Flash/Flex学习笔记(46)：正向运动学

所谓"正向运动学"通俗点讲就是把几个连接部件的一端固定起来，另一个端可以自由(向前/向外)运动。比如人的行走，单个下肢可以理解为脚连接小腿，小腿连接大腿，大腿连接腰。行走的过程，相当于二条腿相对固定于腰部，大腿运动驱动小腿，小腿又驱动脚，从而带动整个连接系统的一系列运动。

先来一个基本的关节类Segment:（就是一个圆角矩形+二个小圆圈）

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package {

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import flash.display.Sprite;

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import flash.geom.Point;

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public class Segment extends Sprite {

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private var color:uint;

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private var segmentWidth:Number;

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private var segmentHeight:Number;

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public var vx:Number=0;

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public var vy:Number=0;

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public function Segment(segmentWidth:Number,segmentHeight:Number,color:uint=0xffffff) {

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this.segmentWidth=segmentWidth;

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this.segmentHeight=segmentHeight;

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this.color=color;

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init();

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}

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public function init():void {

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// 绘制关节 

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graphics.lineStyle(0);

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graphics.beginFill(color);

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graphics.drawRoundRect(- segmentHeight/2,- segmentHeight/2,segmentWidth+segmentHeight,segmentHeight,segmentHeight,segmentHeight);

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graphics.endFill();

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// 绘制两个“枢轴” 

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graphics.drawCircle(0,0,2);

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graphics.drawCircle(segmentWidth,0,2);

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}

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//获得自由端的坐标

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public function getPin():Point {

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var angle:Number=rotation*Math.PI/180;

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var xPos:Number=x+Math.cos(angle)*segmentWidth;

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var yPos:Number=y+Math.sin(angle)*segmentWidth;

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return new Point(xPos,yPos);

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}

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}

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}

为了动态控制关节的旋转，再来一个简单的滑块控件类：（下列代码看起来吃力的同学，建议先看Flash/Flex学习笔记(36)：自己动手实现一个滑块控件(JimmySilder)）

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package {

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import flash.display.Sprite;

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import flash.events.MouseEvent;

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import flash.geom.Rectangle;

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import flash.events.Event;

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public class SimpleSlider extends Sprite {

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private var _width:Number=6;

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private var _height:Number=100;

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private var _value:Number;

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private var _max:Number=100;

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private var _min:Number=0;

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private var _handle:Sprite;

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private var _back:Sprite;

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private var _backWidth:Number=0;

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private var _handleHeight:Number=20;

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private var _backColor:uint=0xcccccc;

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private var _backBorderColor:uint=0x999999;

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private var _handleColor:uint=0x000000;

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private var _handleBorderColor:uint=0xcccccc;

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private var _handleRadius:Number=2;

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private var _backRadius:Number=2;

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public function SimpleSlider(min:Number = 0, max:Number = 100, value:Number = 100 ) {

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_min=min;

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_max=max;

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_value=Math.min(Math.max(value,min),max);

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init();

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}

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private function init():void {

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_back = new Sprite () ;

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addChild(_back);

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_handle = new Sprite () ;

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_handle.buttonMode=true;

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addChild(_handle);

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_handle.addEventListener( MouseEvent.MOUSE_DOWN , MouseDownHandler );

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draw();

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updatePosition();

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}

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private function draw():void {

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drawBack();

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drawHandle();

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}

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private function drawBack():void {

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_back.graphics.clear();

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_back.graphics.beginFill( _backColor );

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_back.graphics.lineStyle( 0, _backBorderColor );

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_back.graphics.drawRoundRect( 0, 0, _backWidth , _height , _backRadius , _backRadius );

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_back.graphics.endFill();

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_back.x=_width/2-_backWidth/2;

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}

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private function drawHandle():void {

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_handle.graphics.clear();

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_handle.graphics.beginFill( _handleColor );

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_handle.graphics.lineStyle( 0, _handleBorderColor );

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_handle.graphics.drawRect( 0, 0, _width , _handleHeight );

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_handle.graphics.endFill();

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}

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private function updatePosition():void {

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var handleRange:Number=_height-_handleHeight;

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var valueRange:Number=_max-_min;

