping = true;
            }
        }

        public List<Vector3> GetVertices()
        {
            return vert;
        }

        public List<int> GetTriangles()
        {
            List<int> indices = new List<int>();
            if (glmode == GL_TRIANGLES)
            {
                for (int i=0; i < vert.Count; i++)
                {
                    indices.Add(i);
                }
            }
            return indices;
        }

        public List<Vector4> GetUVs()
        {
            List<Vector4> uvs = new List<Vector4>();
            Vector4[] UVS = new Vector4[]
            {
                new Vector4(0, 0, 0, 0),
                new Vector4(1, 0, 0, 0),
                new Vector4(1, 1, 0, 0),
                new Vector4(0, 1, 0, 0),
                new Vector4(-1, 1, 0, 0),
                new Vector4(-1, 0, 0, 0),
                new Vector4(-1, -1, 0, 0),
                new Vector4(0, -1, 0, 0),
                new Vector4(1, -1, 0, 0),
                new Vector4(-1, 0, 0, 0),
            };

            if (glmode == GL_TRIANGLES)
            {
                for (int i=2; i < fade.Count; i+=3)
                {
                    int count = 0;
                    if (fade[i-2] > 0) count++;
                    if (fade[i-1] > 0) count++;
                    if (fade[i-0] > 0) count++;
                    if (count == 0) {
                        addUV(0, 1, 1);
                        addUV(0, 1, 1);
                        addUV(0, 1, 1);
                    } else if (count == 3) {
                        addUV(1, fade[i-2], fade[i-2]);
                        addUV(5, fade[i-1], fade[i-1]);
                        addUV(3, fade[i-0], fade[i-0]);
                    } else if (count == 2) {
                        float fadeX = 0, fadeY = 0;
                        for (int j=0; j<3; j++)
                        {
                            float fadeU = 0, fadeV = 0;
                            if (j == 0) {
                                fadeU = fade[i-2];
                                fadeV = fade[i-0];
                            } else if (j == 1) {
                                fadeU = fade[i-1];
                                fadeV = fade[i-2];
                            } else if (j == 2) {
                                fadeU = fade[i-0];
                                fadeV = fade[i-1];
                            }
                            if (fadeU > 0 && fadeV > 0) {
                                fadeX = fadeV;
                                fadeY = fadeU;
                            }
                        }
                        for (int j=0; j<3; j++)
                        {
                            float fadeU = 0, fadeV = 0;
                            if (j == 0) {
                                fadeU = fade[i-2];
                                fadeV = fade[i-0];
                            } else if (j == 1) {
                                fadeU = fade[i-1];
                                fadeV = fade[i-2];
                            } else if (j == 2) {
                                fadeU = fade[i-0];
                                fadeV = fade[i-1];
                            }
                            if (fadeU > 0 && fadeV > 0) {
                                //Debug.Log("fade both");
                                addUV(8, fadeX, fadeY);
                            } else if (fadeU > 0) {
                                //Debug.Log("fadeU");
                                addUV(2, fadeX, fadeY);
                            } else if (fadeV > 0) {
                                //Debug.Log("fadeV");
                                addUV(6, fadeX, fadeY);
                            }
                        }
                    } else if (count == 1 &&
                        fade[i-2] >= 0 && fade[i-1] >= 0 && fade[i-0] >= 0) {
                        float fadeU = 0;
                        float fadeV = 0;
                        for (int j=0; j<3; j++)
                        {
                            if (j == 0) {
                                fadeU = fade[i-2];
                                fadeV = fade[i-0];
                            } else if (j == 1) {
                                fadeU = fade[i-1];
                                fadeV = fade[i-2];
                            } else if (j == 2) {
                                fadeV = fade[i-1];
                                fadeU = fade[i-0];
                            }
                            if (fadeU > 0 || fadeV > 0) {
                                //Debug.Log("fade side");
                                float fader = fadeU > 0 ? fadeU : fadeV;
                                addUV(1, fader, fader);
                            } else {
                                //Debug.Log("corner fade");
                                float fader = fade[i-2] > 0 ? fade[i-2] : fade[i-1] > 0 ? fade[i-1] : fade[i-0];
                                addUV(5, fader, fader);
                            }
                        }
                    } else if (count == 1) {
                        // may be fade is < 0
                        float fadeU = 0;
                        float fadeV = 0;
                        for (int j=0; j<3; j++)
                        {
                            if (j == 0) {
                                fadeU = fade[i-2];
                                fadeV = fade[i-0];
                            } else if (j == 1) {
                                fadeU = fade[i-1];
                                fadeV = fade[i-2];
                            } else if (j == 2) {
                                fadeV = fade[i-1];
                                fadeU = fade[i-0];
                            }
                            if (fadeU > 0 || fadeV > 0) {
                                //Debug.Log("fan fade");
                                float fader = fadeU > 0 ? fadeU : fadeV;
                                addUV(9, fader, fader);
                            } else {
                                //Debug.Log("zero fade");
                                float fader = fade[i-2] > 0 ? fade[i-2] : fade[i-1] > 0 ? fade[i-1] : fade[i-0];
                                addUV(0, fader, fader);
                            }
                        }
                    }
                }
            }
            return uvs;

