PHYSICS

6 files changed, 428 insertions, 0 deletions

diff --git a/hiragana-a.svg b/hiragana-a.svg
new file mode 100644
index 0000000..8086c81
--- /dev/null
+++ b/hiragana-a.svg
@@ -0,0 +1,54 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="200"
+   height="200"
+   viewBox="0 0 200 200"
+   version="1.1"
+   id="hiragana-a"
+   inkscape:version="1.3.2 (091e20ef0f, 2023-11-25, custom)"
+   sodipodi:docname="hiragana-a.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview1"
+     pagecolor="#ffffff"
+     bordercolor="#000000"
+     borderopacity="0.25"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     inkscape:zoom="1.3575939"
+     inkscape:cx="-103.49192"
+     inkscape:cy="160.57821"
+     inkscape:window-width="1536"
+     inkscape:window-height="902"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1" />
+  <defs
+     id="defs1" />
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <path
+       style="fill:none;stroke:currentColor;stroke-width:20;stroke-linejoin:round"
+       d="m 12.784166,48.2633 c 6.810296,-0.0161 13.608098,-0.70428 20.417184,-0.656946 8.339073,0.05797 16.662758,0.833983 25.001807,0.895073 34.613369,0.253565 37.757077,-1.380655 75.497083,-1.862985 9.91666,-0.126739 19.84279,-0.01771 29.74891,0.456642 24.06701,1.15225 14.13856,4.282188 22.44406,1.479181"
+       id="path1" />
+    <path
+       style="fill:none;stroke:currentColor;stroke-width:20;stroke-linejoin:round"
+       d="M 77.515495,8.2192151 C 75.516564,32.199537 75.530182,56.33753 75.541992,80.400969 c 0.0056,11.348185 -0.02805,22.701441 0.317652,34.042571 0.353335,11.59151 1.100709,23.16309 1.778856,34.73524 1.053836,17.98307 4.207218,12.37774 0.282507,18.48794"
+       id="path2" />
+    <path
+       style="fill:none;stroke:currentColor;stroke-width:20;stroke-linejoin:round"
+       d="m 125.70777,69.526531 c -0.69486,3.385925 -3.63293,17.853348 -4.07195,19.06547 -8.71461,24.060549 -19.52078,47.577849 -34.680923,68.388329 -5.193067,7.12857 -11.141846,14.13769 -18.645251,18.77272 -12.126114,7.49057 -27.245849,4.86443 -34.058991,-9.14824 -7.660344,-15.75512 -5.83572,-36.61123 3.067622,-51.35112 3.931406,-6.50862 9.029684,-12.95456 15.761122,-16.490912 16.544317,-8.691539 41.019976,-8.7624 58.602761,-4.619642 24.18531,5.698413 40.76727,10.598274 54.53221,31.135644 3.54089,5.28304 7.29148,11.80223 6.15485,18.05974 -1.42005,7.81773 -7.43918,14.32401 -13.0577,19.94234 -15.76644,15.76589 -18.71398,16.59872 -31.88644,22.27876"
+       id="path4" />
+  </g>
+</svg>
diff --git a/hiragana-ni.svg b/hiragana-ni.svg
new file mode 100644
index 0000000..0bddfde
--- /dev/null
+++ b/hiragana-ni.svg
@@ -0,0 +1,54 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="200"
+   height="200"
+   viewBox="0 0 200 200"
+   version="1.1"
+   id="hiragana-ni"
+   inkscape:version="1.3.2 (091e20ef0f, 2023-11-25, custom)"
+   sodipodi:docname="hiragana-ni.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview1"
+     pagecolor="#ffffff"
+     bordercolor="#000000"
+     borderopacity="0.25"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     inkscape:zoom="1.7276112"
+     inkscape:cx="-45.438465"
+     inkscape:cy="107.08428"
+     inkscape:window-width="1536"
+     inkscape:window-height="902"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1" />
+  <defs
+     id="defs1" />
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <path
+       style="fill:none;fill-opacity:1;stroke:currentColor;stroke-width:20;stroke-linecap:butt;stroke-linejoin:round;stroke-dasharray:none;stroke-opacity:1"
+       d="m 27.966735,16.083962 c -1.000438,1.124839 -2.372955,2.006558 -3.001316,3.374511 -0.890902,1.939519 -1.163631,4.125026 -1.417007,6.244278 -0.773668,6.470962 -1.184352,12.980894 -1.65866,19.480661 -1.990683,27.279717 -2.379566,30.990179 -1.454185,59.744588 0.793536,24.65759 1.788458,47.0885 5.760979,71.28514 0.564082,3.43584 1.988484,6.67372 2.982725,10.01058"
+       id="path7" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:currentColor;stroke-width:20;stroke-linecap:butt;stroke-linejoin:round;stroke-dasharray:none;stroke-opacity:1"
