classifyPoint(point:Vector2f, epsilon:Number = 0.000001):int //判断点与直线的关系，假设你站在a点朝向b点， 则输入点与直线的关系分为：Left, Right or Centered on the line

equals(line:Line2D):Boolean //线段是否相等 （忽略方向）

getDirection():Vector2f //直线方向

intersection(other:Line2D, pIntersectPoint:Vector2f = null):int //判断两个直线关系 this line A = x0, y0 and B = x1, y1 other is A = x2, y2 and B = x3, y3

length():Number  //直线长度

signedDistance(point:Vector2f):Number //给定点到直线的带符号距离，从a点朝向b点，右向为正，左向为负

getSide(sideIndex:int):Line2D //取得指定索引的边(从0开始，顺时针)

getVertex(i:int):Vector2f //根据i返回顶点

isPointIn(testPoint:Vector2f):Boolean //测试给定点是否在三角型中

setVertex(i:int, point:Vector2f):void //根据i指定的索引设置三角形的顶点 

public vertexV : Vector.<Vector2f>   //顶点列表，按顺时针方向排序

cw():void //将多边形的顶点按逆时针排序

isCW():Boolean //将多边形的顶点按顺时针排序

isSimplicity():Boolean //是否是简单多边形

rectangle():Rectangle //返回矩形包围盒  Polygon

union(polygon:Polygon):Vector.<Polygon> //合并两个多边形(Weiler-Athenton算法) 

