Flash/Flex学习笔记(44)：万有引力与粒子系统

万有引用公式:

其中G为万有引力常数

 

var numParticles:uint=50;//粒子总数
var G:Number=0.03;//万有引力常数
var particles:Array=new Array(numParticles);
var bounce:Number=-0.4;//边界反弹系统

//初始化
function init():void {
	particles = new Array();
	for (var i:uint = 0; i < numParticles; i++) {
		var size:Number=Math.random()*12+3;
		var particle:Ball=new Ball(size,Math.random()*0xffffff);
		particle.x=Math.random()*stage.stageWidth;
		particle.y=Math.random()*stage.stageHeight;
		particle.mass=Math.PI * size * size;//质量与球截面积关联，即从视觉效果上看，个头越大，越重
		addChild(particle);
		particles.push(particle);
	}
	addEventListener(Event.ENTER_FRAME, EnterFrameHandler);
}


function EnterFrameHandler(event:Event):void {
	for (var i:uint = 0; i < numParticles; i++) {
		var particle:Ball=particles[i];
		particle.x+=particle.vx;
		particle.y+=particle.vy;
	}
	for (i=0; i < numParticles - 1; i++) {
		var partA:Ball=particles[i];
		for (var j:uint = i + 1; j < numParticles; j++) {
			var partB:Ball=particles[j];
			checkCollision(partA,partB);//检测碰撞
			gravitate(partA, partB);//万有引力处理
		}
		checkWalls(partA);//边界检测
	}
}

//万有引力处理
function gravitate(partA:Ball, partB:Ball):void {
	var dx:Number=partB.x-partA.x;
	var dy:Number=partB.y-partA.y;
	var distSQ:Number=dx*dx+dy*dy;
	var dist:Number=Math.sqrt(distSQ);
	var force:Number=G*partA.mass*partB.mass/distSQ;//计算partA与partB的万有引力
	var forceX:Number=force*dx/dist;//即：force * cos(a) --万有引力在x方向上的分量
	var forceY:Number=force*dy/dist;//即：force * sin(a) --万有引力在y方向上的分量
	partA.vx+=forceX/partA.mass;//牛顿定律a = F/m 在这里得到体现
	partA.vy+=forceY/partA.mass;
	partB.vx-=forceX/partB.mass;
	partB.vy-=forceY/partB.mass;
}

//动量守恒的碰撞检测
function checkCollision(ball0:Ball, ball1:Ball):void {
	var dx:Number=ball1.x-ball0.x;
	var dy:Number=ball1.y-ball0.y;
	var dist:Number=Math.sqrt(dx*dx+dy*dy);
	if (dist<ball0.radius+ball1.radius) {
		var angle:Number=Math.atan2(dy,dx);
		var sin:Number=Math.sin(angle);
		var cos:Number=Math.cos(angle);
		var pos0:Point=new Point(0,0);
		var pos1:Point=rotate(dx,dy,sin,cos,true);
		var vel0:Point=rotate(ball0.vx,ball0.vy,sin,cos,true);
		var vel1:Point=rotate(ball1.vx,ball1.vy,sin,cos,true);
		var vxTotal:Number=vel0.x-vel1.x;
		vel0.x = ((ball0.mass - ball1.mass) * vel0.x + 2 * ball1.mass * vel1.x) / (ball0.mass + ball1.mass);
		vel1.x=vxTotal+vel0.x;
		var sumRadius:Number=ball0.radius+ball1.radius;
		var overlap:Number=sumRadius-Math.abs(pos0.x-pos1.x);
		var aRadio:Number=ball0.radius/sumRadius;
		var bRadio:Number=ball1.radius/sumRadius;
		if (overlap>0) {
			if (pos0.x>pos1.x) {
				pos0.x+=overlap*aRadio;
				pos1.x-=overlap*bRadio;
			} else {
				pos0.x-=overlap*aRadio;
				pos1.x+=overlap*bRadio;
			}
		}
		var pos0F:Object=rotate(pos0.x,pos0.y,sin,cos,false);
		var pos1F:Object=rotate(pos1.x,pos1.y,sin,cos,false);
		ball1.x=ball0.x+pos1F.x;
		ball1.y=ball0.y+pos1F.y;
		ball0.x=ball0.x+pos0F.x;
		ball0.y=ball0.y+pos0F.y;
		var vel0F:Object=rotate(vel0.x,vel0.y,sin,cos,false);
		var vel1F:Object=rotate(vel1.x,vel1.y,sin,cos,false);
		ball0.vx=vel0F.x;
		ball0.vy=vel0F.y;
		ball1.vx=vel1F.x;
		ball1.vy=vel1F.y;
	}
}

