在 JS canvas 动画中为台球物理添加重力
Adding gravity to billiard physics in JS canvas animation
我正在尝试使用 Javascript 编写一个小型物理演示。我有多个球可以很好地相互反弹,但是当我尝试增加重力时出现问题。
我试图在它们撞击后保持动量,但是当我为每个都添加恒定引力时,物理学开始崩溃。
这是我的代码:
class Ball {
constructor ({
x,
y,
vx,
vy,
radius,
color = 'red',
}) {
this.x = x
this.y = y
this.vx = vx
this.vy = vy
this.radius = radius
this.color = color
this.mass = 1
}
render (ctx) {
ctx.save()
ctx.fillStyle = this.color
ctx.strokeStyle = this.color
ctx.translate(this.x, this.y)
ctx.strokeRect(-this.radius, -this.radius, this.radius * 2, this.radius * 2)
ctx.beginPath()
ctx.arc(0, 0, this.radius, Math.PI * 2, false)
ctx.closePath()
ctx.fill()
ctx.restore()
return this
}
getBounds () {
return {
x: this.x - this.radius,
y: this.y - this.radius,
width: this.radius * 2,
height: this.radius * 2
}
}
}
const intersects = (rectA, rectB) => {
return !(rectA.x + rectA.width < rectB.x ||
rectB.x + rectB.width < rectA.x ||
rectA.y + rectA.height < rectB.y ||
rectB.y + rectB.height < rectA.y)
}
const checkWall = (ball) => {
const bounceFactor = 0.5
if (ball.x + ball.radius > canvas.width) {
ball.x = canvas.width - ball.radius
ball.vx *= -bounceFactor
}
if (ball.x - ball.radius < 0) {
ball.x = ball.radius
ball.vx *= -bounceFactor
}
if (ball.y + ball.radius > canvas.height) {
ball.y = canvas.height - ball.radius
ball.vy *= -1
}
if (ball.y - ball.radius < 0) {
ball.y = ball.radius
ball.vy *= -bounceFactor
}
}
const rotate = (x, y, sin, cos, reverse) => {
return {
x: reverse ? x * cos + y * sin : x * cos - y * sin,
y: reverse ? y * cos - x * sin : y * cos + x * sin
}
}
const checkCollision = (ball0, ball1, dt) => {
const dx = ball1.x - ball0.x
const dy = ball1.y - ball0.y
const dist = Math.sqrt(dx * dx + dy * dy)
const minDist = ball0.radius + ball1.radius
if (dist < minDist) {
//calculate angle, sine, and cosine
const angle = Math.atan2(dy, dx)
const sin = Math.sin(angle)
const cos = Math.cos(angle)
//rotate ball0's position
const pos0 = {x: 0, y: 0}
//rotate ball1's position
const pos1 = rotate(dx, dy, sin, cos, true)
//rotate ball0's velocity
const vel0 = rotate(ball0.vx, ball0.vy, sin, cos, true)
//rotate ball1's velocity
const vel1 = rotate(ball1.vx, ball1.vy, sin, cos, true)
//collision reaction
const vxTotal = (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
const absV = Math.abs(vel0.x) + Math.abs(vel1.x)
const overlap = (ball0.radius + ball1.radius) - Math.abs(pos0.x - pos1.x)
pos0.x += vel0.x / absV * overlap
pos1.x += vel1.x / absV * overlap
//rotate positions back
const pos0F = rotate(pos0.x, pos0.y, sin, cos, false)
const pos1F = rotate(pos1.x, pos1.y, sin, cos, false)
//adjust positions to actual screen positions
ball1.x = ball0.x + pos1F.x
ball1.y = ball0.y + pos1F.y
ball0.x = ball0.x + pos0F.x
ball0.y = ball0.y + pos0F.y