            void addUV(int i, float rx, float ry)
            {
                uvs.Add(new Vector4(UVS[i].x, UVS[i].y, rx, ry));
            }
        }

        public List<Color> GetColors()
        {
            return color;
        }
    }
}


================================================
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================================================
FILE: csharp/Docs/README.md
================================================
![Screenshot](Screenshot%20at%202019-10-23%2021-04-21.png)
![Screenshot](Screenshot%20at%202019-10-29%2015-48-55.png)
![Screenshot](Screenshot%20at%202019-10-30%2000-13-05.png)
![Screenshot](Screenshot%20at%202019-11-10%2002-48-59.png)
![Screenshot](Screenshot%20at%202019-12-02%2000-44-00.png)
![Screenshot](Screenshot%20at%202019-12-02%2004-27-00.png)
![Screenshot](Screenshot%20at%202019-12-07%2023-56-00.png)
![Screenshot](Screenshot%20at%202019-12-08%2022-44-00.png)
![Screenshot](Screenshot%20at%202019-12-11%2001-11-10.png)
![Screenshot](Screenshot%20at%202019-12-15%2003-31-00.png)
![Screenshot](Screenshot%20at%202019-12-15%2003-57-00.png)

================================================
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FILE: csharp/README.md
================================================
# Vaser Unity

Vaser Unity is a continuation of [VASE renderer](https://github.com/tyt2y3/vaserenderer), reimplementing the original C++ algorithm in C# while taking advantage of fragment shader to reduce triangle count. A major difference is that "feathering" no longer requires extra vertices. So the following patch requires only 4 vertices (instead of 8 in the C++ version):

![Screenshort](Docs/Screenshot%20at%202019-12-02%2000-44-00.png)

More screenshots:

![Screenshot](Docs/Screenshot%20at%202019-12-11%2001-11-10.png)
![Screenshot](Docs/Screenshot%20at%202019-12-15%2003-31-00.png)
![Screenshot](Docs/Screenshot%20at%202019-12-30%2017-36-00.png)

## Features

- Per vertex coloring and weighting
- Linear gradient along curve
- Brush-like feathering effects
- Premium quality anti-aliasing
- Various caps and joints

More screenshots can be found under [Docs](Docs).

## Status

Current implementation is still experimental, may be buggy and the API is subject to change. While this library can be used standalone, it may eventually be integrated into a larger framework.


================================================
FILE: docs/API.html
================================================
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<head>
	<link rel="stylesheet" type="text/css" href="style.css" />
</head>
<body>
	<div class='vaser_wrap'>
		<div class='bar'>VASEr: better stroke rendering</div>
		<div class='article_name'>
			<h2>VASEr API reference</h2>
		</div>
	<h2>Overview</h2>
		<h3>API design</h3>
<p>VASEr functions have no state, all stateful operations are put into the class <code>renderer</code>. Thus you need to pass many parameters on each VASEr call, and these parameters are stored in structures. Normally if you do not know what options to set, just put <code>0</code> at the parameter <code>polyline_opt*</code>. VASEr ensures empty parameter <code>polyline_opt* options=0</code> <b>and</b> empty structure <code>polyline_opt opt={0};</code> are default options and will not cause any error.
</p>
		<h3>Index</h3>
<div class='textblock'>
	class<br>
	<a href='#renderer'>renderer</a><br>
	structures<br>
	<a href='#gradient'>gradient</a><br>
	<a href='#image'>Image</a><br>
	<a href='#tessellator_opt'>tessellator_opt</a><br>
	<a href='#polyline'>polyline_opt</a><br>
	<a href='#polybezier'>polybezier_opt</a><br>
	functions<br>
	<a href='#polyline'>polyline</a><br>
	<a href='#segment'>segment</a><br>
	<a href='#polybezier'>polybezier</a><br>
</div>