//坐标旋转辅助方法
function rotate(x:Number, y:Number, sin:Number, cos:Number, reverse:Boolean):Point {
	var result:Point = new Point();
	if (reverse) {
		result.x=x*cos+y*sin;
		result.y=y*cos-x*sin;
	} else {
		result.x=x*cos-y*sin;
		result.y=y*cos+x*sin;
	}
	return result;
}


//舞台边界检测  
function checkWalls(b:Ball) {
	if (b.x<b.radius) {
		b.x=b.radius;
		b.vx*=bounce;
	} else if (b.x>stage.stageWidth-b.radius) {
		b.x=stage.stageWidth-b.radius;
		b.vx*=bounce;
	}
	if (b.y<b.radius) {
		b.y=b.radius;
		b.vy*=bounce;
	} else if (b.y>stage.stageHeight-b.radius) {
		b.y=stage.stageHeight-b.radius;
		b.vy*=bounce;
	}
}


init();

btnReset.addEventListener(MouseEvent.MOUSE_DOWN,MouseDownHandler);

function MouseDownHandler(e:MouseEvent):void {
	removeEventListener(Event.ENTER_FRAME, EnterFrameHandler);
	for (var i:uint = 0; i < numParticles; i++) {
		var particle:Ball=particles[i];
		particle.x=Math.random()*stage.stageWidth;
		particle.y=Math.random()*stage.stageHeight;
		particle.vx=0;
		particle.vy=0;
	}
	addEventListener(Event.ENTER_FRAME, EnterFrameHandler);
}

 代码虽然很长，但是其中有很多都是上一篇里封装好的方法直接复制过来的，应该不难理解

再来模拟一下地球绕着太阳转:

var numParticles:uint=2;//粒子总数
var G:Number=0.03;//万有引力常数
var particles:Array=new Array(numParticles);
var i:Number=0;


//初始化
function init():void {
	particles = new Array(); 
	var sun:Ball = new Ball(30, 0xff0000); 
	sun.x = stage.stageWidth / 2; 
	sun.y = stage.stageHeight / 2; 
	sun.mass = 900000; 
	addChild(sun); 
	particles.push(sun); 
	var planet:Ball = new Ball(10, 0x0000ff); 
	planet.x = stage.stageWidth / 2 + 200; 
	planet.y = stage.stageHeight / 2; 
	planet.vy = 8; 
	planet.mass = 1; 
	addChild(planet); 
	particles.push(planet); 
	addEventListener(Event.ENTER_FRAME, EnterFrameHandler);
	graphics.lineStyle(1,0xdddddd);
	graphics.moveTo(planet.x,planet.y);
}


function EnterFrameHandler(event:Event):void {
	for (var i:uint = 0; i < numParticles; i++) {
		var particle:Ball=particles[i];
		particle.x+=particle.vx;
		particle.y+=particle.vy;
	}
	for (i=0; i < numParticles - 1; i++) {
		var partA:Ball=particles[i];
		for (var j:uint = i + 1; j < numParticles; j++) {
			var partB:Ball=particles[j];			
			gravitate(partA, partB);//万有引力处理
		}		
	}
}