//rotate velocities back
const vel0F = rotate(vel0.x, vel0.y, sin, cos, false)
const vel1F = rotate(vel1.x, vel1.y, sin, cos, false)
ball0.vx = vel0F.x
ball0.vy = vel0F.y
ball1.vx = vel1F.x
ball1.vy = vel1F.y
}
}
const canvas = document.createElement('canvas')
const ctx = canvas.getContext('2d')
let oldTime = 0
canvas.width = innerWidth
canvas.height = innerHeight
document.body.appendChild(canvas)
const log = document.getElementById('log')
const balls = new Array(36).fill(null).map(_ => new Ball({
x: Math.random() * innerWidth,
y: Math.random() * innerHeight,
vx: (Math.random() * 2 - 1) * 5,
vy: (Math.random() * 2 - 1) * 5,
radius: 20,
}))
requestAnimationFrame(updateFrame)
function updateFrame (ts) {
const dt = ts - oldTime
oldTime = ts
ctx.clearRect(0, 0, innerWidth, innerHeight)
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
// ADD GRAVITY HERE
ball.vy += 2
ball.x += ball.vx * (dt * 0.005)
ball.y += ball.vy * (dt * 0.005)
checkWall(ball)
}
for (let i = 0; i < balls.length; i++) {
const ball0 = balls[i]
for (let j = i + 1; j < balls.length; j++) {
const ball1 = balls[j]
// CHECK FOR COLLISIONS HERE
checkCollision(ball0, ball1, dt)
}
}
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
ball.render(ctx)
}
// const dist = ball2.x - ball1.x
// if (Math.abs(dist) < ball1.radius + ball2.radius) {
// const vxTotal = ball1.vx - ball2.vx
// ball1.vx = ((ball1.mass - ball2.mass) * ball1.vx + 2 * ball2.mass * ball2.vx) / (ball1.mass + ball2.mass)
// ball2.vx = vxTotal + ball1.vx
// ball1.x += ball1.vx
// ball2.x += ball2.vx
// }
// ball.vy += 0.5
// ball.x += ball.vx
// ball.y += ball.vy
//
// ball.render(ctx)
requestAnimationFrame(updateFrame)
}
* { margin: 0; padding: 0; }
如您所见,我有 checkCollision
辅助方法,计算一个球与另一个球碰撞后的动能和新速度。我的更新循环如下所示:
// add velocities to balls position
// check if its hitting any wall and bounce it back
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
// Add constant gravity to the vertical velocity
// When balls stack up on each other at the bottom, the gravity is still applied and my
// "checkCollision" method freaks out and the physics start to explode
ball.vy += 0.8
ball.x += ball.vx * (dt * 0.005)
ball.y += ball.vy * (dt * 0.005)
checkWall(ball)
}
for (let i = 0; i < balls.length; i++) {
const ball0 = balls[i]
for (let j = i + 1; j < balls.length; j++) {
const ball1 = balls[j]
// Check collisions between two balls
checkCollision(ball0, ball1, dt)
}
}
// Finally render the ball on-screen
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
ball.render(ctx)
}
如何计算 aa 重力,同时防止球开始相互堆叠时发生物理爆炸?
似乎重力与“checkCollision”方法发生碰撞。 checkCollision 方法试图将它们移回原位,但恒定的重力覆盖它并继续将它们拉下。
编辑:经过一些阅读,我明白一些 Verlet 集成是有序的,但我很难理解它。
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
// This line needs to be converted to verlet motion?
