Flash/Flex学习笔记(35)：弹性运动续--弹簧

上一篇里演示的弹性运动加上摩擦力因素后，物体最终基本上都会比较准确的停在目标位置。但是我们回想一下现实世界中的弹簧，如果把弹簧的一头固定起来(即相当于目标点)，而另一端栓一个球，把球拉开或压缩一定距离然后松手，事实上小球永远也不可能到达弹簧固定的那一端(因为弹簧即使压缩到最紧，也总有一定的长度)

所以如果要在Flash里模拟现实中的弹簧，真正的目标点绝不是弹簧的端点，而是目标点再偏移一段距离(即弹簧自然伸展时的长度)

var ball:Ball = new Ball(6);

addChild(ball);

ball.y = 20;

 
ball.x = 20;

var targetX:Number=stage.stageWidth/2;

var targetY:Number=ball.y;

 
var springLength = 100;//弹簧长度

 
var spring = 0.2;//弹性系数

 
var friction = 0.92;//摩擦系数

 
//画辅助线，以便看得更清楚

 
graphics.lineStyle(0.5,0xaaaaaa);

 
graphics.moveTo(ball.x,ball.y);

 
graphics.lineTo(stage.stageWidth-ball.x,ball.y);

 
graphics.moveTo(targetX,targetY-10);

 
graphics.lineTo(targetX,targetY+10);

 
graphics.moveTo(targetX-springLength,targetY-8);

 
graphics.lineTo(targetX-springLength,targetY+8);

 
var rect:Rectangle = new Rectangle(ball.x,ball.y,stage.stageWidth-ball.x*2,0);

 
addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

ball.addEventListener(MouseEvent.MOUSE_DOWN,MouseDownHandler);

 
stage.addEventListener(MouseEvent.MOUSE_UP,MouseUpHandler);

function EnterFrameHandler(e:Event):void{

 
ball.vx += (targetX - springLength - ball.x)*spring;

ball.vx *= friction;

 
ball.x += ball.vx;

}

 
function MouseDownHandler(e:MouseEvent):void{

 
(e.target as Sprite).startDrag(true,rect);

 
removeEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
}

 

function MouseUpHandler(e:MouseEvent):void{

 
ball.stopDrag();

 
addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

}

ball.addEventListener(MouseEvent.MOUSE_OUT,function(){Mouse.cursor = MouseCursor.AUTO});

ball.addEventListener(MouseEvent.MOUSE_OVER,function(){Mouse.cursor = MouseCursor.HAND});

如果考虑到二维坐标的弹簧运动，要稍微复杂一点：

 

var ball:Ball = new Ball(10);

 
addChild(ball);

 
ball.y = 20;

ball.x = 20;

var targetX:Number=stage.stageWidth/2;

 
var targetY:Number=stage.stageHeight/2;

 
var springLength:uint = 100;//弹簧长度

 
var spring:Number = 0.2;//弹性系数

 
var friction:Number = 0.92;//摩擦系数

 
var angle:Number = 0;

addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
ball.addEventListener(MouseEvent.MOUSE_DOWN,MouseDownHandler);

 
stage.addEventListener(MouseEvent.MOUSE_UP,MouseUpHandler);

 
stage.addEventListener(MouseEvent.MOUSE_MOVE,function(){DrawLine()});

 
angle = Math.atan2(targetY - ball.y,targetX -ball.x);//确定夹角

 
trace(angle*180/Math.PI);

 
function EnterFrameHandler(e:Event):void{

 
ball.vx += (targetX - springLength*Math.cos(angle) - ball.x)*spring;//调整目标点

 
ball.vy += (targetY - springLength*Math.sin(angle) - ball.y)*spring;

 
ball.vx *= friction;

 
ball.vy *= friction;

 
ball.x += ball.vx;

 
ball.y += ball.vy;

 
DrawLine();

 
}

function DrawLine():void{

 
graphics.clear();

graphics.lineStyle(1);

graphics.moveTo(targetX,targetY-10);

 
graphics.lineTo(targetX,targetY+10);

 
graphics.moveTo(targetX-10,targetY);

 
graphics.lineTo(targetX+10,targetY);

 
graphics.moveTo(targetX,targetY);

 
graphics.lineStyle(0.5,0xaaaaaa);

 
graphics.lineTo(ball.x,ball.y);

 
}

 
function MouseDownHandler(e:MouseEvent):void{

 
(e.target as Sprite).startDrag(true);

removeEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
}

 
function MouseUpHandler(e:MouseEvent):void{

ball.stopDrag();

 
addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
}

 
ball.addEventListener(MouseEvent.MOUSE_OUT,function(){Mouse.cursor = MouseCursor.AUTO});

 
ball.addEventListener(MouseEvent.MOUSE_OVER,function(){Mouse.cursor = MouseCursor.HAND});