	<h2>Details</h2>
<table class='api_table' style='width:100%;'>

	<tr><td>
	<a name='renderer'></a><h3>class renderer</h3>
<pre>
class renderer
{
public:
	static void init();
	static void before();
	static void after();
	static Image get_image();
};
</pre>
	<p>As stated, all stateful operations are put into the class <code>renderer</code>. <code>init()</code> is intended to set up shaders etc. When calling <code>init()</code>, the open gl context is assumed to be set up by the user already. Call <code>renderer::before()</code> and <code>renderer::after()</code> before and after rendering. For more information, look at <a href='getting_started.html'>getting started</a>.</p>
	<p><code>get_image()</code> captures an image of the current render context, in rgba 32 bit format. the (x,y) pixel (r,g,b,a) is at <code>(image.buf[y*w*b+x*b],image.buf[y*w*b+x*b+1],image.buf[y*w*b+x*b+2],image.buf[y*w*b+x*b+3])</code>, where b=4 and w=image.width.</p>
	</td></tr><!--renderer-->

	<tr><td>
	<a name='gradient'></a><h3>struct gradient</h3>
<pre>
struct gradient_stop
{
	double t; //position
	char type; //GS_xx
	union
	{
		Color color;
		double weight;
	};
};
	const char GS_none  =0;
	const char GS_rgba  =1;
	const char GS_rgb   =2; //rgb only
	const char GS_alpha =3;
	const char GS_weight=4;
struct gradient
{
	gradient_stop* stops; //array must be sorted in ascending order of t
	int length; //number of stops
	char unit; //use_GD_XX
};
	const char GD_ratio =0; //default
	const char GD_length=1;
</pre>
<p>A gradient is an array of stops that specify properties at different positions in a one dimensional space. The properties can be color or weight, and the space parameter (unit) can be the length along a curve. The default parameter is ratio, that frankly speaking t=0.5 is midway along the curve.</p>
<p>Be aware of the union, which means each stop can only hold one type of information, which must be explicitly specified by <code>gradient_stop.type</code>. If the type is unspecified, the stop is ignored.</p>
<p>Stops of each type must be sorted in ascending order of t, but it is okay for say stops of weight come after stops of color. If there is only one stop of a type, then it is considered constant everywhere. If there is no stop of a type, then no change will be applied.</p>
<p>For a concrete example, look at <a href='#polybezier'>polybezier</a>.</p>
	</td></tr><!--gradient-->

	<tr><td>
	<a name='image'></a><h3>struct Image</h3>
<pre>
struct Image
{
	unsigned char* buf; //must **free** buffer manually
	short width;
	short height;
};
</pre>
	the <code>unsigned char* buf</code> must be freed manually as in malloc/free
	</td></tr><!--Image-->

	<tr><td>
	<a name='tessellator_opt'></a><h3>struct tessellator_opt</h3>
<pre>
struct tessellator_opt
{
	//set the whole structure to 0 will give default options
	bool triangulation;
	char parts; //use TS_xx
	bool tessellate_only;
	void* holder; //used as (VASErin::vertex_array_holder*) if tessellate_only is true
};
	//for tessellator_opt.parts
	const char TS_core_fade =0; //default
	const char TS_core      =1;
	const char TS_outer_fade=2;
	const char TS_inner_fade=3;
</pre>
<p>a <code>polyline_opt</code> contains a pointer to <code>tessellator_opt</code> which can be used to control tessellating behavior. in this version, <code>parts</code> is unimplemented. if you don't need this control,, setting <code>polyline_opt.tess</code> to zero pointer is okay.</p>
	</td></tr><!--tessellator_opt-->

	<tr><td>
	<a name='polyline'></a><h3>polyline()</h3>
<pre lang="C++">void polyline(
	Vec2* P,       //array of point of a polyline
	Color* C,      //array of color
	double* weight,//array of weight
	int length,    //length of the array
	polyline_opt* options) //extra options
</pre>
	All arrays must be of the same size otherwise memory error will occur.<br>
	There are 3 other variants if you do not need varying color or weight.
<pre lang="C++">
//constant color and weight
void polyline( const Vec2*, Color, double W, int length, const polyline_opt*);
//constant weight
void polyline( const Vec2*, const Color*, double W, int length, const polyline_opt*);
//constant color
void polyline( const Vec2*, Color, const double* W, int length, const polyline_opt*);
</pre>

	<h4>Options</h4>
<pre lang="C++">
struct polyline_opt
{
	//set the whole structure to 0 will give default options
	const tessellator_opt* tess;
	char joint; //use PLJ_xx
	char cap;   //use PLC_xx
	bool feather;
		double feathering;
		bool no_feather_at_cap;
		bool no_feather_at_core;
};
	//for polyline_opt.joint
	const char PLJ_miter =0; //default
	const char PLJ_bevel =1;
	const char PLJ_round =2;
	//for polyline_opt.cap
	const char PLC_butt  =0; //default
	const char PLC_round =1;
	const char PLC_square=2;
	const char PLC_rect  =3;
	const char PLC_both  =0; //default
	const char PLC_first =10;
	const char PLC_last  =20;
	const char PLC_none  =30;
</pre>
	