ball.vy += 2
ball.x += ball.vx * (dt * 0.005)
ball.y += ball.vy * (dt * 0.005)
checkWall(ball)
}
球不重叠
碰撞测试存在一个根本缺陷,因为碰撞仅在 2 个球重叠时计算。在现实世界中,这永远不会发生。
当许多球相互作用时,“重叠碰撞”的结果将导致不守恒系统总能量的行为。
按碰撞顺序解决
您可以解决碰撞,使球永远不会重叠,但每帧的处理量是不确定的,随着球密度的增加呈指数增长。
该方法是在帧之间的时间内定位球之间的第一次碰撞。解决该碰撞,然后根据该碰撞的新位置找到距离上一次碰撞时间最近的下一次碰撞。这样做直到该帧没有未决的冲突。 (不止于此)结果是模拟永远不会处于球重叠的不可能状态。
在 CodePen 上查看我的 Pool simulator 使用此方法模拟台球。球可以有任何速度并且总是正确解决。
Verlet 集成。
然而,您可以通过使用 verlet 积分来减少使用重叠碰撞的噪音,这将使球的总能量保持在更稳定的水平。
为此,我们引入了球的 2 个新属性,px
、py
,它们保持球的先前位置。
每一帧我们计算球的速度作为当前位置和新位置之间的差异。该速度用于计算框架。
当球改变方向(撞墙或另一个球)时,我们还需要改变球之前的位置以匹配它在新轨迹上的位置。
使用常数时间步长。
使用基于自上一帧以来的时间的时间步长也会引入噪声,不应在重叠碰撞方法中使用。
减少时间,增加迭代
为了进一步消除噪音,您需要降低球的整体速度以减少它们重叠的数量,从而更接近地表现得好像它们在 ballA.radius + ballB.radius
分开的点碰撞。此外,你应该测试每个球与其他每个球的对比,而不仅仅是 balls
数组中它上方的球。
为了保持动画速度,你解决了每帧几次球 V 球 V 墙碰撞问题。该示例执行 5。最佳值取决于球的总能量、可接受的噪音级别以及 运行 设备的 CPU 功率。
准确性很重要
你的碰撞功能也很好。我快速看了一下,它看起来不对。我在示例中添加了一个替代方案。
当球撞到墙上时,它会在帧之间的某个时间这样做。您必须将球从墙上移开正确的距离。不这样做就像模拟一个每次撞击时都会粘在墙上一点点的球,进一步偏离实际情况。
例子
这是对您的原始代码的重写。点击canvas补充一些能量。
const ctx = canvas.getContext("2d");
const BOUNCE = 0.75;
const resolveSteps = 5;
var oldTime = 0;
const $setOf = (count, fn = (i) => i) => {var a = [], i = 0; while (i < count) { a.push(fn(i++)) } return a };
const $rand = (min = 1, max = min + (min = 0)) => Math.random() * (max - min) + min;
const $randP = (min = 1, max = min + (min = 0), p = 2) => Math.random() ** p * (max - min) + min;
var W = canvas.width, H = canvas.height;
const BALL_COUNT = 80;
const BALL_RADIUS = 15, BALL_MIN_RADIUS = 6;
const GRAV = 0.5 / resolveSteps;
requestAnimationFrame(updateFrame);
canvas.addEventListener("click", () => {
balls.forEach(b => {
b.px = b.x + (Math.random() * 18 - 9);
b.py = b.y + (Math.random() * -18);
})
});
class Ball {
constructor({x, y, vx, vy, radius}) {
this.x = x;
this.y = y;
this.px = x - vx;
this.py = y - vy;
this.vx = vx;
this.vy = vy;
this.radius = radius;
this.mass = radius * radius * Math.PI * (4 / 3); // use sphere volume as mass
}
render(ctx) {
ctx.moveTo(this.x + this.radius, this.y);
ctx.arc(this.x, this.y, this.radius, Math.PI * 2, false);
}
move() {
this.vx = this.x - this.px;
this.vy = this.y - this.py;
this.vy += GRAV;
this.px = this.x;
this.py = this.y;
this.x += this.vx;
this.y += this.vy;
this.checkWall();
}
checkWall() {
const ball = this;
const top = ball.radius;
const left = ball.radius;
const bottom = H - ball.radius;
const right = W - ball.radius;
if (ball.x > right) {
const away = (ball.x - right) * BOUNCE;
ball.x = right - away;
ball.vx = -Math.abs(ball.vx) * BOUNCE;
ball.px = ball.x - ball.vx;
} else if (ball.x < left) {
const away = (ball.x - left) * BOUNCE;
ball.x = left + away;
ball.vx = Math.abs(ball.vx) * BOUNCE;
ball.px = ball.x - ball.vx;
}
if (ball.y > bottom) {
const away = (ball.y - bottom) * BOUNCE;
ball.y = bottom - away;
ball.vy = -Math.abs(ball.vy) * BOUNCE;
ball.py = ball.y - ball.vy;
} else if (ball.y < top) {
const away = (ball.y - top) * BOUNCE;
ball.y = top + away;
ball.vy = Math.abs(ball.vy) * BOUNCE;
ball.py = ball.y - ball.vy;
}
}
collisions() {
var b, dx, dy, nx, ny, cpx, cpy, p, d, i = 0;
var {x, y, vx, vy, px, py, radius: r, mass: m} = this;
while (i < balls.length) {
b = balls[i++];
if (this !== b) {
const rr = r + b.radius;
if (x + rr > b.x && x < b.x + rr && y + rr > b.y && y < b.y + rr) {
dx = x - b.x;
dy = y - b.y;
