Javascript HTML5画布-碰撞球物理故障

我用牛顿方程让我正在做的程序中的球在相互碰撞时被“分开”，但有时它们会相互卡住，这会造成很多麻烦

这是我的代码：

<center>
<canvas id="canvas" style="border: 2px solid black; cursor: crosshair;" width="1000"                 height="500"></canvas>
</center>

<script>
var canvas = document.getElementById("canvas")
var ctx = canvas.getContext("2d")

var w = canvas.width
var h = canvas.height

var ball = []

var gravity = 0.3
var force = 0.2

var mouse = {
d: false,
x1: 0,
y1: 0,
x2: 0,
y2: 0,
}




window.onmousedown = function(e) {
mouse.d = true
mouse.x1 = mouse.x2 = e.pageX - canvas.getBoundingClientRect().left
mouse.y1 = mouse.y2 = e.pageY - canvas.getBoundingClientRect().top
}
window.onmousemove = function(e) {
if (mouse.d) {
    mouse.x2 = e.pageX - canvas.getBoundingClientRect().left
    mouse.y2 = e.pageY - canvas.getBoundingClientRect().top
} else {
    mouse.x1 = mouse.x2 = e.pageX - canvas.getBoundingClientRect().left
    mouse.y1 = mouse.y2 = e.pageY - canvas.getBoundingClientRect().top
}
}
window.onmouseup = function() {
if (mouse.d) {
    mouse.d = false

    var dx = (mouse.x1 - mouse.x2);
    var dy = (mouse.y1 - mouse.y2);
    var mag = Math.sqrt(dx * dx + dy * dy);

    ball.push({
        x: mouse.x1,
        y: mouse.y1,
        r: Math.floor(Math.random() * 20) + 10,
        vx: dx / mag * -(mag * force),
        vy: dy / mag * -(mag * force),
        b: 0.7,
    })
}
}
document.onselectstart = function() {return false}
document.oncontextmenu = function() {return false}


setInterval(update, 1000 / 60)
function update() {
ctx.clearRect(0, 0, w, h)

ctx.beginPath()
ctx.moveTo(mouse.x1, mouse.y1)
ctx.lineTo(mouse.x2, mouse.y2)
ctx.stroke()
ctx.closePath()

for (i = 0; i < ball.length; i++) {
    ball[i].vy += gravity
    ball[i].x += ball[i].vx
    ball[i].y += ball[i].vy

    if (ball[i].x > w - ball[i].r) {
        ball[i].x = w - ball[i].r
        ball[i].vx *= -ball[i].b
    }
    if (ball[i].x < ball[i].r) {
        ball[i].x = ball[i].r
        ball[i].vx *= -ball[i].b
    }
    if (ball[i].y > h - ball[i].r) {
        ball[i].y = h - ball[i].r
        ball[i].vy *= -ball[i].b
    }
    if (ball[i].y < ball[i].r) {
        ball[i].y = ball[i].r
        ball[i].vy *= -ball[i].b
    }

    for (j = i + 1; j < ball.length; j++) {
        var dx = ball[i].x - ball[j].x
        var dy = ball[i].y - ball[j].y
        var dist = Math.sqrt(dx * dx + dy * dy)
        if (Math.abs(dx) + Math.abs(dy) != 0 && dist <= ball[i].r + ball[j].r) {
            var angle = Math.atan2(dy, dx)

            var sp1 = Math.sqrt(ball[i].vx*ball[i].vx + ball[i].vy*ball[i].vy);
            var sp2 = Math.sqrt(ball[j].vx*ball[j].vx + ball[j].vy*ball[j].vy);

            var dir1 = Math.atan2(ball[i].vy, ball[i].vx);
            var dir2 = Math.atan2(ball[j].vy, ball[j].vx);

            var vx1 = sp1 * Math.cos(dir1 - angle);
            var vy1 = sp1 * Math.sin(dir1 - angle);
            var vx2 = sp2 * Math.cos(dir2 - angle);
            var vy2 = sp2 * Math.sin(dir2 - angle);

            var fvx1 = ((ball[i].r - ball[j].r) * vx1 + (2 * ball[j].r) * vx2) / (ball[i].r + ball[j].r);
            var fvx2 = ((2 * ball[i].r) * vx1 + (ball[j].r - ball[i].r) * vx2) / (ball[i].r + ball[j].r);
            var fvy1 = vy1;
            var fvy2 = vy2;