上面的例子中，移动的方向(即夹角)与目标点都是固定的，如果改成动态的（比如鼠标当前所在位置），效果可能更逼真

 
function EnterFrameHandler(e:Event):void{

 
targetX = mouseX;//改成动态目标

 
targetY = mouseY;

angle = Math.atan2(targetY - ball.y,targetX -ball.x);//动态夹角

 
ball.vx += (targetX - springLength*Math.cos(angle) - ball.x)*spring;

 
ball.vy += (targetY - springLength*Math.sin(angle) - ball.y)*spring;

 
ball.vx *= friction;

 
ball.vy *= friction;

ball.x += ball.vx;

 
ball.y += ball.vy;

 
DrawLine();

}

如果二个物体相互以对方所在位置为目标做弹性运动，同时再考虑弹簧长度，边界检测等因素，可以用AS3模拟出一个极逼真的弹簧模型：

 
var ball_1:Ball = new Ball(10,0xff0000);

var ball_2:Ball = new Ball(10,0x0000ff);

 
ball_1.x = stage.stageWidth * Math.random();

 
ball_1.y = stage.stageHeight * Math.random();

 
ball_2.x = stage.stageWidth/2;

 
ball_2.y = stage.stageHeight/2;

 
addChild(ball_1);

 
addChild(ball_2);

 
var spring:Number = 0.1;

 
var springLength:uint = 100;

 
var friction:Number = 0.9;

 
var darggingBall:Ball;

 
addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
ball_1.addEventListener(MouseEvent.MOUSE_DOWN,MouseDownHandler);

 
ball_2.addEventListener(MouseEvent.MOUSE_DOWN,MouseDownHandler);

 
stage.addEventListener(MouseEvent.MOUSE_UP,MouseUpHandler);

 
stage.addEventListener(MouseEvent.MOUSE_MOVE,function(){DrawLine();});

 
ball_1.addEventListener(MouseEvent.MOUSE_OVER,MouseOverHandler);

 
ball_1.addEventListener(MouseEvent.MOUSE_OUT,MouseOutHandler);

 
ball_2.addEventListener(MouseEvent.MOUSE_OVER,MouseOverHandler);

 
ball_2.addEventListener(MouseEvent.MOUSE_OUT,MouseOutHandler);

 
function MouseOutHandler(e:MouseEvent){

 
Mouse.cursor = MouseCursor.AUTO;

 
}

 
function MouseOverHandler(e:MouseEvent){

 
Mouse.cursor = MouseCursor.HAND;

 
}

function MouseDownHandler(e:MouseEvent):void{

 
(e.target as Sprite).startDrag(true,new Rectangle(20,20,stage.stageWidth-40,stage.stageHeight-40));

 
darggingBall = e.target as Ball;

 
removeEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
}

 
function MouseUpHandler(e:MouseEvent):void{

 
if (darggingBall!=null){

 
darggingBall.stopDrag();

 
darggingBall = null;

 
addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
}   

 
}

 
function EnterFrameHandler(e:Event):void{

 
var dx1 = ball_2.x -ball_1.x;

var dy1 = ball_2.y -ball_1.y;   

 
var angle1:Number = Math.atan2(dy1,dx1);    

ball_1.vx += (ball_2.x - springLength * Math.cos(angle1) - ball_1.x) * spring;

 
ball_1.vy += (ball_2.y - springLength * Math.sin(angle1) - ball_1.y) * spring;  

 
ball_1.vx *= friction;

 
ball_1.vy *= friction;  

 
ball_1.x += ball_1.vx;

 
ball_1.y += ball_1.vy;

 
var dx2 = ball_1.x -ball_2.x;

 
var dy2 = ball_1.y -ball_2.y;   

var angle2:Number = Math.atan2(dy2,dx2);    

 
ball_2.vx += (ball_1.x - springLength * Math.cos(angle2) - ball_2.x) * spring;

 
ball_2.vy += (ball_1.y - springLength * Math.sin(angle2) - ball_2.y) * spring;  

 
ball_2.vx *= friction;

 
ball_2.vy *= friction;  

 
ball_2.x += ball_2.vx;

 
ball_2.y += ball_2.vy;

 
DrawLine();

 
CheckBoundary(ball_1);

CheckBoundary(ball_2);

 
}

 
function DrawLine():void{

 
graphics.clear();

 
graphics.lineStyle(0.5,0x666666);

 
graphics.moveTo(ball_1.x,ball_1.y);

 
graphics.lineTo(ball_2.x,ball_2.y);