d = (dx * dx + dy * dy) ** 0.5;
if (d < rr) {
nx = (b.x - x) / d;
ny = (b.y - y) / d;
p = 2 * (vx * nx + vy * ny - b.vx * nx - b.vy * ny) / (m + b.mass);
cpx = (x * b.radius + b.x * r) / rr;
cpy = (y * b.radius + b.y * r) / rr;
x = cpx + r * (x - b.x) / d;
y = cpy + r * (y - b.y) / d;
b.x = cpx + b.radius * (b.x - x) / d;
b.y = cpy + b.radius * (b.y - y) / d;
px = x - (vx -= p * b.mass * nx);
py = y - (vy -= p * b.mass * ny);
b.px = b.x - (b.vx += p * m * nx);
b.py = b.y - (b.vy += p * m * ny);
}
}
}
}
this.x = x;
this.y = y;
this.px = px;
this.py = py;
this.vx = vx;
this.vy = vy;
this.checkWall();
}
}
const balls = (() => {
return $setOf(BALL_COUNT, () => new Ball({
x: $rand(BALL_RADIUS, W - BALL_RADIUS),
y: $rand(BALL_RADIUS, H - BALL_RADIUS),
vx: $rand(-2, 2),
vy: $rand(-2, 2),
radius: $randP(BALL_MIN_RADIUS, BALL_RADIUS, 4),
}));
})();
function updateFrame(ts) {
var i = 0, j = resolveSteps;
ctx.clearRect(0, 0, W, H);
while (i < balls.length) { balls[i++].move() }
while (j--) {
i = 0;
while (i < balls.length) { balls[i++].collisions(balls) }
}
ctx.fillStyle = "#0F0";
ctx.beginPath();
i = 0;
while (i < balls.length) { balls[i++].render(ctx) }
ctx.fill();
requestAnimationFrame(updateFrame)
}
<canvas id="canvas" width="400" height="180" style="border:1px solid black;"></canvas>
<div style="position: absolute; top: 10px; left: 10px;">Click to stir</div>
我正在尝试使用 Javascript 编写一个小型物理演示。我有多个球可以很好地相互反弹,但是当我尝试增加重力时出现问题。
我试图在它们撞击后保持动量,但是当我为每个都添加恒定引力时,物理学开始崩溃。
这是我的代码:
class Ball {
constructor ({
x,
y,
vx,
vy,
radius,
color = 'red',
}) {
this.x = x
this.y = y
this.vx = vx
this.vy = vy
this.radius = radius
this.color = color
this.mass = 1
}
render (ctx) {
ctx.save()
ctx.fillStyle = this.color
ctx.strokeStyle = this.color
ctx.translate(this.x, this.y)
ctx.strokeRect(-this.radius, -this.radius, this.radius * 2, this.radius * 2)
ctx.beginPath()
ctx.arc(0, 0, this.radius, Math.PI * 2, false)
ctx.closePath()
ctx.fill()
ctx.restore()
return this
}
getBounds () {
return {
x: this.x - this.radius,
y: this.y - this.radius,
width: this.radius * 2,
height: this.radius * 2
}
}
}
const intersects = (rectA, rectB) => {
return !(rectA.x + rectA.width < rectB.x ||
rectB.x + rectB.width < rectA.x ||
rectA.y + rectA.height < rectB.y ||
rectB.y + rectB.height < rectA.y)
}
const checkWall = (ball) => {
const bounceFactor = 0.5
if (ball.x + ball.radius > canvas.width) {
ball.x = canvas.width - ball.radius
ball.vx *= -bounceFactor
}
if (ball.x - ball.radius < 0) {
ball.x = ball.radius
ball.vx *= -bounceFactor
}
if (ball.y + ball.radius > canvas.height) {
ball.y = canvas.height - ball.radius
ball.vy *= -1
}
if (ball.y - ball.radius < 0) {
ball.y = ball.radius
ball.vy *= -bounceFactor
}
}
const rotate = (x, y, sin, cos, reverse) => {
return {
x: reverse ? x * cos + y * sin : x * cos - y * sin,
y: reverse ? y * cos - x * sin : y * cos + x * sin
}
}
const checkCollision = (ball0, ball1, dt) => {
const dx = ball1.x - ball0.x
const dy = ball1.y - ball0.y
const dist = Math.sqrt(dx * dx + dy * dy)
const minDist = ball0.radius + ball1.radius
if (dist < minDist) {
//calculate angle, sine, and cosine
const angle = Math.atan2(dy, dx)
const sin = Math.sin(angle)
const cos = Math.cos(angle)
//rotate ball0's position
const pos0 = {x: 0, y: 0}
//rotate ball1's position
const pos1 = rotate(dx, dy, sin, cos, true)
