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[分形几何]IFS系统的实现

作者：EmilMatthew   类型:闪吧BBS   来源:闪吧

　　 IFS(Iterator Function System)是分形几何中一个十分生动而且吸引人的领域.
       用这个系统，可以生成很多自然景观，如树等.
       先看用这个系统可以生成的一些效果:
        点击浏览该文件
       
       很有意思，不是吗?
       那么，这样的图形是如何通过程序进行控制的呢，其实从应用的角度去理解，还是相当好懂的。
       那就是仿射坐标变换.
       何谓仿射坐标变换,便是旋转，扭曲，平移三种效果的迭加。
       数学上对应的变换矩阵为:
      
       所以，只要能根据我们最后所需要的迭代效果，确定出a,b,c,d,e,f的具体取值（当然，这同时也是最难的），根据我们所定出的需要显示的像素点，便能达到显示的效果.
       下面摘录一些我所收集的IFS系统的相应参数(xml文件数据格式)
       <data>中的参数依次为a,b,c,d,e,f,p(p指的是这种迭代效果出现的概率)
 
    LEVY曲线:
<inputDatas iterLimit=’10000’  fps=’20’ offsetX=’100’ offsetY=’250’ conditionTimes=’2’ scale=’100’>                                                          
       <data>0.5,-0.5,0.5,0.5,0,0,0.5</data>
       <data>0.5,0.5,-0.5,0.5,0.5,0.5,1</data>
</inputDatas>
    分形树:
<inputDatas iterLimit=’10000’  fps=’20’ offsetX=’100’ offsetY=’250’ conditionTimes=’4’ scale=’300’>                                                          
       <data>0,0,0,0.5,0,0,0.05</data>
       <data>0.42,-0.42,0.42,0.42,0,0.2,0.45</data>
       <data>0.42,0.42,-0.42,0.42,0,0.2,0.85</data>
       <data>0.1,0,0,0.1,0,0.2,1</data>
</inputDatas>
     羊齿草:
<?xml version="1.0" encoding="gb2312" ?> 
 <inputDatas iterLimit="20000" fps="20" offsetX="150" offsetY="500" conditionTimes="4" scale="50">
  <data>0,0,0,0.16,0,0,0.01</data> 
  <data>0.85,0.04,-0.04,0.85,0,1.6,0.86</data> 
  <data>0.2,-0.26,0.23,0.22,0,1.6,0.93</data> 
  <data>-0.15,0.28,0.26,0.24,0,0.44,1</data> 
  </inputDatas>
    FLAMBOYENT皇冠:
<?xml version="1.0" encoding="gb2312"?>
<inputDatas iterLimit=’20000’  fps=’20’ offsetX=’150’ offsetY=’500’ conditionTimes=’5’ scale=’200’>                                                          
       <data>0.25,0,0,0.5,0,0,0.154</data>
       <data>0.5,0,0,0.5,-0.25,0.5,0.461</data>
       <data>-0.25,0,0,-0.25,0.25,1,0.539</data>
       <data>0.5,0,0,0.5,0,0.75,0.846</data>
       <data>0.5,0,0,-0.25,0.5,1.25,1</data>
</inputDatas>
    下面给出的是AS2中的具体实现(只列出核心部分):
function mainF(inTransXml:XML)
{
       var i:Number=0;
       var j:Number=0;
       var tmpStr:String=new String();
       var tmpArr:Array=new Array();
       
       _root.gIteratorLimit=parseInt(inTransXml.firstChild.attributes.iterLimit);
       _root.gFps=parseInt(inTransXml.firstChild.attributes.fps);
 
       _root.gXOffset=parseInt(inTransXml.firstChild.attributes.offsetX);
       _root.gYOffset=parseInt(inTransXml.firstChild.attributes.offsetY);
       
       _root.gConditionTimes=parseInt(inTransXml.firstChild.attributes.conditionTimes);
       
       _root.gScale=parseInt(inTransXml.firstChild.attributes.scale);
       
       for(i=0;i<_root.gConditionTimes;i++)
       {
              tmpStr=new String(inTransXml.firstChild.childNodes[i].childNodes[0]);
              tmpArr=tmpStr.split(",");
       
              _root.a[i]=Number(tmpArr[0]);
              _root.b[i]=Number(tmpArr[1]);
              _root.c[i]=Number(tmpArr[2]);
              _root.d[i]=Number(tmpArr[3]);
              _root.e[i]=Number(tmpArr[4]);
              _root.f[i]=Number(tmpArr[5]);
              _root.gCondition[i]=Number(tmpArr[6]);
       }
              
       _root.Xn=_root.Xn_1=_root.Yn=_root.Yn_1=0;
       _root.gIterTimes=0;
       _root.gIntervalID=setInterval(IFSFun,_root.gFps);
}
 
function  IFSFun():Void
{
       var curIndex:Number=0;
       var stepLen:Number=100;
       var i:Number=0;
       
       i=0;
       //trace(String(_root.a[0])+String(_root.b[0])+String(_root.c[0])+String(_root.d[0])+String(_root.e[0])+String(_root.f[0])+String(_root.gCondition[0]));
       //trace(String(a[1])+String(b[1])+String(c[1])+String(d[1])+String(e[1])+String(f[1])+String(_root.gCondition[1]));
       while(i<stepLen&&_root.gIterTimes<_root.gIteratorLimit)
       {
              curIndex=Math.random();
              //trace(_root.gIterTimes);
              //trace(curIndex);
              switch(_root.gConditionTimes)
              {
              case 2:
                     if(curIndex>=0&&curIndex<=_root.gCondition[0])
                     {
                            _root.Xn_1=_root.a[0]*_root.Xn+_root.b[0]*_root.Yn+_root.e[0];
                            _root.Yn_1=_root.c[0]*_root.Xn+_root.d[0]*_root.Yn+_root.f[0];
                            //trace("===level1==");
                            