            ball[i].vx = Math.cos(angle) * fvx1 + Math.cos(angle + Math.PI/2) * fvy1;
            ball[i].vy = Math.sin(angle) * fvx1 + Math.sin(angle + Math.PI/2) * fvy1;
            ball[j].vx = Math.cos(angle) * fvx2 + Math.cos(angle + Math.PI/2) * fvy2;
            ball[j].vy = Math.sin(angle) * fvx2 + Math.sin(angle + Math.PI/2) * fvy2;
        }
    }


    ctx.beginPath()
    ctx.arc(ball[i].x, ball[i].y, ball[i].r, 0, Math.PI * 2, false)
    ctx.fillStyle = "black"
    ctx.fill()
    ctx.closePath()
}
}
</script>

var canvas=document.getElementById（“画布”）
var ctx=canvas.getContext（“2d”）
var w=画布宽度
var h=画布高度
var ball=[]
var重力=0.3
var力=0.2
变量鼠标={
d:错，
x1:0，
y1:0，
x2:0，
y2:0，
}
window.onmousedown=函数（e）{
mouse.d=true
mouse.x1=mouse.x2=e.pageX-canvas.getBoundingClientRect（）.左
mouse.y1=mouse.y2=e.pageY-canvas.getBoundingClientRect（）.top
}
window.onmousemove=函数（e）{
如果（鼠标d）{
mouse.x2=e.pageX-canvas.getBoundingClientRect（）.left
mouse.y2=e.pageY-canvas.getBoundingClientRect（）.top
}否则{
mouse.x1=mouse.x2=e.pageX-canvas.getBoundingClientRect（）.左
mouse.y1=mouse.y2=e.pageY-canvas.getBoundingClientRect（）.top
}
}
window.onmouseup=函数（）{
如果（鼠标d）{
mouse.d=false
var dx=（mouse.x1-mouse.x2）；
var dy=（mouse.y1-mouse.y2）；
var mag=Math.sqrt（dx*dx+dy*dy）；
球推({
x:mouse.x1，
y:老鼠。y1，
r:Math.floor（Math.random（）*20）+10，
vx:dx/mag*-（mag*力），
vy:dy/mag*-（mag*力），
b:0.7，
})
}
}
document.onselectstart=函数（）{return false}
document.oncontextmenu=函数（）{return false}
设置间隔（更新，1000/60）
函数更新（）{
ctx.clearRect（0，0，w，h）
ctx.beginPath（）
ctx.moveTo（mouse.x1，mouse.y1）
ctx.lineTo（mouse.x2，mouse.y2）
ctx.stroke（）
ctx.closePath（）
对于（i=0；iw-ball[i].r）{
球[i].x=w-球[i].r
ball[i].vx*=-ball[i].b
}
if（ball[i].xh-ball[i].r）{
球[i].y=h-球[i].r
ball[i].vy*=-ball[i].b
}
if（ball[i].y如果（Math.abs（dx）+Math.abs（dy）！=0&&dist您的解决方案似乎只有基于速度的惩罚力。这允许球体穿透，并且当任何球体中没有速度时，它们都不会尝试修复穿透。要解决此问题，您需要添加基于位置的惩罚。
一个非常简单的解决方案是使用弹簧。计算穿透长度，并使用弹簧将相交球体相互推离

最好的解决方案是使用隐式接触求解算法。这允许使用更多的刚性接触，但其算法要复杂得多。我建议您使用2D物理引擎以获得快速而良好的结果：似乎最常用的是。我非常同意@schteppe的上述答案。我只是想告诉您有关这个问题的信息这里是链接：