//rotate ball0's velocity
const vel0 = rotate(ball0.vx, ball0.vy, sin, cos, true)
//rotate ball1's velocity
const vel1 = rotate(ball1.vx, ball1.vy, sin, cos, true)
//collision reaction
const vxTotal = (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
const absV = Math.abs(vel0.x) + Math.abs(vel1.x)
const overlap = (ball0.radius + ball1.radius) - Math.abs(pos0.x - pos1.x)
pos0.x += vel0.x / absV * overlap
pos1.x += vel1.x / absV * overlap
//rotate positions back
const pos0F = rotate(pos0.x, pos0.y, sin, cos, false)
const pos1F = rotate(pos1.x, pos1.y, sin, cos, false)
//adjust positions to actual screen positions
ball1.x = ball0.x + pos1F.x
ball1.y = ball0.y + pos1F.y
ball0.x = ball0.x + pos0F.x
ball0.y = ball0.y + pos0F.y
//rotate velocities back
const vel0F = rotate(vel0.x, vel0.y, sin, cos, false)
const vel1F = rotate(vel1.x, vel1.y, sin, cos, false)
ball0.vx = vel0F.x
ball0.vy = vel0F.y
ball1.vx = vel1F.x
ball1.vy = vel1F.y
}
}
const canvas = document.createElement('canvas')
const ctx = canvas.getContext('2d')
let oldTime = 0
canvas.width = innerWidth
canvas.height = innerHeight
document.body.appendChild(canvas)
const log = document.getElementById('log')
const balls = new Array(36).fill(null).map(_ => new Ball({
x: Math.random() * innerWidth,
y: Math.random() * innerHeight,
vx: (Math.random() * 2 - 1) * 5,
vy: (Math.random() * 2 - 1) * 5,
radius: 20,
}))
requestAnimationFrame(updateFrame)
function updateFrame (ts) {
const dt = ts - oldTime
oldTime = ts
ctx.clearRect(0, 0, innerWidth, innerHeight)
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
// ADD GRAVITY HERE
ball.vy += 2
ball.x += ball.vx * (dt * 0.005)
ball.y += ball.vy * (dt * 0.005)
checkWall(ball)
}
for (let i = 0; i < balls.length; i++) {
const ball0 = balls[i]
for (let j = i + 1; j < balls.length; j++) {
const ball1 = balls[j]
// CHECK FOR COLLISIONS HERE
checkCollision(ball0, ball1, dt)
}
}
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
ball.render(ctx)
}
// const dist = ball2.x - ball1.x
// if (Math.abs(dist) < ball1.radius + ball2.radius) {
// const vxTotal = ball1.vx - ball2.vx
// ball1.vx = ((ball1.mass - ball2.mass) * ball1.vx + 2 * ball2.mass * ball2.vx) / (ball1.mass + ball2.mass)
// ball2.vx = vxTotal + ball1.vx
// ball1.x += ball1.vx
// ball2.x += ball2.vx
// }
// ball.vy += 0.5
// ball.x += ball.vx
// ball.y += ball.vy
//
// ball.render(ctx)
requestAnimationFrame(updateFrame)
}
* { margin: 0; padding: 0; }
如您所见,我有 checkCollision
辅助方法,计算一个球与另一个球碰撞后的动能和新速度。我的更新循环如下所示:
// add velocities to balls position
// check if its hitting any wall and bounce it back
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
// Add constant gravity to the vertical velocity
// When balls stack up on each other at the bottom, the gravity is still applied and my
// "checkCollision" method freaks out and the physics start to explode
ball.vy += 0.8
ball.x += ball.vx * (dt * 0.005)
ball.y += ball.vy * (dt * 0.005)
checkWall(ball)
}
for (let i = 0; i < balls.length; i++) {
const ball0 = balls[i]
for (let j = i + 1; j < balls.length; j++) {
const ball1 = balls[j]
// Check collisions between two balls
checkCollision(ball0, ball1, dt)
}
}
// Finally render the ball on-screen
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
ball.render(ctx)
}
如何计算 aa 重力,同时防止球开始相互堆叠时发生物理爆炸?
