PHYSICS

1 files changed, 210 insertions, 0 deletions

diff --git a/script.js b/script.js
new file mode 100644
index 0000000..00140c1
--- /dev/null
+++ b/script.js
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+// Inject SVG into DOM synchronously because we can't access the DOM of SVGs inside img tags
+function injectSVG(svg) {
+	let req = new XMLHttpRequest()
+	req.open("GET", svg, false)
+	req.send()
+	document.body.innerHTML += req.responseText
+}
+
+// Draw 200x200 SVGs in Inkscape with the pencil tool and a stroke width of 20
+// Make sure the scale is set to 1 and that the id is set to a unique value
+// Also, change the stroke to currentColor so we can style the color with CSS
+injectSVG("hiragana-ni.svg")
+injectSVG("hiragana-small-ya.svg")
+injectSVG("hiragana-a.svg")
+
+let rad = 10
+let size = 200
+let A = []
+let cnt = 0
+document.querySelectorAll("svg").forEach(function(svg) {
+	svg.style.left = 1.5 * size * cnt++ + "px"
+	svg.style.top = "50px"
+	let a = {
+		id: svg.id, // Unique ID
+		p: [], // Collision circles of Array instances creates a new array populated with the results of calling a provided function on every element in the calling array. Try it Syntax js map(callbackFn) map(callbackFn, thisArg) Parameters callbackFn A function to execute for each element in the array.
+
+		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 += rad) {
+			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
+	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('hi')
+}
+
+// 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})
+		}
+	}
+}
+
+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++) {
+			let a = A[i]
+			let b = A[j]
+			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!
+								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
+					let norm = Math.sqrt(n.x ** 2 + n.y ** 2)
+					n.x /= norm
+					n.y /= norm
+					console.log(c.cnt, c, n)
+					collide(a, b, c, n)
+				}
+			}
+		}
+	}
+
+	// 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
+	}
+
+	// TODO: Display spreading out circles
+
+}
+
+cnt = 0
+setInterval(tick, 1)
+document.addEventListener("click", updatev)