HTML5 Canvas - 与球物理故障的碰撞

Question

我正在使用牛顿方程来制作这个程序中的球,我正在解决它们彼此碰撞时"分开",但有时候它们会相互碰撞并导致很多麻烦.

.

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>

当你有很多球产生并且它们的速度很快时会发生这种情况:

为什么？有谁知道如何解决这个问题？

Answer 1

您的解决方案似乎仅具有基于速度的惩罚力。这允许球体穿透，并且当任何球体没有速度时，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胡克定律将相交的球体相互推开。

最好的解决方案是使用隐式接触求解算法。这允许更刚性的接触，但其算法要复杂得多。我建议您使用 2D 物理引擎来获得快速且良好的结果：Box2D 的 JavaScript 端口似乎使用得最多。