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_handle.y = handleRange - ( _value - _min ) / valueRange * handleRange ;

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}

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private function updateValue():void {

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var handleRange:Number=_height-_handleHeight;

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var valueRange:Number=_max-_min;

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_value = ( handleRange - _handle.y ) / handleRange * valueRange + _min ;

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dispatchEvent( new Event ( Event.CHANGE ));

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}

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private function MouseUpHandler( e:MouseEvent ):void {

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stage.removeEventListener( MouseEvent.MOUSE_MOVE , MouseMoveHandler );

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stage.removeEventListener( MouseEvent.MOUSE_UP , MouseUpHandler );

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_handle.stopDrag();

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}

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private function MouseDownHandler( e:MouseEvent ):void {

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stage.addEventListener( MouseEvent.MOUSE_MOVE , MouseMoveHandler );

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stage.addEventListener( MouseEvent.MOUSE_UP , MouseUpHandler );

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_handle.startDrag( false , new Rectangle ( 0, 0, 0, _height - _handleHeight ));

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}

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private function MouseMoveHandler( e:MouseEvent ):void {

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updateValue();

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}

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public function invalidate():void {

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draw();

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}

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public function move( x:Number , y:Number ):void {

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this.x=x;

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this.y=y;

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}

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public function setSize( w:Number , h:Number ):void {

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_width=w;

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_height=h;

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draw();

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}

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public function set backBorderColor( n:uint ):void {

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_backBorderColor=n;

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draw();

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}

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public function get backBorderColor():uint {

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return _backBorderColor;

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}

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public function set backColor( n:uint ):void {

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_backColor=n;

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draw();

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}

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public function get backColor():uint {

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return _backColor;

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}

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public function set backRadius( n:Number ):void {

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_backRadius=n;

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}

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public function get backRadius():Number {

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return _backRadius;

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}

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public function set backWidth( n:Number ):void {

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_backWidth=n;

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draw();

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}

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public function get backWidth():Number {

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return _backWidth;

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}

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public function set handleBorderColor( n:uint ):void {

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_handleBorderColor=n;

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draw();

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}

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public function get handleBorderColor():uint {

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return _handleBorderColor;

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}

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public function set handleColor( n:uint ):void {

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_handleColor=n;

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draw();

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}

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public function get handleColor():uint {

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return _handleColor;

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}

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public function set handleRadius( n:Number ):void {

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_handleRadius=n;

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draw();

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}

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public function get handleRadius():Number {

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return _handleRadius;

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}

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public function set handleHeight( n:Number ):void {

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_handleHeight=n;

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draw();

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updatePosition();

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}

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public function get handleHeight():Number {

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return _handleHeight;

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}

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override public function set height( n:Number ):void {

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_height=n;

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draw();

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}

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override public function get height():Number {

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return _height;

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}

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public function set max( n:Number ):void {

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_max=n;

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updatePosition();

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}

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public function get max():Number {

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return _max;

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}

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public function set min( n:Number ):void {

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_min=n;

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updatePosition();

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}

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public function get min():Number {

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return _min;

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}

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public function set value( n:Number ):void {

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_value=n;

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_value=Math.min(_max,Math.max(_value,_min));

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updatePosition();

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}

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public function get value():Number {

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return _value;

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}

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override public function set width( n:Number ):void {

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_width=n;

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draw();

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}

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override public function get width():Number {

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return _width;

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}

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}

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}

基本测试：

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var segment:Segment=new Segment(100,20);

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addChild(segment);

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segment.x=50;

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segment.y=120;

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var slider:SimpleSlider=new SimpleSlider(-90,90,0);

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addChild(slider);

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slider.x=200;

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slider.y=70;

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slider.addEventListener(Event.CHANGE,onChange);

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function onChange(event:Event):void {

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segment.rotation=slider.value;

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}

双关节运动测试：

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package {

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import flash.display.Sprite;

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import flash.events.Event;

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public class TwoSegments extends Sprite {

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private var slider0:SimpleSlider;       

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private var slider1:SimpleSlider;

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private var segment0:Segment;

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private var segment1:Segment;

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public function TwoSegments() {

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init();

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}

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private function init():void {