	<code>
		<table>
			<caption>opt.joint</caption>
			<tr><td>PLJ_miter<br><img src='sample_images/PLJ_miter.png' /></td>
				<td>PLJ_bevel<br><img src='sample_images/PLJ_bevel.png' /></td>
				<td>PLJ_round<br><img src='sample_images/PLJ_round.png' /></td>
			</tr>
		</table>
		<br>
		<table>
			<caption>opt.cap</caption>
			<tr><td>PLC_butt<br><img src='sample_images/PLC_butt.png' /></td>
				<td>PLC_round<br><img src='sample_images/PLC_round.png' /></td>
				<td>PLC_square<br><img src='sample_images/PLC_square.png' /></td>
			</tr>
			<tr><td colspan=3 style='text-align:left;'>PLC_rect<br>
				PLC_rect is related to feathering. PLC_rect puts the fade polygon out of the end points of a polyline.<br>When feather=false, PLC_rect looks very close to PLC_butt. The difference is only obvious at high value of feathering.
				</td>
			</tr>
			<tr>
				<td>PLC_rect<br><img src='sample_images/PLC_rect.png' /></td>
				<td colspan=2>PLC_butt<br><img src='sample_images/PLC_butt_high_feathering.png' /></td>
			</tr>
			<tr><td colspan=3 style='text-align:left;'>There are modifiers and can be numerically added together to the value to control rendering of cap parts. it is necessary if you need to join segments yourself.</td>
			</tr>
			<tr><td>PLC_butt+PLC_both<br><img src='sample_images/PLC_both.png' /></td>
				<td>PLC_butt+PLC_first<br><img src='sample_images/PLC_first.png' /></td>
				<td>PLC_butt+PLC_none<br><img src='sample_images/PLC_none.png' /></td>
			</tr>
		</table>
		<br>
		<table>
			<caption>opt.feather, opt.feathering, opt.no_feather_at_cap, opt.no_feather_at_core</caption>
			<tr><td style='text-align:left;'>feathering is a multiplier to the magnitude of the outset-fade polygon. do not set it to lower than 1.0 .<br>
			feathering is unique to VASEr. A feathered polyline with round cap and round joint can mimic the feel of an air brush stroke.
			</td>
			<td><img src='sample_images/PL_mimic_airbrush.png'/></td>
		</tr>
		</table>
		<table>
			<tr>	
				<td>opt.feather = false;<br><img src='sample_images/PLJ_miter.png' /></td>
				
				<td>opt.feather = true;<br>opt.feathering = 8.0;<br>
				<img src='sample_images/PL_feathering_8.png' />
				</td>
			</tr>
			<tr>
				<td>opt.feather = true;<br>
				opt.feathering = 8.0;<br>
				opt.no_feather_at_cap = true;<br>
				opt.no_feather_at_core = false;<br>
				<img src='sample_images/PL_no_feather_at_cap.png' />
				</td>
				
				<td>opt.feather = true;<br>
				opt.feathering = 8.0;<br>
				opt.no_feather_at_cap = false;<br>
				opt.no_feather_at_core = true;<br>
				<img src='sample_images/PL_no_feather_at_core.png' />
				</td>
			</tr>
			<tr><td colspan=2>
				remarks: no_feather_at_cap only affects cap type PLC_butt,
				PLC_square and PLC_rect .
				</td>
			</tr>
		</table>
		<br>
	</code>

		<h4>Usage</h4>
	<div style='float:right'>
	<img src='sample_images/polyline_4.png' /><br>
	<img src='sample_images/polyline_3.png' />
	</div>
	<pre lang="C++">
void sample_polyline1()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color col={ 0.5, 0.8, 1.0, 1};
	polyline( AP, col, 8.0, size_of_AP, 0);
}
void sample_polyline2()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color AC[size_of_AP];
		{ Color col={1 , 0, 0, 0.5}; AC[0]=col;}
		{ Color col={.8,.8, 0, 0.5}; AC[1]=col;}
		{ Color col={ 0, 0, 1, 0.5}; AC[2]=col;}
		{ Color col={1 , 0, 0, 0.5}; AC[3]=col;}
	double AW[size_of_AP];
		AW[0] = 1.0;
		AW[1] = 15.0;
		AW[2] = 15.0;
		AW[3] = 1.0;
	
	polyline_opt opt={0};
	polyline( AP, AC, AW, size_of_AP, &opt);
}
</pre>
	<div style='clear:both'></div>

example program is at <code>samples/samples.cpp</code> under VASEr package.