//万有引力处理
function gravitate(partA:Ball, partB:Ball):void {	
	
	var dx:Number=partB.x-partA.x;
	var dy:Number=partB.y-partA.y;
	var distSQ:Number=dx*dx+dy*dy;
	var dist:Number=Math.sqrt(distSQ);
	var force:Number=G*partA.mass*partB.mass/distSQ;//计算partA与partB的万有引力
	var forceX:Number=force*dx/dist;//即：force * cos(a) --万有引力在x方向上的分量
	var forceY:Number=force*dy/dist;//即：force * sin(a) --万有引力在y方向上的分量
	/*
	partA.vx+=forceX/partA.mass;//牛顿定律a = F/m 在这里得到体现
	partA.vy+=forceY/partA.mass;
	*/
	partB.vx-=forceX/partB.mass;
	partB.vy-=forceY/partB.mass;
	trace(i);
	if (i<=1000){
		graphics.lineTo(partB.x,partB.y);
		i++;		
	}
	else{
		graphics.clear();
		graphics.lineStyle(1,0xdddddd);
		graphics.moveTo(partB.x,partB.y);
		i=0;
	}
	
}

init();

代码就是在第一段的基础上修改的，可以看到在"远日点"速度较慢(因为距离越远，万有引力越小，对应的加速度也较小)，在"近日点"速度较快(距离越近，万有引力越大，对应的加速度也较大)

节点花园NodeGarden:

为啥叫这个名字，我也说不上来，反正ActionScript3.0 in Animation一书的作者是这么叫的。

var particles:Array;
var numParticles:uint=60;
var minDist:Number=100;
var springAmount:Number=0.0004;
var friction:Number = 0.9995;

function init():void {
	stage.scaleMode=StageScaleMode.NO_SCALE;
	stage.align=StageAlign.TOP_LEFT;
	particles = new Array();
	for (var i:uint = 0; i < numParticles; i++) {
		var particle:Ball=new Ball(Math.random()*3+2,0xffffff);
		particle.x=Math.random()*stage.stageWidth;
		particle.y=Math.random()*stage.stageHeight;
		particle.vx=Math.random()*6-3;
		particle.vy=Math.random()*6-3;
		addChild(particle);
		particles.push(particle);
	}
	addEventListener(Event.ENTER_FRAME, EnterFrameHandler);
}

function EnterFrameHandler(event:Event):void {
	graphics.clear();
	for (var i:uint = 0; i < numParticles; i++) {
		var particle:Ball=particles[i];
		particle.x+=particle.vx;
		particle.y+=particle.vy;
		
		//屏幕环绕处理
		if (particle.x>stage.stageWidth) {
			particle.x=0;
		} else if (particle.x < 0) {
			particle.x=stage.stageWidth;
		}
		if (particle.y>stage.stageHeight) {
			particle.y=0;
		} else if (particle.y < 0) {
			particle.y=stage.stageHeight;
		}
	}
	for (i=0; i < numParticles - 1; i++) {
		var partA:Ball=particles[i];
		for (var j:uint = i + 1; j < numParticles; j++) {
			var partB:Ball=particles[j];
			spring(partA, partB);//每个粒子均与其它粒子进行弹性运动处理
		}	
		
		partA.vx *= friction;
		partA.vy *= friction;
	}
}

function spring(partA:Ball, partB:Ball):void {
	var dx:Number=partB.x-partA.x;
	var dy:Number=partB.y-partA.y;
	var dist:Number=Math.sqrt(dx*dx+dy*dy);
	if (dist<minDist) {		
		graphics.lineStyle(1, 0x00ff00, 1 - dist / minDist);//注意这里的透明度设置:二球越来越近时，线条越来越明显，距离越来越远时，线条越来越淡
		graphics.moveTo(partA.x, partA.y);
		graphics.lineTo(partB.x, partB.y);
		//类似弹性运动处理
		var ax:Number=dx*springAmount;
		var ay:Number=dy*springAmount;
		//A球加速
		partA.vx+=ax;
		partA.vy+=ay;
		//B球减速
		partB.vx-=ax;
		partB.vy-=ay;
		//一个球越来越快，一个球越来越慢，所以会不断拉近(当然：前提是在有效距离内)
		