                            //trace("Xn_1"+String(_root.Xn_1));
                            //trace("Yn_1"+String(_root.Yn_1));
                     }
                     else
                     {
                            _root.Xn_1=_root.a[1]*_root.Xn+_root.b[1]*_root.Yn+_root.e[1];
                            _root.Yn_1=_root.c[1]*_root.Xn+_root.d[1]*_root.Yn+_root.f[1];
                            //trace("===level2==");
                            
                            //trace("Xn_1"+String(_root.Xn_1));
                            //trace("Yn_1"+String(_root.Yn_1));
                     }
                     break;
       
              case 3:
              if(curIndex>=0&&curIndex<=_root.gCondition[0])
              {
                            _root.Xn_1=_root.a[0]*_root.Xn+_root.b[0]*_root.Yn+_root.e[0];
                            _root.Yn_1=_root.c[0]*_root.Xn+_root.d[0]*_root.Yn+_root.f[0];
              }
              else if(curIndex<=_root.gCondition[1])
              {
                            _root.Xn_1=_root.a[1]*_root.Xn+_root.b[1]*_root.Yn+_root.e[1];
                            _root.Yn_1=_root.c[1]*_root.Xn+_root.d[1]*_root.Yn+_root.f[1];
              }
              else
              {
                            _root.Xn_1=_root.a[2]*_root.Xn+_root.b[2]*_root.Yn+_root.e[2];
                            _root.Yn_1=_root.c[2]*_root.Xn+_root.d[2]*_root.Yn+_root.f[2];
              }
              break;
       
              case 4:
              if(curIndex>=0&&curIndex<=_root.gCondition[0])
              {
                            _root.Xn_1=_root.a[0]*_root.Xn+_root.b[0]*_root.Yn+_root.e[0];
                            _root.Yn_1=_root.c[0]*_root.Xn+_root.d[0]*_root.Yn+_root.f[0];
              }
              else if(curIndex<=_root.gCondition[1])
              {
                            _root.Xn_1=_root.a[1]*_root.Xn+_root.b[1]*_root.Yn+_root.e[1];
                            _root.Yn_1=_root.c[1]*_root.Xn+_root.d[1]*_root.Yn+_root.f[1];
              }
              else if(curIndex<=_root.gCondition[2])
              {
                            _root.Xn_1=_root.a[2]*_root.Xn+_root.b[2]*_root.Yn+_root.e[2];
                            _root.Yn_1=_root.c[2]*_root.Xn+_root.d[2]*_root.Yn+_root.f[2];
              }
              else
              {     
                            _root.Xn_1=_root.a[3]*_root.Xn+_root.b[3]*_root.Yn+_root.e[3];
                            _root.Yn_1=_root.c[3]*_root.Xn+_root.d[3]*_root.Yn+_root.f[3];
              }
              break;
       
              case 5:
              if(curIndex>=0&&curIndex<=_root.gCondition[0])
              {
                            _root.Xn_1=_root.a[0]*_root.Xn+_root.b[0]*_root.Yn+_root.e[0];
                            _root.Yn_1=_root.c[0]*_root.Xn+_root.d[0]*_root.Yn+_root.f[0];
              }
              else if(curIndex<=_root.gCondition[1])
              {
                            _root.Xn_1=_root.a[1]*_root.Xn+_root.b[1]*_root.Yn+_root.e[1];
                            _root.Yn_1=_root.c[1]*_root.Xn+_root.d[1]*_root.Yn+_root.f[1];
              }
              else if(curIndex<=_root.gCondition[2])
              {
                            _root.Xn_1=_root.a[2]*_root.Xn+_root.b[2]*_root.Yn+_root.e[2];
                            _root.Yn_1=_root.c[2]*_root.Xn+_root.d[2]*_root.Yn+_root.f[2];
              }
              else if(curIndex<=_root.gCondition[3])
              {     
                            _root.Xn_1=_root.a[3]*_root.Xn+_root.b[3]*_root.Yn+_root.e[3];
                            _root.Yn_1=_root.c[3]*_root.Xn+_root.d[3]*_root.Yn+_root.f[3];
              }
              else
              {     
                            _root.Xn_1=_root.a[4]*_root.Xn+_root.b[4]*_root.Yn+_root.e[4];
                            _root.Yn_1=_root.c[4]*_root.Xn+_root.d[4]*_root.Yn+_root.f[4];
              }
              
                     break;
 
              default:
                     trace3("error while random num produce\n");
                     trace("error while random num produce\n");
                     break;
              }
              //switch ends
              //draw new node
              drawNode2(_root.gXOffset+Xn_1*_root.gScale,_root.gYOffset-Yn_1*_root.gScale,_root.gColorArr[13]);
              //update data.
              _root.Xn=_root.Xn_1;
              _root.Yn=_root.Yn_1;
              i++;
              _root.gIterTimes++;
       }     
       
       if(_root.gIterTimes==_root.gIteratorLimit)
              clearInterval(_root.gIntervalID);
}
 
function drawNode2(x:Number,y:Number,nodeColor:Number):Void
{
       //trace("invoke");
       with(eval("_root.gBrush"))
       {
              lineStyle(1,nodeColor,100);
              moveTo(x-0.5,y);
              lineTo(x+0.5,y);
       }
}
源码下载
   责任编辑:uufeng    时间:2005年11月17日
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