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segment0=new Segment(100,20);

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addChild(segment0);

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segment0.x=50;

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segment0.y=150;

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segment1=new Segment(100,20);

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addChild(segment1);

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//关键：segment1的固定端连接到segment0的自由端

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segment1.x=segment0.getPin().x;

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segment1.y=segment0.getPin().y;

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slider0=new SimpleSlider(-90,90,0);

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addChild(slider0);

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slider0.x=320;

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slider0.y=90;

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slider0.addEventListener(Event.CHANGE,onChange);

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slider1=new SimpleSlider(-90,90,0);

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addChild(slider1);

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slider1.x=340;

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slider1.y=90;

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slider1.addEventListener(Event.CHANGE,onChange);

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}

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private function onChange(event:Event):void {

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segment0.rotation=slider0.value;

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segment1.rotation=slider1.value;

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segment1.x=segment0.getPin().x;

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segment1.y=segment0.getPin().y;

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}

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}

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}

如果把segment0与segment1分别看做人的胳膊与手臂，上面这个示例显然有二个地方不自然：

1.没有人的（前）手臂向下做-90度的弯曲(除非脱臼)

2.人的上肢整体向上抬时，手臂会随着胳膊一起绕肩关节向上旋转，而不应该一直固定于某个角度

修正的方法很简单，onChange改成下面这样：

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private function onChange(event:Event):void {

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segment0.rotation=slider0.value;

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segment1.rotation=slider1.value + segment0.rotation;//注意这行

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segment1.x=segment0.getPin().x;

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segment1.y=segment0.getPin().y;

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}

同时限制一下slider1的角度范围，改成下面这样：

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slider1=new SimpleSlider(-160,0,0);

单腿原地“踢”模拟

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package {

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import flash.display.Sprite;

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import flash.events.Event;

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public class Walking1 extends Sprite {

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private var segment0:Segment;

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private var segment1:Segment;

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private var cycle:Number=0;

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private var offset:Number = -Math.PI/2;//小腿的运动看上去应该滞后于大腿，所以需要加入反向偏移量

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public function Walking1() {

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init();

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trace(Math.PI/180);

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trace(0.05*180/Math.PI);

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}

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private function init():void {

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segment0=new Segment(100,20);

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addChild(segment0);

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segment0.x=200;

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segment0.y=200;

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segment1=new Segment(100,20);

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addChild(segment1);

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segment1.x=segment0.getPin().x;

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segment1.y=segment0.getPin().y;

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addEventListener(Event.ENTER_FRAME,onEnterFrame);

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}

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private function onEnterFrame(event:Event):void {

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cycle+=.05;

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var angle0:Number=Math.sin(cycle)*45 + 90;//-45到45整体加上90度以后，就变成45到135，即：大腿垂直方向左右摆动45度

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var angle1:Number = Math.sin(cycle + offset) * 45 + 45;//即：小腿相对大腿末端做0-90度的正向旋转。建议大家尝试修改一下这里的+45值的大小，看看效果有什么不同

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segment0.rotation=angle0;

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segment1.rotation=segment0.rotation+angle1;

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segment1.x=segment0.getPin().x;

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segment1.y=segment0.getPin().y;

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}

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}

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}

双腿原地行走：

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package {

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import flash.display.Sprite;

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import flash.events.Event;

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public class Walking4 extends Sprite {

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private var segment0:Segment;

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private var segment1:Segment;

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private var segment2:Segment;

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private var segment3:Segment;

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private var cycle:Number=0;

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private var offset:Number=- Math.PI/2;//小腿的运动看上去应该滞后于大腿，所以需要加入反向偏移量

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public function Walking4() {

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init();         

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}

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private function init():void {

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segment0=new Segment(100,35);//第一条大腿

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addChild(segment0);

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segment0.x=200;

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segment0.y=50;

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segment1=new Segment(100,20);           

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addChild(segment1);

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segment1.x=segment0.getPin().x;//第一条小腿连接到第一条大腿

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segment1.y=segment0.getPin().y;

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segment2=new Segment(100,35);//第二条大腿

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segment2.x = segment0.x;//第二条大腿与第一条大腿坐标相同，视觉效果上看，就象都固定在腰部

