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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)
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