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：