Flash/Flex学习笔记(39)：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：