		<h4>Notes</h4>
Varying color is stable but will cause overdraw at degenerated cases.<br>
Varying weight is stable most of the time but will go wild when extreme case occur.<br>
This version of polyline is improved to render dense vertices for curves.<br>

		<h4>Further work</h4>
After solving the above mentioned problems, can provide the choice between color blending profiles, possibly 'hard' and 'soft'. and besides gradient, provide texture along path.
	</td></tr><!--polyline-->
	
	<tr><td>
		<a name='segment'></a><h3>segment()</h3>
		<pre lang="C++">
void segment( Vec2,  Vec2,
              Color, Color,
              double, double, //weight
              const polyline_opt*); //same use as polyline
void segment( Vec2, Vec2, Color, double W, const polyline_opt*); //constant color and weight
void segment( Vec2, Vec2, Color, Color, double W, const polyline_opt*); //constant weight
void segment( Vec2, Vec2, Color, double W1, double W2, const polyline_opt*); //const color
</pre>
	<code>segment()</code> is merely a wrapper over <code>polyline()</code>. There are also three variants.
			<h4>Usage</h4>
			<pre lang="C++">
void sample_spectrum()
{
	for ( int i=0; i < 20; i++)
	{
		Vec2  P1 = { 5+29.7*i, 187};
		Vec2  P2 = { 35+29.7*i, 8};
		Color C1 = { 1.0,0.0,0.5, 1.0};
		Color C2 = { 0.5,0.0,1.0, 1.0};
		double W1= 0.3*(i+1);
		double W2= W1;
		
		segment(P1,P2, C1,C2, W1,W2, 0);
	}
}

void sample_radial_spectrum()
{
	for ( double ag=0, i=0; ag < 2*vaser_pi-0.1; ag+=vaser_pi/12, i+=1)
	{
		double r1 = 30.0;
		double r2 = 90.0;
		
		double tx2=r2*cos(ag);
		double ty2=r2*sin(ag);
		double tx1=r1*cos(ag);
		double ty1=r1*sin(ag);
		double Ox = 120;
		double Oy = 194+97;
		
		Vec2  P1 = { Ox+tx1,Oy-ty1};
		Vec2  P2 = { Ox+tx2,Oy-ty2};
		Color C1 = { 1.0,0.0,0.5, 1.0};
		Color C2 = { 0.5,0.0,1.0, 1.0};
		double W1= 0.3*(i+1);
		double W2= W1;
		
		segment(P1,P2, C1,C2, W1,W2, 0);
	}
}
</pre>
	example program is at <code>samples/samples.cpp<</code> under VASEr package. In the below spectrums, each segment is 0.3 pixel heavier than the previous segment, demonstrating sub pixel accuracy and anti aliasing quality of VASEr.
	<img src='sample_images/segment.png'/>
	</td></tr><!--segment-->
	
	<tr><td>
	<a name='polybezier'></a><h3>polybezier()</h3>
	<pre>
void polybezier( const Vec2* P, const gradient*, int length, const polybezier_opt*);
void polybezier( const Vec2* P, Color, double W, int length, const polybezier_opt*);
	</pre>
The <code></code> <code>P</code> is an array of control points. The evaluated curve is continuous, with adjacent bezier sections sharing a common control point. so n cubic bezier sections require 3n+1 points. A pointer to <a href='#gradient'>gradient</a> or constant color and width can be passed in.
		<h4>Options</h4>
<pre>
struct polybezier_opt
{
	//set the whole structure to 0 will give default options
	const polyline_opt* poly;
};
</pre>
Under the hood, bezier curves will be evaluated, and the set of points will be sent to <code>polyline()</code> for rendering, using <code>const polyline_opt* poly</code> as options if specified.
		<h4>Usage</h4>
	<div style='float:right'>
	<img src='sample_images/bezier_3.png' /><br>
	<img src='sample_images/bezier_4.png' />
	</div>
	<pre>
void sample_bezier1()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color col={ 0.5, 0.8, 1.0, 1};
	polybezier( AP, col, 12.0, size_of_AP, 0);
}
void sample_bezier2()
{
	int size_of_AP=4;
	Vec2 AP[size_of_AP];
		AP[0].x=200; AP[0].y=50;
		AP[1].x=100; AP[1].y=150;
		AP[2].x=300; AP[2].y=150;
		AP[3].x=200; AP[3].y=250;
	Color AC[size_of_AP];
		{ Color col={1 , 0, 0, 0.5}; AC[0]=col;}
		{ Color col={.8,.8, 0, 0.5}; AC[1]=col;}
		{ Color col={ 0, 0, 1, 0.5}; AC[2]=col;}
		{ Color col={1 , 0, 0, 0.5}; AC[3]=col;}
	double AW[size_of_AP];
		AW[0] = 1.0;
		AW[1] = 15.0;
		AW[2] = 15.0;
		AW[3] = 1.0;
	gradient grad = {0};
		gradient_stop stop[10] = {0};
		grad.stops = stop;
		grad.length = 10;
		stop[0].t = 0.00; stop[0].type = GS_rgba; stop[0].color = AC[0];
		stop[1].t = 0.50; stop[1].type = GS_rgba; stop[1].color = AC[2];
		stop[2].t = 1.00; stop[2].type = GS_rgba; stop[2].color = AC[3];
		stop[3].t = 0.00; stop[3].type = GS_weight; stop[3].weight = AW[0];
		stop[4].t = 0.33; stop[4].type = GS_weight; stop[4].weight = AW[1];
		stop[5].t = 0.66; stop[5].type = GS_weight; stop[5].weight = AW[2];
		stop[6].t = 1.00; stop[6].type = GS_weight; stop[6].weight = AW[3];
	polybezier( AP, &grad, size_of_AP, 0);
}
</pre>
	<div style='clear:both'></div>
Again, example program is at <code>samples/samples.cpp</code>.
	</td></tr><!--polybezier-->
	
