Source: src/pixi/utils/Polyk.js

/*
    PolyK library
    url: http://polyk.ivank.net
    Released under MIT licence.

    Copyright (c) 2012 Ivan Kuckir

    Permission is hereby granted, free of charge, to any person
    obtaining a copy of this software and associated documentation
    files (the "Software"), to deal in the Software without
    restriction, including without limitation the rights to use,
    copy, modify, merge, publish, distribute, sublicense, and/or sell
    copies of the Software, and to permit persons to whom the
    Software is furnished to do so, subject to the following
    conditions:

    The above copyright notice and this permission notice shall be
    included in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
    OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
    HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
    WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
    OTHER DEALINGS IN THE SOFTWARE.

    This is an amazing lib!

    Slightly modified by Mat Groves (matgroves.com);
*/

/**
 * Based on the Polyk library http://polyk.ivank.net released under MIT licence.
 * This is an amazing lib!
 * Slightly modified by Mat Groves (matgroves.com);
 * @class PolyK
 */
PIXI.PolyK = {};

/**
 * Triangulates shapes for webGL graphic fills.
 *
 * @method Triangulate
 */
PIXI.PolyK.Triangulate = function(p)
{
    var sign = true;

    var n = p.length >> 1;
    if(n < 3) return [];

    var tgs = [];
    var avl = [];
    for(var i = 0; i < n; i++) avl.push(i);

    i = 0;
    var al = n;
    while(al > 3)
    {
        var i0 = avl[(i+0)%al];
        var i1 = avl[(i+1)%al];
        var i2 = avl[(i+2)%al];

        var ax = p[2*i0],  ay = p[2*i0+1];
        var bx = p[2*i1],  by = p[2*i1+1];
        var cx = p[2*i2],  cy = p[2*i2+1];

        var earFound = false;
        if(PIXI.PolyK._convex(ax, ay, bx, by, cx, cy, sign))
        {
            earFound = true;
            for(var j = 0; j < al; j++)
            {
                var vi = avl[j];
                if(vi === i0 || vi === i1 || vi === i2) continue;

                if(PIXI.PolyK._PointInTriangle(p[2*vi], p[2*vi+1], ax, ay, bx, by, cx, cy)) {
                    earFound = false;
                    break;
                }
            }
        }

        if(earFound)
        {
            tgs.push(i0, i1, i2);
            avl.splice((i+1)%al, 1);
            al--;
            i = 0;
        }
        else if(i++ > 3*al)
        {
            // need to flip flip reverse it!
            // reset!
            if(sign)
            {
                tgs = [];
                avl = [];
                for(i = 0; i < n; i++) avl.push(i);

                i = 0;
                al = n;

                sign = false;
            }
            else
            {
             //   window.console.log("PIXI Warning: shape too complex to fill");
                return null;
            }
        }
    }

    tgs.push(avl[0], avl[1], avl[2]);
    return tgs;
};

/**
 * Checks whether a point is within a triangle
 *
 * @method _PointInTriangle
 * @param px {Number} x coordinate of the point to test
 * @param py {Number} y coordinate of the point to test
 * @param ax {Number} x coordinate of the a point of the triangle
 * @param ay {Number} y coordinate of the a point of the triangle
 * @param bx {Number} x coordinate of the b point of the triangle
 * @param by {Number} y coordinate of the b point of the triangle
 * @param cx {Number} x coordinate of the c point of the triangle
 * @param cy {Number} y coordinate of the c point of the triangle
 * @private
 * @return {Boolean}
 */
PIXI.PolyK._PointInTriangle = function(px, py, ax, ay, bx, by, cx, cy)
{
    var v0x = cx-ax;
    var v0y = cy-ay;
    var v1x = bx-ax;
    var v1y = by-ay;
    var v2x = px-ax;
    var v2y = py-ay;

    var dot00 = v0x*v0x+v0y*v0y;
    var dot01 = v0x*v1x+v0y*v1y;
    var dot02 = v0x*v2x+v0y*v2y;
    var dot11 = v1x*v1x+v1y*v1y;
    var dot12 = v1x*v2x+v1y*v2y;

    var invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
    var u = (dot11 * dot02 - dot01 * dot12) * invDenom;
    var v = (dot00 * dot12 - dot01 * dot02) * invDenom;

    // Check if point is in triangle
    return (u >= 0) && (v >= 0) && (u + v < 1);
};

/**
 * Checks whether a shape is convex
 *
 * @method _convex
 * @private
 * @return {Boolean}
 */
PIXI.PolyK._convex = function(ax, ay, bx, by, cx, cy, sign)
{
    return ((ay-by)*(cx-bx) + (bx-ax)*(cy-by) >= 0) === sign;
};