		
	}
	
}

init();

关于这个效果，建议初次接触的同学们，先回顾一下弹性运动:Flash/Flex学习笔记(40)：弹性运动续--弹簧

可以稍加改进，加入质量因素：

var particles:Array;
var numParticles:uint=30;
var minDist:Number=120;
var springAmount:Number=0.03;
var friction:Number = 0.998;
var stageHeight:Number = stage.stageHeight;
var stageWidth:Number = stage.stageWidth;

function init():void {
	stage.scaleMode=StageScaleMode.NO_SCALE;
	stage.align=StageAlign.TOP_LEFT;
	particles = new Array();
	for (var i:uint = 0; i < numParticles; i++) {
		var particle:Ball=new Ball(Math.random()*5+2,0xffffff);
		particle.x=Math.random()*stageWidth;
		particle.y=Math.random()*stageHeight;
		particle.vx=Math.random()*6-3;
		particle.vy=Math.random()*6-3;
		particle.mass = Math.PI*particle.radius*particle.radius;//加入质量
		addChild(particle);
		particles.push(particle);
	}
	addEventListener(Event.ENTER_FRAME, EnterFrameHandler);
	stage.addEventListener(MouseEvent.MOUSE_MOVE,MouseMoveHandler);
}

//鼠标互动
function MouseMoveHandler(e:MouseEvent):void{	
	var dx:Number = mouseX - stageWidth/2;
	var dy:Number = mouseY - stageHeight/2;		
	for (var i:uint = 0; i < numParticles; i++) {
		var b:Ball=particles[i];		
		b.x -= dx/b.mass;
		b.y -= dy/b.mass;
	}	
}

function EnterFrameHandler(e:Event):void {
	graphics.clear();
	for (var i:uint = 0; i < numParticles; i++) {
		var particle:Ball=particles[i];
		particle.x+=particle.vx;
		particle.y+=particle.vy;		
		//屏幕环绕处理
		if (particle.x>stageWidth) {
			particle.x=0;
		} else if (particle.x < 0) {
			particle.x=stageWidth;
		}
		if (particle.y>stageHeight) {
			particle.y=0;
		} else if (particle.y < 0) {
			particle.y=stageHeight;
		}
	}
	for (i=0; i < numParticles - 1; i++) {
		var partA:Ball=particles[i];
		for (var j:uint = i + 1; j < numParticles; j++) {
			var partB:Ball=particles[j];
			spring(partA, partB);//每个粒子均与其它粒子进行弹性运动处理
		}	
		
		partA.vx *= friction;
		partA.vy *= friction;
	}
}

function spring(partA:Ball, partB:Ball):void {
	var dx:Number=partB.x-partA.x;
	var dy:Number=partB.y-partA.y;
	var dist:Number=Math.sqrt(dx*dx+dy*dy);
	if (dist<minDist) {		
		graphics.lineStyle(1, 0x00ff00, 1 - dist / minDist);//注意这里的透明度设置:二球越来越近时，线条越来越明显，距离越来越远时，线条越来越淡
		graphics.moveTo(partA.x, partA.y);
		graphics.lineTo(partB.x, partB.y);
		//类似弹性运动处理
		var ax:Number=dx*springAmount;
		var ay:Number=dy*springAmount;
		//A球加速
		partA.vx+=ax/partA.mass;
		partA.vy+=ay/partA.mass;
		//B球减速
		partB.vx-=ax/partB.mass;
		partB.vy-=ay/partB.mass;
		//一个球越来越快，一个球越来越慢，所以会不断拉近(当然：前提是在有效距离内)		
	}	
}

init();