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segment2.y = segment0.y;

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addChild(segment2);

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segment3=new Segment(100,20);           

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addChild(segment3);

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segment3.x=segment2.getPin().x;//第二条小腿连接到第二条大腿

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segment3.y=segment2.getPin().y;

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addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

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}

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private function EnterFrameHandler(event:Event):void {

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walk(segment0, segment1, cycle); 

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walk(segment2, segment3, cycle + Math.PI);//注意这里的:+Math.PI,如果不加这个，二条腿的频率/角度完全相同，将重叠在一起，加上180度以后，正好反相过来，一条腿在前，另一条腿在后

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cycle += .05;

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}

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//把"走"的动作封装起来

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private function walk(segA:Segment, segB:Segment, cyc:Number):void {

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var angleA:Number=Math.sin(cyc)*45+90;

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var angleB:Number=Math.sin(cyc+offset)*45+45;

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segA.rotation=angleA;

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segB.rotation=segA.rotation+angleB;

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segB.x=segA.getPin().x;

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segB.y=segA.getPin().y;

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}

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}

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}

加入滑块控制条后的样子：

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package {

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import flash.display.Sprite;

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import flash.events.Event;

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public class Walking5 extends Sprite {

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private var segment0:Segment;

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private var segment1:Segment;

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private var segment2:Segment;

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private var segment3:Segment;

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private var speedSlider:SimpleSlider;

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private var thighRangeSlider:SimpleSlider;

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private var thighBaseSlider:SimpleSlider;

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private var calfRangeSlider:SimpleSlider;

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private var calfOffsetSlider:SimpleSlider;

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private var cycle:Number=0;

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public function Walking5() {

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init();

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}

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private function init():void {

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segment0=new Segment(100,30);

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addChild(segment0);

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segment0.x=200;

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segment0.y=100;

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segment1=new Segment(100,20);

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addChild(segment1);

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segment1.x=segment0.getPin().x;

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segment1.y=segment0.getPin().y;

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segment2=new Segment(100,30);

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addChild(segment2);

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segment2.x=200;

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segment2.y=100;

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segment3=new Segment(100,20);

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addChild(segment3);

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segment3.x=segment2.getPin().x;

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segment3.y=segment2.getPin().y;

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//控制速度的滑块

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speedSlider=new SimpleSlider(0,0.5,0.11);

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addChild(speedSlider);

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speedSlider.x=10;

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speedSlider.y=10;

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//控制大腿能分开的最大角度

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thighRangeSlider=new SimpleSlider(0,90,45);

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addChild(thighRangeSlider);

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thighRangeSlider.x=30;

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thighRangeSlider.y=10;

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//大腿旋转的偏移量

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thighBaseSlider=new SimpleSlider(0,180,90);

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addChild(thighBaseSlider);          

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thighBaseSlider.x=50;

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thighBaseSlider.y=10;

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//小腿旋转的偏移量

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calfRangeSlider=new SimpleSlider(0,90,45);

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addChild(calfRangeSlider);          

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calfRangeSlider.x=70;

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calfRangeSlider.y=10;

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//小腿相对大腿滞后的偏移量

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calfOffsetSlider=new SimpleSlider(-3.14,3.14,-1.57);

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addChild(calfOffsetSlider);         

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calfOffsetSlider.x=90;

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calfOffsetSlider.y=10;

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addEventListener(Event.ENTER_FRAME, EnterFrameHandler);

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}

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private function EnterFrameHandler(e:Event):void {

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walk(segment0, segment1, cycle);

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walk(segment2, segment3, cycle + Math.PI);

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cycle+=speedSlider.value;

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}

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private function walk(segA:Segment, segB:Segment,cyc:Number):void {

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var angleA:Number = Math.sin(cyc) * thighRangeSlider.value + thighBaseSlider.value;

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var angleB:Number = Math.sin(cyc +calfOffsetSlider.value) * calfRangeSlider.value + calfRangeSlider.value;

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segA.rotation=angleA;

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segB.rotation=segA.rotation+angleB;

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segB.x=segA.getPin().x;

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segB.y=segA.getPin().y;

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}

84
}

85
}

真正的行走：

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