+       d="m 61.803371,47.19668 c 1.248756,-0.907498 2.287696,-2.21703 3.746279,-2.722487 3.4894,-1.209225 7.188566,-1.722283 10.831328,-2.329273 9.225962,-1.537319 18.442605,-3.263583 27.758222,-4.100892 28.83951,-2.592158 58.01616,-0.884141 86.89226,-0.03718"
+       id="path8" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:currentColor;stroke-width:20;stroke-linecap:butt;stroke-linejoin:round;stroke-dasharray:none;stroke-opacity:1"
+       d="m 87.045007,122.0222 c -1.118643,1.0562 -2.453734,1.92242 -3.355924,3.1686 -5.781083,7.98538 -13.117144,21.43086 -4.884465,30.77813 4.323739,4.90911 10.049889,8.7611 16.126165,11.18451 7.326277,2.92194 15.374477,3.78432 23.228367,4.51127 11.20859,1.03744 22.50545,0.60682 33.76085,0.76354 26.66878,0.37137 14.44172,-1.00144 26.91889,0.59627"
+       id="path9" />
+  </g>
+</svg>
diff --git a/hiragana-small-ya.svg b/hiragana-small-ya.svg
new file mode 100644
index 0000000..a994ef5
--- /dev/null
+++ b/hiragana-small-ya.svg
@@ -0,0 +1,54 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="200"
+   height="200"
+   viewBox="0 0 200 200"
+   version="1.1"
+   id="hiragana-small-ya"
+   inkscape:version="1.3.2 (091e20ef0f, 2023-11-25, custom)"
+   sodipodi:docname="hiragana-small-ya.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview1"
+     pagecolor="#ffffff"
+     bordercolor="#000000"
+     borderopacity="0.25"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     inkscape:zoom="1.381533"
+     inkscape:cx="-121.24213"
+     inkscape:cy="98.441371"
+     inkscape:window-width="1536"
+     inkscape:window-height="902"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1" />
+  <defs
+     id="defs1" />
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <path
+       style="fill:none;stroke:currentColor;stroke-width:20;stroke-linejoin:round"
+       d="m 22.318281,66.024742 c 3.522764,-5.501248 1.310196,-3.074172 12.511103,-6.879934 18.486357,-6.281155 31.10176,-9.525165 51.481112,-11.33282 17.781294,-1.577204 56.822334,-3.535437 75.702734,3.133648 12.25208,4.327774 13.15313,16.159869 5.86791,25.022203 -9.89215,12.033627 -30.4193,21.729881 -44.13131,27.517921 -1.60362,0.6769 -3.45533,0.42408 -5.18299,0.63612"
+       id="path1" />
+    <path
+       style="fill:none;stroke:currentColor;stroke-width:20;stroke-linejoin:round"
+       d="m 39.84223,19.392328 c 2.395717,4.499876 5.306115,8.761481 7.187149,13.499629 2.029237,5.111447 3.134124,10.546481 4.476386,15.879684 3.417985,13.580674 6.331658,27.285733 9.802138,40.853088 7.475495,29.224441 16.236122,57.535541 27.425749,85.593431"
+       id="path2" />
+    <path
+       style="fill:none;stroke:currentColor;stroke-width:20;stroke-linejoin:round"
+       d="m 95.63708,19.155587 c 2.853869,14.957057 9.67911,28.437868 14.84236,42.573525 2.10119,5.752511 3.81797,11.638235 5.72695,17.457352"
+       id="path3" />
+  </g>
+</svg>
diff --git a/index.html b/index.html
new file mode 100644
index 0000000..822899d
--- /dev/null
+++ b/index.html
@@ -0,0 +1,11 @@
+<!DOCTYPE html>
+<html>
+	<head>
+		<title>dumb physics engine</title>
+		<meta name="description" content="Converts SVGs into a list of circles and use those circles for dumb collision checking">
+		<link rel="stylesheet" href="style.css">
+	</head>
+	<body>
+		<script src="script.js"></script>
+	</body>
+</html>
diff --git a/script.js b/script.js
new file mode 100644
index 0000000..00140c1
--- /dev/null
+++ b/script.js
@@ -0,0 +1,210 @@
+// 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)
diff --git a/style.css b/style.css
new file mode 100644
index 0000000..fe2652d
--- /dev/null
+++ b/style.css
@@ -0,0 +1,45 @@
+body {
+/* 	background-image: url("catgirl.png"); */
+	background-size: auto 100vh;
+	background-position: center;
+	background-repeat: no-repeat;
+	background-attachment: fixed;
+	touch-action: manipulation;
+}
+
+@keyframes color {
+	10% {
+		color: #a43535;
+	}
+	20% {
+		color: #ff7b00;
+	}
+	30% {
+		color: #ffff51;
+	}
+	40% {
+		color: #a7ff4e;
+	}
+	50% {
+		color: #7addfe;
+	}
+	60% {
+		color: #6b6bfd;
+	}
+	70% {
+		color: #ca61ff;
+	}
+	80% {
+		color: #ff54af;
+	}
+	90% {
+		color: #f3bbff;
+	}
+}
+
+svg {
+	color: #f3bbff;
+	font-size: 240px;
+	animation: color 10s infinite linear;
+	position: absolute;
+}