Flash/Flex学习笔记(40)：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？