path: root/script.js

// Inject SVG into DOM synchronously because we can't access the DOM of SVGs inside img tags
document.querySelectorAll("svg").forEach(function(svg) {
	let req = new XMLHttpRequest()
	req.open("GET", svg.id + ".svg", false)
	req.send()
	svg.outerHTML = req.responseText
})

let rad = 10 // Stroke width
let size = 200 // SVG width and height
let A = [] // Objects
let cnt = 0
document.querySelectorAll("svg").forEach(function(svg) {
	// Move objects so they aren't overlapping
	svg.style.left = 1.5 * size * cnt++ + "px"
	svg.style.top = "50px"
	let a = {
		id: svg.id, // Unique ID
		p: [], // Collision circles
		cm: svg.createSVGPoint(), // Center of mass
		vx: Math.random(), // x velocity
		vy: Math.random(), // y velocity
		th: 0, // Angular position
		w: Math.random() / 100 // Angular velocity
	}
	svg.querySelectorAll("path").forEach(function(path) {
		// Get circles on path for collision checking
		for (let i = 0; i < path.getTotalLength(); i += 5) {
			const p = path.getPointAtLength(i)
			a.cm.x += p.x
			a.cm.y += p.y
			a.p.push(p)
			// Show circles for debugging
			/* let circle = document.createElementNS("http://www.w3.org/2000/svg", "circle")
			circle.setAttribute("cx", p.x)
			circle.setAttribute("cy", p.y)
			circle.setAttribute("r", rad)
			circle.setAttribute("fill", "red")
			svg.appendChild(circle) */
		}
	})
	a.cm.x /= a.p.length
	a.cm.y /= a.p.length
	// Change origin to center of mass
	const rect = svg.getBoundingClientRect()
	a.x = rect.x + a.cm.x // Position of center of mass
	a.y = rect.y + a.cm.y // Position of center of mass
	for (const p of a.p) {
		p.x -= a.cm.x
		p.y -= a.cm.y
	}
	svg.style.transformOrigin = a.cm.x + "px " + a.cm.y + "px"
	a.m = a.p.length // Mass
	a.mi = 0 // Moment of inertia
	for (const p of a.p) a.mi += p.x ** 2 + p.y ** 2
	A.push(a)
})

// Actual position of p in object a
function rot(a, p) {
	const c = Math.cos(a.th)
	const s = Math.sin(a.th)
	return {x: a.x + p.x * c - p.y * s, y: a.y + p.x * s + p.y * c}
}

// Distance squared between a and b
function ds(a, b) {
	return (a.x - b.x) ** 2 + (a.y - b.y) ** 2
}

// Cross product
function cr(a, b) {
	return a.x * b.y - a.y * b.x
}

// Collision of object a with b at point c with normal n
function collide(a, b, c, n) {
	// https://physics.stackexchange.com/questions/783524/angular-motion-in-collisions/783565#783565
	// https://physics.stackexchange.com/questions/786641/collision-calculation-in-2d/786969#786969
	// https://physics.stackexchange.com/questions/686640/resolving-angular-components-in-2d-circular-rigid-body-collision-response
	// I still don't know how to derive this magic but I'm convinced it works
	// No idea if there's a sign error
	// It looks fine though
	const ca = {x: a.x - c.x, y: a.y - c.y}
	const cb = {x: b.x - c.x, y: b.y - c.y}
	const v = n.x * (a.vx - b.vx) + n.y * (a.vy - b.vy) - a.w * cr(ca, n) + b.w * cr(cb, n)
	const m = 1 / (1 / a.m + 1 / b.m + cr(ca, n) ** 2 / a.mi + cr(cb, n) ** 2 / b.mi)
	const j = 2 * m * v
	a.vx += -n.x * j / a.m
	a.vy += -n.y * j / a.m
	a.w += cr(ca, n) * j / a.mi
	b.vx += n.x * j / b.m
	b.vy += n.y * j / b.m
	b.w += -cr(cb, n) * j / b.mi
	console.log('boop')
}