下面这种效果也是很多Flash网站上都有的，效果还不错，而且原理也很简单：

var ballCount:uint = 100;
var friction:Number = 0.95;
var massRadio = 0.005;
var arrBall:Array = new Array(ballCount);
var stageWidth:Number = stage.stageWidth;
var stageHeight:Number = stage.stageHeight;

for(var i:uint=0;i<ballCount;i++){
	arrBall[i] = new Ball(Math.random()*10+3,Math.random()*0xffffff);
	arrBall[i].x = Math.random()*stageWidth;
	arrBall[i].y = Math.random()*stageHeight;
	arrBall[i].mass = massRadio * arrBall[i].radius;
	addChild(arrBall[i]);
}


stage.addEventListener(Event.ENTER_FRAME,EnterFrameHandler);
stage.addEventListener(MouseEvent.MOUSE_MOVE,MouseMoveHandler);

function EnterFrameHandler(e:Event):void{		
	for(var i:uint=0;i<ballCount;i++){
		var b:Ball = arrBall[i];		
		b.vx *=friction;
		b.vy *=friction;
		b.x += b.vx;
		b.y += b.vy;
		
		//屏幕环绕处理
		if (b.x>stageWidth+b.radius){
			b.x=-b.radius;
		}
		else if (b.x<-b.radius){
			b.x = stageWidth+b.radius;
		}		
		if (b.y>stageHeight+b.radius){
			b.y=-b.radius;
		}
		else if (b.y<-b.radius){
			b.y = stageHeight+b.radius;
		}
	}		
}

function MouseMoveHandler(e:MouseEvent):void{	
	var CenterX:Number = 0.5*stageWidth;
	var CenterY:Number = 0.5*stageHeight;
	var dx:Number = mouseX - CenterX;
	var dy:Number = mouseY - CenterY;	
	for(var i:uint=0;i<ballCount;i++){
		var b:Ball = arrBall[i];
		//设置速度
		b.vx = -dx*b.mass;
		b.vy = -dy*b.mass;		
	}		
}

下面这个是它的变种：

var ballCount:uint=200;
var friction:Number=0.95;
var massRadio=0.1;
var arrBall:Array=new Array(ballCount);
var stageWidth:Number=stage.stageWidth;
var stageHeight:Number=stage.stageHeight;
var _oldX:Number,_oldY:Number;
var _frameCount =0;

for (var i:uint=0; i<ballCount; i++) {
	arrBall[i]=new Ball(Math.random()*10+2,Math.random()*0xffffff);
	arrBall[i].x=Math.random()*stageWidth;
	arrBall[i].y=Math.random()*stageHeight;
	arrBall[i].mass=massRadio*arrBall[i].radius;
	addChild(arrBall[i]);
}

stage.addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

function EnterFrameHandler(e:Event):void {
	var dx:Number=mouseX-_oldX;
	var dy:Number=mouseY-_oldY;
	for (i=0; i<ballCount; i++) {
		var b:Ball=arrBall[i];
		if (Math.abs(dx)>0) {
			b.vx=- dx*b.mass;
		}
		if (Math.abs(dy)>0) {
			b.vy=- dy*b.mass;
		}
		b.vx*=friction;
		b.vy*=friction;
		b.x+=b.vx;
		b.y+=b.vy;

		//屏幕环绕处理
		if (b.x>stageWidth+b.radius) {
			b.x=- b.radius;
		} else if (b.x < -b.radius) {
			b.x=stageWidth+b.radius;
		}
		if (b.y>stageHeight+b.radius) {
			b.y=- b.radius;
		} else if (b.y < -b.radius) {
			b.y=stageHeight+b.radius;
		}
	}
	trace(_frameCount);
	//每2帧记录一下"速度" 
	if (_frameCount>=2){
		_frameCount = 0;
		_oldX=mouseX;
		_oldY=mouseY;
	}
	else{
		_frameCount ++;
	}
	
}