似乎重力与“checkCollision”方法发生碰撞。 checkCollision 方法试图将它们移回原位,但恒定的重力覆盖它并继续将它们拉下。
编辑:经过一些阅读,我明白一些 Verlet 集成是有序的,但我很难理解它。
for (let i = 0; i < balls.length; i++) {
const ball = balls[i]
// This line needs to be converted to verlet motion?
ball.vy += 2
ball.x += ball.vx * (dt * 0.005)
ball.y += ball.vy * (dt * 0.005)
checkWall(ball)
}
球不重叠
碰撞测试存在一个根本缺陷,因为碰撞仅在 2 个球重叠时计算。在现实世界中,这永远不会发生。
当许多球相互作用时,“重叠碰撞”的结果将导致不守恒系统总能量的行为。
按碰撞顺序解决
您可以解决碰撞,使球永远不会重叠,但每帧的处理量是不确定的,随着球密度的增加呈指数增长。
该方法是在帧之间的时间内定位球之间的第一次碰撞。解决该碰撞,然后根据该碰撞的新位置找到距离上一次碰撞时间最近的下一次碰撞。这样做直到该帧没有未决的冲突。 (不止于此)结果是模拟永远不会处于球重叠的不可能状态。
在 CodePen 上查看我的 Pool simulator 使用此方法模拟台球。球可以有任何速度并且总是正确解决。
Verlet 集成。
然而,您可以通过使用 verlet 积分来减少使用重叠碰撞的噪音,这将使球的总能量保持在更稳定的水平。
为此,我们引入了球的 2 个新属性,px
、py
,它们保持球的先前位置。
每一帧我们计算球的速度作为当前位置和新位置之间的差异。该速度用于计算框架。
当球改变方向(撞墙或另一个球)时,我们还需要改变球之前的位置以匹配它在新轨迹上的位置。
使用常数时间步长。
使用基于自上一帧以来的时间的时间步长也会引入噪声,不应在重叠碰撞方法中使用。
减少时间,增加迭代
为了进一步消除噪音,您需要降低球的整体速度以减少它们重叠的数量,从而更接近地表现得好像它们在 ballA.radius + ballB.radius
分开的点碰撞。此外,你应该测试每个球与其他每个球的对比,而不仅仅是 balls
数组中它上方的球。
为了保持动画速度,你解决了每帧几次球 V 球 V 墙碰撞问题。该示例执行 5。最佳值取决于球的总能量、可接受的噪音级别以及 运行 设备的 CPU 功率。
准确性很重要
你的碰撞功能也很好。我快速看了一下,它看起来不对。我在示例中添加了一个替代方案。
当球撞到墙上时,它会在帧之间的某个时间这样做。您必须将球从墙上移开正确的距离。不这样做就像模拟一个每次撞击时都会粘在墙上一点点的球,进一步偏离实际情况。
例子
这是对您的原始代码的重写。点击canvas补充一些能量。
const ctx = canvas.getContext("2d");
const BOUNCE = 0.75;
const resolveSteps = 5;
var oldTime = 0;
const $setOf = (count, fn = (i) => i) => {var a = [], i = 0; while (i < count) { a.push(fn(i++)) } return a };
const $rand = (min = 1, max = min + (min = 0)) => Math.random() * (max - min) + min;
const $randP = (min = 1, max = min + (min = 0), p = 2) => Math.random() ** p * (max - min) + min;
var W = canvas.width, H = canvas.height;
const BALL_COUNT = 80;
const BALL_RADIUS = 15, BALL_MIN_RADIUS = 6;
const GRAV = 0.5 / resolveSteps;
requestAnimationFrame(updateFrame);
canvas.addEventListener("click", () => {
balls.forEach(b => {
b.px = b.x + (Math.random() * 18 - 9);
b.py = b.y + (Math.random() * -18);
})
});
class Ball {
constructor({x, y, vx, vy, radius}) {
this.x = x;
this.y = y;
this.px = x - vx;
this.py = y - vy;
this.vx = vx;
this.vy = vy;
this.radius = radius;
this.mass = radius * radius * Math.PI * (4 / 3); // use sphere volume as mass
}
render(ctx) {
ctx.moveTo(this.x + this.radius, this.y);
ctx.arc(this.x, this.y, this.radius, Math.PI * 2, false);
}
move() {
this.vx = this.x - this.px;
this.vy = this.y - this.py;
this.vy += GRAV;
this.px = this.x;
this.py = this.y;
this.x += this.vx;
this.y += this.vy;