查看“我为什么要使用它？”部分。它可能会暗示您的问题的答案，即您的代码到底出了什么问题

顺便说一句，我也一直在努力使您的代码正常工作，但没有取得实质性的结果。您可以在这里查看我的小提琴（我从您的小提琴复制而来）：

var canvas=document.getElementById（“canvas”）
var ctx=canvas.getContext（“2d”）
var w=画布宽度
var h=画布高度
var d=5；//碰撞时移动的距离
var ball=[]
var重力=0.3
var力=0.2
变量鼠标={
d:错，
x1:0，
y1:0，
x2:0，
y2:0，
}
window.onmousedown=函数（e）{
mouse.d=true
mouse.x1=mouse.x2=e.pageX-canvas.getBoundingClientRect（）.左
mouse.y1=mouse.y2=e.pageY-canvas.getBoundingClientRect（）.top
}
window.onmousemove=函数（e）{
如果（鼠标d）{
mouse.x2=e.pageX-canvas.getBoundingClientRect（）.left
mouse.y2=e.pageY-canvas.getBoundingClientRect（）.top
}否则{
mouse.x1=mouse.x2=e.pageX-canvas.getBoundingClientRect（）.左
mouse.y1=mouse.y2=e.pageY-canvas.getBoundingClientRect（）.top
}
}
window.onmouseup=函数（）{
如果（鼠标d）{
mouse.d=false
var dx=（mouse.x1-mouse.x2）；
var dy=（mouse.y1-mouse.y2）；
var mag=Math.sqrt（dx*dx+dy*dy）；
球推({
x:mouse.x1，
y:老鼠。y1，
r:Math.floor（Math.random（）*20）+10，
vx:dx/mag*-（mag*力），
vy:dy/mag*-（mag*力），
b:0.7，
})
}
}
函数getRandomColor（）{
变量字母='0123456789ABCDEF'。拆分（''）；
var color='#'；
对于（变量i=0；i<6；i++）{
颜色+=字母[Math.floor（Math.random（）*16）]；
}
返回颜色；
}
document.onselectstart=函数（）{
返回错误
}
document.oncontextmenu=函数（）{
返回错误
}
设置间隔（更新，1000/60）
函数更新（）{
ctx.clearRect（0，0，w，h）
ctx.beginPath（）
ctx.moveTo（mouse.x1，mouse.y1）
ctx.lineTo（mouse.x2，mouse.y2）
ctx.stroke（）
ctx.closePath（）
对于（i=0；iw-ball[i].r）{
球[i].x=w-球[i].r
ball[i].vx*=-ball[i].b
}
if（ball[i].xh-ball[i].r）{
球[i].y=h-球[i].r
ball[i].vy*=-ball[i].b
}
if（ball[i].yvar canvas = document.getElementById("canvas")
var ctx = canvas.getContext("2d")

var w = canvas.width
var h = canvas.height

var d = 5; //distance to move on collision

var ball = []

var gravity = 0.3
var force = 0.2

var mouse = {
    d: false,
    x1: 0,
    y1: 0,
    x2: 0,
    y2: 0,
}




window.onmousedown = function (e) {
    mouse.d = true
    mouse.x1 = mouse.x2 = e.pageX - canvas.getBoundingClientRect().left
    mouse.y1 = mouse.y2 = e.pageY - canvas.getBoundingClientRect().top
}
window.onmousemove = function (e) {
    if (mouse.d) {
        mouse.x2 = e.pageX - canvas.getBoundingClientRect().left
        mouse.y2 = e.pageY - canvas.getBoundingClientRect().top
    } else {
        mouse.x1 = mouse.x2 = e.pageX - canvas.getBoundingClientRect().left
        mouse.y1 = mouse.y2 = e.pageY - canvas.getBoundingClientRect().top
    }
}
window.onmouseup = function () {
    if (mouse.d) {
        mouse.d = false

        var dx = (mouse.x1 - mouse.x2);
        var dy = (mouse.y1 - mouse.y2);
        var mag = Math.sqrt(dx * dx + dy * dy);

        ball.push({
            x: mouse.x1,
            y: mouse.y1,
            r: Math.floor(Math.random() * 20) + 10,
            vx: dx / mag * -(mag * force),
            vy: dy / mag * -(mag * force),
            b: 0.7,
        })
    }
}

function getRandomColor() {
    var letters = '0123456789ABCDEF'.split('');
    var color = '#';
    for (var i = 0; i < 6; i++ ) {
        color += letters[Math.floor(Math.random() * 16)];
    }
    return color;
}

document.onselectstart = function () {
    return false
}
document.oncontextmenu = function () {
    return false
}


setInterval(update, 1000/60)