	<tr><td>
	<a name='template'></a><h3></h3>
	</td></tr><!--template-->

</table><!--table of API-->
</body>


================================================
FILE: docs/getting_started.html
================================================
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<head>
	<link rel="stylesheet" type="text/css" href="style.css" />
</head>
<body>
	<div class='vaser_wrap'>
		<div class='bar'>VASEr: better stroke rendering</div>
		<div class='article_name'>
			<h2>VASEr getting started</h2>
		</div>
	<h3>The role of a renderer</h3>
<p>To use VASEr properly, you need to understand what role does VASEr play in the rendering pipeline. Suppose your application has a 2D rendering pipeline like:
</p>

<table>
<tr><td>transformation</td></tr>
<tr><td>clipping</td></tr>
<tr class='box_redlight'>
	<td>primitives generation<br>
		<code>glDrawArrays();</code>
		or
		<code>glBegin(); glEnd();</code>
	</td>
</tr>
<tr><td>composition</td></tr>
</table>

<p>VASEr merely takes care the primitives generation part (redlighted). Call <code>renderer::before()</code> and <code>renderer::after()</code> before and after rendering. VASEr API is namespaced <code>VASEr</code>.
</p>

<div class='box_tips'>
Example: <a onclick='box_tips_switchsize(this)'>hide</a><br>
How to correctly set gl states for VASEr..
<p>Suppose you have a helloworld application that only renders a line segment in draw():</p>
<pre lang="C++">
void draw()
{
	glMatrixMode(GL_PROJECTION);
	glPushMatrix();
		glLoadIdentity();
		glOrtho( 0,context_width,context_height,0,0.0f,100.0f);
		<b>glLineWidth(2.0);
		glBegin(GL_LINES);
			glColor4f(1,0,0.5, 1);
			glVertex2f(10,100);
			glColor4f(0.5,0,1, 1);
			glVertex2f(100,300);
		glEnd();
		//other drawings</b>
	glMatrixMode(GL_PROJECTION);
	glPopMatrix();
}</pre>
then change to:
<pre lang="C++">
void draw()
{
	<b>using namespace VASEr;</b>
	glMatrixMode(GL_PROJECTION);
	glPushMatrix();
		glLoadIdentity();
		glOrtho( 0,context_width,context_height,0,0.0f,100.0f);
		<b>renderer::before();
			{	Vec2  P1 = {10,100};
				Vec2  P2 = {100,300};
				Color C1 = {1,0,0.5, 1};
				Color C2 = {0.5,0,1, 1};
				double W1= 2.0;
				double W2= W1;
				segment(P1,P2, C1,C2, W1,W2, 0);
			}
			//other VASEr renderings
		renderer::after();</b>
	glMatrixMode(GL_PROJECTION);
	glPopMatrix();
}</pre>
</div> <!--class='box_tips' -->