/*
* @author 白连忱
* date Jan 22, 2010
*/
package org.blch.geom
{import flash.display.Sprite;import flash.geom.Rectangle;import flash.text.TextField;import flash.text.TextFieldAutoSize;import flash.text.TextFormat;/*** Delaunay* @langversion ActionScript 3.0* @playerversion Flash 10.0*/public class Delaunay{public function Delaunay(){}private static const EPSILON:Number = 0.000001;    //精度private var polygonV:Vector.<Polygon>;        //所有多边形，第0个元素为区域外边界 (输入数据)private var vertexV:Vector.<Vector2f>;        //所有顶点列表, 前outEdgeVecNmu个为外边界顶点private var edgeV:Vector.<Line2D>;            //所有约束边private var outEdgeVecNmu:int;            //区域外边界顶点数private  var lineV:Vector.<Line2D>;    //线段堆栈private var triangleV:Vector.<Triangle>;     //生成的Delaunay三角形public function createDelaunay(polyV:Vector.<Polygon>):Vector.<Triangle> {//Step1.     建立单元大小为 E*E 的均匀网格，并将多边形的顶点和边放入其中.//            其中 E=sqrt(w*h/n)，w 和 h 分别为多边形域包围盒的宽度、高度，n 为多边形域的顶点数 .
            initData(polyV);//Step2.    取任意一条外边界边 p1p2 .var initEdge:Line2D = getInitOutEdge();lineV.push(initEdge);var edge:Line2D;do {//Step3.     计算 DT 点 p3，构成约束 Delaunay 三角形 Δp1p2p3 .edge = lineV.pop();
//                trace("开始处理edge###########:", edge);var p3:Vector2f = findDT(edge);if (p3 == null) continue;var line13:Line2D = new Line2D(edge.getPointA(), p3);var line32:Line2D = new Line2D(p3, edge.getPointB());//Delaunay三角形放入输出数组var trg:Triangle = new Triangle(edge.getPointA(), edge.getPointB(), p3);//                trace("DT 点p3", p3);
//                trace("Triangle", trg);
                triangleV.push(trg);//Step4.    如果新生成的边 p1p3 不是约束边，若已经在堆栈中，//            则将其从中删除；否则，将其放入堆栈；类似地，可处理 p3p2 .var index:int;if (indexOfVector(line13, this.edgeV) < 0) {index = indexOfVector(line13, lineV);if (index > -1) {lineV.splice(index, 1);} else {lineV.push(line13);}}if (indexOfVector(line32, this.edgeV) < 0) {index = indexOfVector(line32, lineV);if (index > -1) {lineV.splice(index, 1);} else {lineV.push(line32);}}//Step5.    若堆栈不空，则从中取出一条边，转Step3；否则，算法停止 .
//                trace("处理结束edge###########\n");} while (lineV.length > 0);return triangleV;}/*** 初始化数据* @param polyV*/        private function initData(polyV:Vector.<Polygon>):void {//填充顶点和线列表vertexV = new Vector.<Vector2f>();edgeV = new Vector.<Line2D>();var poly:Polygon;for (var i:int=0; i<polyV.length; i++) {poly = polyV[i];putVertex(vertexV, poly.vertexV);putEdge(edgeV, poly.vertexV);}outEdgeVecNmu = polyV[0].vertexNmu;lineV = new Vector.<Line2D>();triangleV = new Vector.<Triangle>();}/*** 获取初始外边界* @return */        private function getInitOutEdge():Line2D {var initEdge:Line2D = edgeV[0];//检查是否有顶点p在该边上，如果有则换一个外边界var loopSign:Boolean;var loopIdx:int = 0;do {loopSign = false;loopIdx++;for each (var testV:Vector2f in this.vertexV) {if ( testV.equals(initEdge.getPointA()) || testV.equals(initEdge.getPointB()) ) continue;if (initEdge.classifyPoint(testV, EPSILON) == PointClassification.ON_LINE) {loopSign = true;initEdge = edgeV[loopIdx];break;}}} while (loopSign && loopIdx<outEdgeVecNmu-1);    //只取外边界return initEdge;}/*** 将srcV中的点放入dstV* @param dstV* @param srcV*/        private function putVertex(dstV:Vector.<Vector2f>, srcV:Vector.<Vector2f>):void {for each (var item:Vector2f in srcV) {dstV.push(item);}}/*** 根据srcV中的点生成多边形线段，并放入dstV* @param dstV* @param srcV*/        private function putEdge(dstV:Vector.<Line2D>, srcV:Vector.<Vector2f>):void {if (srcV.length < 3) return;    //不是一个多边形var p1:Vector2f = srcV[0];var p2:Vector2f;for (var i:int=1; i<srcV.length; i++) {p2 = srcV[i];dstV.push(new Line2D(p1, p2));p1 = p2;}p2 = srcV[0];dstV.push(new Line2D(p1, p2));}/*** 判断线段是否是约束边* @param line* @return 线段的索引，如果没有找到，返回-1*/        private function indexOfVector(line:Line2D, vector:Vector.<Line2D>):int {var lt:Line2D;for (var i:int=0; i<vector.length; i++) {lt = vector[i];if (lt.equals(line)) return i;}return -1;}/*** 计算 DT 点* @param line* @return */        private function findDT(line:Line2D):Vector2f {var p1:Vector2f = line.getPointA();var p2:Vector2f = line.getPointB();//搜索所有可见点             TODO 按y方向搜索距线段终点最近的点var allVPoint:Vector.