this.checkWall();
}
checkWall() {
const ball = this;
const top = ball.radius;
const left = ball.radius;
const bottom = H - ball.radius;
const right = W - ball.radius;
if (ball.x > right) {
const away = (ball.x - right) * BOUNCE;
ball.x = right - away;
ball.vx = -Math.abs(ball.vx) * BOUNCE;
ball.px = ball.x - ball.vx;
} else if (ball.x < left) {
const away = (ball.x - left) * BOUNCE;
ball.x = left + away;
ball.vx = Math.abs(ball.vx) * BOUNCE;
ball.px = ball.x - ball.vx;
}
if (ball.y > bottom) {
const away = (ball.y - bottom) * BOUNCE;
ball.y = bottom - away;
ball.vy = -Math.abs(ball.vy) * BOUNCE;
ball.py = ball.y - ball.vy;
} else if (ball.y < top) {
const away = (ball.y - top) * BOUNCE;
ball.y = top + away;
ball.vy = Math.abs(ball.vy) * BOUNCE;
ball.py = ball.y - ball.vy;
}
}
collisions() {
var b, dx, dy, nx, ny, cpx, cpy, p, d, i = 0;
var {x, y, vx, vy, px, py, radius: r, mass: m} = this;
while (i < balls.length) {
b = balls[i++];
if (this !== b) {
const rr = r + b.radius;
if (x + rr > b.x && x < b.x + rr && y + rr > b.y && y < b.y + rr) {
dx = x - b.x;
dy = y - b.y;
d = (dx * dx + dy * dy) ** 0.5;
if (d < rr) {
nx = (b.x - x) / d;
ny = (b.y - y) / d;
p = 2 * (vx * nx + vy * ny - b.vx * nx - b.vy * ny) / (m + b.mass);
cpx = (x * b.radius + b.x * r) / rr;
cpy = (y * b.radius + b.y * r) / rr;
x = cpx + r * (x - b.x) / d;
y = cpy + r * (y - b.y) / d;
b.x = cpx + b.radius * (b.x - x) / d;
b.y = cpy + b.radius * (b.y - y) / d;
px = x - (vx -= p * b.mass * nx);
py = y - (vy -= p * b.mass * ny);
b.px = b.x - (b.vx += p * m * nx);
b.py = b.y - (b.vy += p * m * ny);
}
}
}
}
this.x = x;
this.y = y;
this.px = px;
this.py = py;
this.vx = vx;
this.vy = vy;
this.checkWall();
}
}
const balls = (() => {
return $setOf(BALL_COUNT, () => new Ball({
x: $rand(BALL_RADIUS, W - BALL_RADIUS),
y: $rand(BALL_RADIUS, H - BALL_RADIUS),
vx: $rand(-2, 2),
vy: $rand(-2, 2),
radius: $randP(BALL_MIN_RADIUS, BALL_RADIUS, 4),
}));
})();
function updateFrame(ts) {
var i = 0, j = resolveSteps;
ctx.clearRect(0, 0, W, H);
while (i < balls.length) { balls[i++].move() }
while (j--) {
i = 0;
while (i < balls.length) { balls[i++].collisions(balls) }
}
ctx.fillStyle = "#0F0";
ctx.beginPath();
i = 0;
while (i < balls.length) { balls[i++].render(ctx) }
ctx.fill();
requestAnimationFrame(updateFrame)
}
<canvas id="canvas" width="400" height="180" style="border:1px solid black;"></canvas>
<div style="position: absolute; top: 10px; left: 10px;">Click to stir</div>