[ActionScript 3.0] AS3 绘制正二十面体（线条）

分析：

正二十面体共有12个顶点、30条棱，其20个面都是正三角形。每条棱所对应的弧度值为1.1071487177940904弧度，这个弧度值可通过求Math.sqrt(5)/5的反余弦值求得。正二十面体的12个点按相对应的位置可以分为6对，把其中一对顶点置于Y轴上，此两点到坐标原点距离相等，则另外五对顶点皆呈倾斜状态，它们穿过坐标原点并环绕Y轴以72度递增旋转。根据这一点，可以先算好第一对倾斜顶点的坐标，然后让它绕Y轴以72度递增旋转4次得到另外四对顶点坐标，至此正二十面体的12个顶点坐标都已清楚，便可以创建模型了。

 package
 {
     import flash.display.MovieClip;
     import flash.display.Sprite;
     import flash.events.Event;
     import flash.geom.Vector3D;
     import flash.net.LocalConnection;

     /**
      * @author Frost.Yen
      * @E-mail 871979853@qq.com
      * @create 2015-9-7 下午12:58:27
      *
      */
     [SWF(width="800",height="600")]
     public class LineIcosahedron extends Sprite
     {
         private var _r:Number = 100;
         private var _faceArr:Array = [];
         private var _focus:Number = 400;
         private var _container:Sprite;
         private var _lineContainer:Sprite;
         public function LineIcosahedron()
         {
             initViews();
             initEventlisteners();
         }
         private function initViews():void
         {
             _container = new Sprite();
             _lineContainer = new Sprite();
             _container.x = _lineContainer.x = 400;
             _container.y = _lineContainer.y = 300;
             this.addChild(_container);
             this.addChild(_lineContainer);
             createFace();
         }
         private function initEventlisteners():void
         {
             this.addEventListener(Event.ENTER_FRAME,onEnterFrame);
         }
         private function onEnterFrame(e:Event):void
         {
             _lineContainer.graphics.clear();

             _lineContainer.graphics.lineStyle(3,0x00ffff);
             for(var i:int  = 0;i<_faceArr.length;i++){
                 (_faceArr[i] as MovieClip).transform.matrix3D.appendRotation(-(mouseX-_container.x)/50,Vector3D.Y_AXIS);
                 (_faceArr[i] as MovieClip).transform.matrix3D.appendRotation((mouseY-_container.y)/50,Vector3D.X_AXIS);
                 //利用焦距实现透视
                 _faceArr[i].Z = (_faceArr[i] as MovieClip).transform.getRelativeMatrix3D(_container).position.z;
                 _faceArr[i].X = (_faceArr[i] as MovieClip).transform.getRelativeMatrix3D(_container).position.x*(_focus/(_focus+_faceArr[i].Z));
                 _faceArr[i].Y = (_faceArr[i] as MovieClip).transform.getRelativeMatrix3D(_container).position.y*(_focus/(_focus+_faceArr[i].Z));
             }

             drawLine();
         }
         private function createFace():void
         {
             var angle:Number = 0.5*Math.PI - Math.acos(Math.sqrt(5)/5);
             for(var i:int = 0;i<12;i++){
                 var mc:MovieClip = new MovieClip();
                 _container.addChild(mc);
                 _faceArr.push(mc);
                 if(i==0){
                     mc.x = 0;
                     mc.y = -_r;
                     mc.z = 0;
                 }else if(i==11){
                     mc.x = 0;
                     mc.y = _r;
                     mc.z = 0;
                 }else if(i<=5){
                     mc.x = _r*Math.cos(angle);
                     mc.y = -_r*Math.sin(angle);
                     mc.z = 0;
                 }else{
                     mc.x = -_r*Math.cos(angle);
                     mc.y = _r*Math.sin(angle);
                     mc.z = 0;
                 }
             }
             for(i = 1;i<11;i++){
                 (_faceArr[i] as MovieClip).transform.matrix3D.appendRotation(i*72,Vector3D.Y_AXIS);
             }
         }
         private function drawLine():void
         {
             for(var i:int = 1;i<6;i++ ){
                 _lineContainer.graphics.moveTo(_faceArr[0].X,_faceArr[0].Y);
                 _lineContainer.graphics.lineTo(_faceArr[i].X,_faceArr[i].Y);
             }
             for(i=1;i<6;i++){
                 _lineContainer.graphics.lineTo(_faceArr[i].X,_faceArr[i].Y);
             }
             for(i = 6;i<11;i++){
                 _lineContainer.graphics.moveTo(_faceArr[11].X,_faceArr[11].Y);
                 _lineContainer.graphics.lineTo(_faceArr[i].X,_faceArr[i].Y);
             }
             for(i=6;i<11;i++){
                 _lineContainer.graphics.lineTo(_faceArr[i].X,_faceArr[i].Y);
             }