<Vector2f> = new Vector.<Vector2f>();        // line的所有可见点for each (var vt:Vector2f in this.vertexV) {if (isVisiblePointOfLine(vt, line)) {allVPoint.push(vt);}}if (allVPoint.length == 0) return null;var p3:Vector2f = allVPoint[0];   var loopSign:Boolean = false;do {loopSign = false;//Step1. 构造 Δp1p2p3 的外接圆 C（p1，p2，p3）及其网格包围盒 B（C（p1，p2，p3））var circle:Circle = this.circumCircle(p1, p2, p3);var boundsBox:Rectangle = this.circleBounds(circle);//Step2. 依次访问网格包围盒内的每个网格单元：//         若某个网格单元中存在可见点 p, 并且 ∠p1pp2 > ∠p1p3p2，则令 p3=p，转Step1；否则，转Step3.var angle132:Number = Math.abs(lineAngle(p1, p3, p2));    // ∠p1p3p2for each (var vec:Vector2f in allVPoint) {if ( vec.equals(p1) || vec.equals(p2) || vec.equals(p3) ) {continue;}//不在包围盒中if (boundsBox.contains(vec.x, vec.y) == false) {continue;}//夹角var a1:Number = Math.abs(lineAngle(p1, vec, p2));if (a1 > angle132) {/////转Step1p3 = vec;loopSign = true;break;}}///转Step3} while (loopSign); //Step3. 若当前网格包围盒内所有网格单元都已被处理完，//         也即C（p1，p2，p3）内无可见点，则 p3 为的 p1p2 的 DT 点return p3;}/*** 返回顶角在o点，起始边为os，终止边为oe的夹角, 即∠soe (单位：弧度) * 角度小于pi，返回正值;   角度大于pi，返回负值 */        private function lineAngle(s:Vector2f, o:Vector2f, e:Vector2f):Number { var cosfi:Number, fi:Number, norm:Number; var dsx:Number = s.x - o.x; var dsy:Number = s.y - o.y; var dex:Number = e.x - o.x; var dey:Number = e.y - o.y; cosfi = dsx*dex + dsy*dey; norm = (dsx*dsx + dsy*dsy) * (dex*dex + dey*dey); cosfi /= Math.sqrt( norm ); if (cosfi >=  1.0 ) return 0; if (cosfi <= -1.0 ) return -Math.PI; fi = Math.acos(cosfi); if (dsx*dey - dsy*dex > 0) return fi;      // 说明矢量os 在矢量 oe的顺时针方向 return -fi; } /*** 返回圆的包围盒* @param c* @return */        private function circleBounds(c:Circle):Rectangle {return new Rectangle(c.center.x-c.r, c.center.y-c.r, c.r*2, c.r*2);}/*** 返回三角形的外接圆* @param p1* @param p2* @param p3* @return */        private function circumCircle(p1:Vector2f, p2:Vector2f, p3:Vector2f):Circle {var m1:Number,m2:Number,mx1:Number,mx2:Number,my1:Number,my2:Number;var dx:Number,dy:Number,rsqr:Number,drsqr:Number;var xc:Number, yc:Number, r:Number;/* Check for coincident points */if ( Math.abs(p1.y-p2.y) < EPSILON && Math.abs(p2.y-p3.y) < EPSILON ){trace("CircumCircle: Points are coincident.");return null;}m1 = - (p2.x - p1.x) / (p2.y - p1.y);m2 = - (p3.x-p2.x) / (p3.y-p2.y);mx1 = (p1.x + p2.x) / 2.0;mx2 = (p2.x + p3.x) / 2.0;my1 = (p1.y + p2.y) / 2.0;my2 = (p2.y + p3.y) / 2.0;if ( Math.abs(p2.y-p1.y) < EPSILON ) {xc = (p2.x + p1.x) / 2.0;yc = m2 * (xc - mx2) + my2;} else if ( Math.abs(p3.y - p2.y) < EPSILON ) {xc = (p3.x + p2.x) / 2.0;yc = m1 * (xc - mx1) + my1;    } else {xc = (m1 * mx1 - m2 * mx2 + my2 - my1) / (m1 - m2);yc = m1 * (xc - mx1) + my1;}dx = p2.x - xc;dy = p2.y - yc;rsqr = dx*dx + dy*dy;r = Math.sqrt(rsqr);return new Circle(new Vector2f(xc, yc), r);}/*** 判断点vec是否为line的可见点* @param vec* @param line* @return true:vec是line的可见点*/        private function isVisiblePointOfLine(vec:Vector2f, line:Line2D):Boolean {if (vec.equals(line.getPointA()) || vec.equals(line.getPointB())) {return false;}//（1） p3 在边 p1p2 的右侧 (多边形顶点顺序为顺时针)；if (line.classifyPoint(vec, EPSILON) != PointClassification.RIGHT_SIDE){return false;}//（2） p3 与 p1 可见，即 p1p3 不与任何一个约束边相交；if (isVisibleIn2Point(line.getPointA(), vec) == false) {return false;}//（3） p3 与 p2 可见if (isVisibleIn2Point(line.getPointB(), vec) == false) {return false;}return true;}/*** 点pa和pb是否可见(pa和pb构成的线段不与任何约束边相交，不包括顶点)* @param pa* @param pb* @return */private function isVisibleIn2Point(pa:Vector2f, pb:Vector2f):Boolean {var linepapb:Line2D = new Line2D(pa, pb);var interscetVector:Vector2f = new Vector2f();        //线段交点for each (var lineTmp:Line2D in this.edgeV) {//两线段相交if (linepapb.intersection(lineTmp, interscetVector) == LineClassification.SEGMENTS_INTERSECT) {//交点是不是端点if ( !pa.equals(interscetVector) && !pb.equals(interscetVector) ) {return false;}}}return true;}}
}import org.blch.geom.Vector2f;
/*** 圆* @author blc*/
class Circle {public var center:Vector2f;        //圆心public var r:Number;            //半径public function Circle(cen:Vector2f, r:Number) {this.center = cen;this.r = r;}
}