	<h3>include and compile</h3>
<p>Provide these structs to VASEr <b>before</b> include by:</p>
<pre lang="C++">
namespace VASEr
{
	struct Vec2 { double x,y;};
	struct Color { float r,g,b,a;};
} </pre>
<b>or</b>
<pre lang="C++">
namespace VASEr
{
	typedef your_vec2 Vec2;
	typedef your_color Color;
} </pre>
<p>then <code>#include "vaser.h"</code>. There is only one file to compile, <code>vaser.cpp</code>. It is a unity build; no make file, no hassle. Alternatively, <code>#include "vaser.cpp"</code> just works, because implementation is namespaced in <code>VASErin</code> to prevent collision.</p>
<p>defining a Vec2 with <code>float</code> precision may work but may lead to undesirable precision lost, because internally VASEr use <code>double</code> for floating point operations.</p>
<script>
/*
(function()
{	//init
	var tips_list = document.getElementsByClassName('box_tips');
	for ( var i=0; i<tips_list.length; i++)
	{
		var a_list = tips_list[i].getElementsByTagName('a');
		if ( a_list.length > 0)
		{
			var instr = a_list[0].innerHTML;
			if ( instr.length==4)
				if ( instr=='hide')
					box_tips_switchsize( a_list[0]);
		}
	}
}());*/
function box_tips_switchsize(obj)
{
	if ( obj.innerHTML=='show')
	{	//show the box tips
		obj.parentNode.style.height='auto';
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	}
	else
	{	//hide it
		obj.parentNode.style.height='140px';
		obj.innerHTML='show';
	}
}
</script>
</body>


================================================
FILE: docs/index.html
================================================
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<head>
	<title>VASE renderer: better stroke rendering</title>
	<link rel="stylesheet" type="text/css" href="style.css" />
</head>
<body>
	<div class='vaser_wrap'>
		<div class='bar'>VASEr: better stroke rendering</div>
		<div class='article_name'>
			<h1>VASE<span style='line-height:40px;'> renderer</span></h1>
		</div>
<h2>About</h2>
<p>VASE renderer version 0.42 (VASEr 0.42) is a tessellating library for rendering high quality vector graphics. It is an attempt to address unconventional features in 2d graphics. It is intended for OpenGL 1.1+, but much of the code is API independent C++.</p>
 
<h2>Unconventional features</h2>
	<h3>Per vertex coloring and weighting</h3>
<div style='position:relative; overflow:hidden; height:220px; float:left;'><img style='position:relative; top:-40px;' src='sample_images/polyline_3.png' /></div>
<br><br>VASEr revolutionarily lets you control the color and thickness at each vertex for a polyline. This feature is unseen on any commonly available graphics library.
	<div style='clear:both'></div>

	<h3>Linear gradient along curve</h3>
<div style='position:relative; overflow:hidden; height:200px; float:right;'><img style='position:relative; top:-60px;' src='sample_images/bezier_2.png' /></div>
<br>A similar feature is also available to curves. Because there are so many vertices on a curve that it is impractical to specify data on each point, VASEr lets you define a linear gradient of color and thickness along the length of a curve, giving you two more degrees of expressive freedom.
	<div style='clear:both'></div>

	<h3>Feathering for brush like effects</h3>
<img src='sample_images/bezier_3.png' style='float:left;' />
<img src='sample_images/bezier_4.png' style='float:left;' />
<img src='sample_images/bezier_5.png' style='float:left;' />
<br>VASEr must use an outsetting polygon anyway, so it is free (as in computational cost) to scale it up, and it is called feathering in VASEr.
	<div style='clear:both'></div>

	<h3>Premium quality anti aliasing</h3>
	<div style='background:#333; margin: 10px; border:5px solid #AAA; float:left; height: 150px; overflow:hidden;'>
	<img src='sample_images/fade_intro_1.png' />
	<img src='sample_images/fade_intro_2.png' />
	<img src='sample_images/fade_intro_3.png' />
	<img src='sample_images/fade_intro_4.png' />
	</div>
<br><br>From left to right: raw polygon without anti aliasing, <br>
anti aliased with outset fade polygon, <br>
exaggerated outsetting polygon with wireframe, <br>
same as left without wireframe.
	<div style='clear:both'></div>
<p>Outset-fade polygon is the high quality, fast, portable, consistent and hassle free technique for anti aliasing. The difficulties are to calibrate the outsetting distance to achieve believable result and to perform tedious tessellation. Luckily VASEr did this for you.</p>
<p>Below are line rendering comparison between VASEr and Cairo, click flip to compare:</p>
<div>
	<div id='ab_va'>VASEr<br><img src='sample_images/ab_vaser_line_thickness1.png' /></div>
	<div id='ab_ca' style='display:none;'>Cairo<br><img src='sample_images/ab_cairo_line_thickness.png' /></div>
	<button onclick="
	if ( !document.getElementById('ab_va').style.display) {
	document.getElementById('ab_va').style.display='none';
	document.getElementById('ab_ca').style.display='';
	} else {
	document.getElementById('ab_va').style.display='';
	document.getElementById('ab_ca').style.display='none';
	}
	" style="width: 606px;">flip</button>
</div>
<p>between VASEr and AGG:</p>
<div>
	<div id='a_va'>VASEr<br><img src='sample_images/a_vaser_line_thickness.png' /></div>
	<div id='a_agg' style='display:none;'>AGG<br><img src='sample_images/agg_line_thickness.png' /></div>
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<p>There is small difference, but it is more a matter of taste than correctness. In terms of clarity VASEr is like between Cairo and AGG, and VASEr is the most crisp among the three. VASEr even do pixel alignment to 1px completely horizontal or vertical lines.</p>
<p>The flaw is, because the outsetting distance is resolution dependent, while the triangulation is unaffected under rotational transformation, fidelity will be lost under scale and sheer.</p>