// Collision of object a with wall at position k and direction d
function wallCollide(a, k, d) {
	if ((d == 0 && Math.abs(a.x - k) < size) || (d == 1 && Math.abs(a.y - k) < size)) {
		let c = {x: 0, y: 0, cnt: 0}
		for (const p of a.p.map(x => rot(a, x))) {
			if ((d == 0 && Math.abs(p.x - k) < rad) || (d == 1 && Math.abs(p.y - k) < rad)) {
				c.x += p.x
				c.y += p.y
				c.cnt++
			}
		}
		if (c.cnt > 0) {
			c.x /= c.cnt
			c.y /= c.cnt
			let b = c
			b.vx = b.vy = b.w = 0
			b.m = b.mi = 1e9
			collide(a, b, c, {x: 1 - d, y: d})
		}
	}
}

// Collision of object a with object b
function objectsCollide(a, b) {
	if (ds(a, b) < size * size) {
		// Objects are close
		let c = {x: 0, y: 0, cnt: 0}
		let n = {x: 0, y: 0}
		for (const p of a.p.map(x => rot(a, x))) {
			// p is close to object b
			if (ds(p, b) < size * size) {
				for (const q of b.p.map(x => rot(b, x))) {
					const d = ds(p, q)
					if (d < 4 * rad * rad) {
						// Collision!
						// These calculations are a bit sketchy but I guess they work?
						c.x += p.x + q.x
						c.y += p.y + q.y
						c.cnt++
						n.x += (p.x - q.x) / d
						n.y += (p.y - q.y) / d
					}
				}
			}
		}
		if (c.cnt > 0) {
			c.x /= 2 * c.cnt
			c.y /= 2 * c.cnt
			// Normalize n
			let norm = Math.sqrt(n.x ** 2 + n.y ** 2)
			n.x /= norm
			n.y /= norm
			collide(a, b, c, n)
		}
	}
}

function tick() {
	// Move each object one step
	for (let a of A) {
		a.x += a.vx
		a.y += a.vy
		a.th += a.w
		if (Math.abs(a.vx) > 0.001) a.vx -= 0.001 * Math.sign(a.vx)
		if (Math.abs(a.vy) > 0.001) a.vy -= 0.001 * Math.sign(a.vy)
		if (Math.abs(a.w) > 0.00001) a.w -= 0.00001 * Math.sign(a.w)
	}

	// Check wall collisions
	for (let a of A) {
		wallCollide(a, 0, 0)
		wallCollide(a, window.innerWidth, 0)
		wallCollide(a, 0, 1)
		wallCollide(a, window.innerHeight, 1)
	}

	// Check collisions between objects
	for (let i = 0; i < A.length; i++) {
		for (let j = i + 1; j < A.length; j++) {
			objectsCollide(A[i], A[j])
		}
	}

	// Render every 10ms
	cnt++
	if (cnt == 10) {
		cnt = 0
		for (a of A) {
			let e = document.getElementById(a.id)
			e.style.left = a.x - a.cm.x + "px"
			e.style.top = a.y - a.cm.y + "px"
			e.style.rotate = a.th + "rad"
		}
	}
}

// Use click to update velocities
function updatev(event) {
	for (a of A) {
		let d = ds(a, {x: event.clientX, y: event.clientY})
		a.vx += 100 * (a.x - event.clientX) / d
		a.vy += 100 * (a.y - event.clientY) / d
	}

	// Display spreading out circles
	let circle = document.createElement("div")
	circle.style.width = circle.style.height = "10px"
	circle.style.left = event.clientX - 5 + "px"
	circle.style.top = event.clientY - 5 + "px"
	document.body.appendChild(circle)
	circle.offsetWidth
	circle.style.transform = "scale(500)"
	circle.style.opacity = "0"
	setTimeout(function () {
		document.body.removeChild(circle)
	}, 1000)
}

cnt = 0
setInterval(tick, 1)
document.addEventListener("click", updatev)