}

 
function CheckBoundary(b:Ball){

 
if (b.x>stage.stageWidth-b.width/2 || b.x<=b.width/2){

 
b.x -= b.vx;        

b.vx *= -1;

 
}

 
if (b.y>stage.stageHeight-b.height/2 || b.y<=b.height/2){

 
b.y -= b.vy;

 
b.vy *= -1;

 
}

 
}

如果玩得再疯狂一点，多放一些小球，让第二个以第一个为目标，第三个以第二个为目标...最后一个再以第一个为目标，这样构成一个环，大概就是下面这个样子：

var spring:Number=0.1;

 
var springLength:uint=150;

 
var friction:Number=0.8;//摩擦力

 
var darggingBall:Ball;

var ballNumber:uint = 3;//小球个数

var arrBalls:Array = new Array(ballNumber);

 
for(var i:uint=0,j=arrBalls.length;i<j;i++){

 
arrBalls[i] = new Ball(20,Math.random() * 0xffffff);

 
var _ball:Ball = arrBalls[i];

 
_ball.x=stage.stageWidth*Math.random();

 
_ball.y=stage.stageHeight*Math.random();

 
addChild(_ball);

 
_ball.addEventListener(MouseEvent.MOUSE_OVER,MouseOverHandler);

_ball.addEventListener(MouseEvent.MOUSE_OUT,MouseOutHandler);

 
_ball.addEventListener(MouseEvent.MOUSE_DOWN,MouseDownHandler);

 
}

addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 

 

stage.addEventListener(MouseEvent.MOUSE_UP,MouseUpHandler);

 

stage.addEventListener(MouseEvent.MOUSE_MOVE,function(){DrawLine();});

 
//切换光标

 
function MouseOutHandler(e:MouseEvent) {

 
Mouse.cursor=MouseCursor.AUTO;

 
}

//切换光标

 
function MouseOverHandler(e:MouseEvent) {

 
Mouse.cursor=MouseCursor.HAND;

 
}

 
//开始拖动

 
function MouseDownHandler(e:MouseEvent):void {

 
(e.target as Sprite).startDrag(true,new Rectangle(20,20,stage.stageWidth-40,stage.stageHeight-40));

 
darggingBall=e.target as Ball;

 
removeEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
}

 
//结束拖动

 
function MouseUpHandler(e:MouseEvent):void {

if (darggingBall!=null) {

 
darggingBall.stopDrag();

 
darggingBall=null;

 
addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

}

 
}

function EnterFrameHandler(e:Event):void {

 
for(var i:uint=0,j=arrBalls.length-1;i<j;i++){

 
SpringTo(arrBalls[i],arrBalls[i+1]);        

 
}

 
SpringTo(arrBalls[arrBalls.length-1],arrBalls[0]);

 
DrawLine(); 

 
for(i=0,j=arrBalls.length;i<j;i++){

CheckBoundary(arrBalls[i]);

 
}

 
}

//画连接线

 
function DrawLine():void {

 
graphics.clear();

 
graphics.lineStyle(0.5,0x666666);

 
//graphics.moveTo(ball_1.x,ball_1.y);

 
//graphics.lineTo(ball_2.x,ball_2.y);

 
for(var i:uint=0,j=arrBalls.length-1;i<j;i++){

 
graphics.moveTo(arrBalls[i].x,arrBalls[i].y);

 
graphics.lineTo(arrBalls[i+1].x,arrBalls[i+1].y);

 
}

 
graphics.lineTo(arrBalls[0].x,arrBalls[0].y);

 
}

 
//弹性运动处理  
function SpringTo(targetBall:Ball,moveBall:Ball):void{

 
var dy=targetBall.y-moveBall.y;

 
var dx=targetBall.x-moveBall.x; 

 
var angle1:Number=Math.atan2(dy,dx);

 
moveBall.vx += (targetBall.x - springLength * Math.cos(angle1) - moveBall.x) * spring;

moveBall.vy += (targetBall.y - springLength * Math.sin(angle1) - moveBall.y) * spring;

 
moveBall.vx *= friction;

 
moveBall.vy *= friction;

 
moveBall.x += moveBall.vx;

 
moveBall.y += moveBall.vy;

 
}

 
//检测边界

 
function CheckBoundary(b:Ball) {

 
if (b.x>stage.stageWidth-b.width/2||b.x<=b.width/2) {

 
b.x-=b.vx;

 
b.vx*=-1;

 
}

 
if (b.y>stage.stageHeight-b.height/2||b.y<=b.height/2) {

b.y-=b.vy;

b.vy*=-1;

 
}

}

思考一下：这样为啥不会造成死循环？