             _lineContainer.graphics.moveTo(_faceArr[1].X,_faceArr[1].Y);
             var id:int = 9;
             for(i=0;i<9;i++){
                 _lineContainer.graphics.lineTo(_faceArr[id].X,_faceArr[id].Y);
                 if(i<3){
                     id = i+11-id;
                 }else{
                     id = i+6-id;
                 }
             }
             _lineContainer.graphics.lineTo(_faceArr[1].X,_faceArr[1].Y);
         }
     }
 }

下面是源代码中drawLine()函数的原型

 private function drawLine2():void
         {
             _lineContainer.graphics.moveTo(_faceArr[0].X,_faceArr[0].Y);
             _lineContainer.graphics.lineTo(_faceArr[1].X,_faceArr[1].Y);

             _lineContainer.graphics.moveTo(_faceArr[0].X,_faceArr[0].Y);
             _lineContainer.graphics.lineTo(_faceArr[2].X,_faceArr[2].Y);

             _lineContainer.graphics.moveTo(_faceArr[0].X,_faceArr[0].Y);
             _lineContainer.graphics.lineTo(_faceArr[3].X,_faceArr[3].Y);

             _lineContainer.graphics.moveTo(_faceArr[0].X,_faceArr[0].Y);
             _lineContainer.graphics.lineTo(_faceArr[4].X,_faceArr[4].Y);

             _lineContainer.graphics.moveTo(_faceArr[0].X,_faceArr[0].Y);
             _lineContainer.graphics.lineTo(_faceArr[5].X,_faceArr[5].Y);

             _lineContainer.graphics.lineTo(_faceArr[1].X,_faceArr[1].Y);
             _lineContainer.graphics.lineTo(_faceArr[2].X,_faceArr[2].Y);
             _lineContainer.graphics.lineTo(_faceArr[3].X,_faceArr[3].Y);
             _lineContainer.graphics.lineTo(_faceArr[4].X,_faceArr[4].Y);
             _lineContainer.graphics.lineTo(_faceArr[5].X,_faceArr[5].Y);

             _lineContainer.graphics.moveTo(_faceArr[11].X,_faceArr[11].Y);
             _lineContainer.graphics.lineTo(_faceArr[6].X,_faceArr[6].Y);

             _lineContainer.graphics.moveTo(_faceArr[11].X,_faceArr[11].Y);
             _lineContainer.graphics.lineTo(_faceArr[7].X,_faceArr[7].Y);

             _lineContainer.graphics.moveTo(_faceArr[11].X,_faceArr[11].Y);
             _lineContainer.graphics.lineTo(_faceArr[8].X,_faceArr[8].Y);

             _lineContainer.graphics.moveTo(_faceArr[11].X,_faceArr[11].Y);
             _lineContainer.graphics.lineTo(_faceArr[9].X,_faceArr[9].Y);

             _lineContainer.graphics.moveTo(_faceArr[11].X,_faceArr[11].Y);
             _lineContainer.graphics.lineTo(_faceArr[10].X,_faceArr[10].Y);

             _lineContainer.graphics.lineTo(_faceArr[6].X,_faceArr[6].Y);
             _lineContainer.graphics.lineTo(_faceArr[7].X,_faceArr[7].Y);
             _lineContainer.graphics.lineTo(_faceArr[8].X,_faceArr[8].Y);
             _lineContainer.graphics.lineTo(_faceArr[9].X,_faceArr[9].Y);
             _lineContainer.graphics.lineTo(_faceArr[10].X,_faceArr[10].Y);

             _lineContainer.graphics.moveTo(_faceArr[1].X,_faceArr[1].Y);
             _lineContainer.graphics.lineTo(_faceArr[9].X,_faceArr[9].Y);
             _lineContainer.graphics.lineTo(_faceArr[2].X,_faceArr[2].Y);
             _lineContainer.graphics.lineTo(_faceArr[10].X,_faceArr[10].Y);
             _lineContainer.graphics.lineTo(_faceArr[3].X,_faceArr[3].Y);
             _lineContainer.graphics.lineTo(_faceArr[6].X,_faceArr[6].Y);
             _lineContainer.graphics.lineTo(_faceArr[4].X,_faceArr[4].Y);
             _lineContainer.graphics.lineTo(_faceArr[7].X,_faceArr[7].Y);
             _lineContainer.graphics.lineTo(_faceArr[5].X,_faceArr[5].Y);
             _lineContainer.graphics.lineTo(_faceArr[8].X,_faceArr[8].Y);
             _lineContainer.graphics.lineTo(_faceArr[1].X,_faceArr[1].Y);
         }