	<h3>Performant</h3>
<div style='position:relative; overflow:hidden; width:300px; height:250px; float:left;'><img style='position:relative; top:-20px; left:-50px;' src='sample_images/polyline_5.png' /></div>
<p>VASEr is for real time rendering. Tessellation is done on CPU and the triangles are then sent off to GPU for rasterization. VASEr is fast regardless of the rendering resolution.</p>
<p>Can tessellation be accelerated by GPU? Probably, but I have no plan to do so. The performance enhancement strategy of VASEr is adaptation, that means doing expensive joint processing only when necessary and unperceivablely switch to approximation for thin lines and curves. The decision requires some global information and result in lots of branching, which makes it harder to write GPU programs. But after all, correctness is the first priority and performance is the last.</p>
	<div style='clear:both'></div>

<h2>"Next generation" 2d graphics?</h2>
<p>Q: Who needs "Per vertex coloring and weighting", "Linear gradient along curve" or "Feathering for brush like effects" in vector graphics? A: Same answer as "who needs typesetting and beautiful fonts on their computers?".</p>
<p>Q: These effects can be achieved by vector graphics package XXX using tool AAA then effect BBB, so who needs VASE renderer? A: Arguably true. But the fundamental change is <b>making vertex a three dimensional entity</b> (position, color, weight), and to <b>supercharge the intrinsic properties of strokes</b>. The idea is, it should be <i>natural</i> to apply colors and thickness to a stroke.</p>

<h2>Status</h2>
<p>VASEr is production ready for conventional use. The unconventional features are largely usable for normal circumstances, but may have defects at extreme cases. In particular, varying thickness is undesirable at acute angles and when weight difference is large. So it is not bullet proof yet. The tessellation code is tediously written for each point for each triangle for each circumstance, because a general outsetting and tessellating algorithm is doomed to be slow.</p>
<p>Currently VASEr is only a programming library and is not used in any vector graphics tool. I do have a plan (a plan only) to develop associated tools.</p>
<p>VASEr is not (yet) a general purpose graphics library like Cairo, its feature is still very limited. It has been developed slowly over the years. I always wanted to develop VASEr into a general purpose graphics library, but just do not have the time. It takes more effort than you may think to develop a rendering routine. Any comment, bug report or patch is greatly appreciated. In any case, sending me any form of encouragement (e.g. great work, thank you, donation) will help.</p>

<h2>Documentation</h2>
<div class='textblock'>
	<a href='getting_started.html'>getting started</a><br>
	<a href='API.html'>API reference</a><br>
	Articles<br>
	<a href='http://artgrammer.blogspot.com/2011/07/drawing-polylines-by-tessellation.html' target='_blank'>Drawing polylines by tessellation.</a><br>
	<a href='http://artgrammer.blogspot.hk/2011/05/drawing-nearly-perfect-2d-line-segments.html'>Drawing nearly perfect 2D line segments in OpenGL</a>
</div>

<h2>Source code</h2>
<p><a href='https://github.com/tyt2y3/vaserenderer'>Package with documentation, source code, sample images and sample programs is on github</a>. Comments, discussions, and contributions are greatly appreciated. You can reach me via email or on github.</p>

<h2>License</h2>

<p>VASE renderer version 0.42 (VASEr 0.42) is licensed under The 3-Clause BSD License.</p>
<p>Copyright (2011-2016) Tsang Hao Fung (Chris Tsang) tyt2y3@gmail.com</p>
<p>Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:</p>

<p>1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.</p>

<p>2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.</p>

<p>3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.</p>

<p>THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</p>

<p>Bezier curve subdivision code is extracted from Anti-Grain Geometry V2.4 Copyright 2002-2005 Maxim Shemanarev (McSeem) [Modified BSD License]</p>

	</div> <!--<div id='wrap'>-->
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