function update() {
    ctx.clearRect(0, 0, w, h)

    ctx.beginPath()
    ctx.moveTo(mouse.x1, mouse.y1)
    ctx.lineTo(mouse.x2, mouse.y2)
    ctx.stroke()
    ctx.closePath()

    for (i = 0; i < ball.length; i++) {
        ball[i].vy += gravity
        ball[i].x += ball[i].vx
        ball[i].y += ball[i].vy

        if (ball[i].x > w - ball[i].r) {
            ball[i].x = w - ball[i].r
            ball[i].vx *= -ball[i].b
        }
        if (ball[i].x < ball[i].r) {
            ball[i].x = ball[i].r
            ball[i].vx *= -ball[i].b
        }
        if (ball[i].y > h - ball[i].r) {
            ball[i].y = h - ball[i].r
            ball[i].vy *= -ball[i].b
        }
        if (ball[i].y < ball[i].r) {
            ball[i].y = ball[i].r
            ball[i].vy *= -ball[i].b
        }

        for (j = i + 1; j < ball.length; j++) {
            var dx = ball[i].x - ball[j].x
            var dy = ball[i].y - ball[j].y
            var dist = Math.sqrt(dx * dx + dy * dy)
            if (Math.abs(dx) + Math.abs(dy) != 0 && dist <= ball[i].r + ball[j].r) {

                var angle = Math.atan2(dy, dx)

                var sp1 = Math.sqrt(ball[i].vx * ball[i].vx + ball[i].vy * ball[i].vy);
                var sp2 = Math.sqrt(ball[j].vx * ball[j].vx + ball[j].vy * ball[j].vy);

                var dir1 = Math.atan2(ball[i].vy, ball[i].vx);
                var dir2 = Math.atan2(ball[j].vy, ball[j].vx);

                d = Math.ceil(ball[i].r+ball[j].r-dist)/2;

                //moving them back
                ball[i].x = ball[i].x - Math.cos(dir1)*d-1;
                ball[i].y = ball[i].y - Math.sin(dir1)*d-1;
                ball[j].x = ball[j].x + Math.cos(dir2)*d+1;
                ball[j].y = ball[j].y + Math.sin(dir2)*d+1;

                //Checking for distance again
                /*dx = ball[i].x - ball[j].x;
                dy = ball[i].y - ball[j].y;
                dist = Math.sqrt(dx * dx + dy * dy);
                if (Math.abs(dx) + Math.abs(dy) != 0 && dist <= ball[i].r + ball[j].r){
                      ball[i].x = ball[i].x + Math.cos(dir1)*2*d;
                        ball[i].y = ball[i].y + Math.sin(dir1)*d*2;
                        ball[j].x = ball[j].x - Math.cos(dir2)*d*2;
                      ball[j].y = ball[j].y - Math.sin(dir2)*d*2;
                }*/

                var vx1 = sp1 * Math.cos(dir1 - angle);
                var vy1 = sp1 * Math.sin(dir1 - angle);
                var vx2 = sp2 * Math.cos(dir2 - angle);
                var vy2 = sp2 * Math.sin(dir2 - angle);

                var fvx1 = ((ball[i].r - ball[j].r) * vx1 + (2 * ball[j].r) * vx2) / (ball[i].r + ball[j].r);
                var fvx2 = ((2 * ball[i].r) * vx1 + (ball[j].r - ball[i].r) * vx2) / (ball[i].r + ball[j].r);
                var fvy1 = vy1;
                var fvy2 = vy2;

                ball[i].vx = Math.cos(angle) * fvx1 + Math.cos(angle + Math.PI / 2) * fvy1;
                ball[i].vy = Math.sin(angle) * fvx1 + Math.sin(angle + Math.PI / 2) * fvy1;
                ball[j].vx = Math.cos(angle) * fvx2 + Math.cos(angle + Math.PI / 2) * fvy2;
                ball[j].vy = Math.sin(angle) * fvx2 + Math.sin(angle + Math.PI / 2) * fvy2;
            }
        }


        ctx.beginPath()
        ctx.arc(ball[i].x, ball[i].y, ball[i].r, 0, Math.PI * 2, false)
        ctx.fillStyle = getRandomColor();
        ctx.fill();
        ctx.closePath();
    }
}