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How to calculate all pixels on the circumference of an ellipse?

I am drawing an ellipse in a "canvas" element with the following lines of code:
let centerX = 250, centerY = 250;
let widthEllipse = 75;
let heightEllipse = 50;
context.beginPath();
context.lineWidth = 1;
context.ellipse(centerX, centerY, heightEllipse, widthEllipse, Math.PI / 4, 0, 2 * Math.PI);
context.stroke();
As a result, I get this drawing:
How can I calculate all the pixels on the circumference of an ellipse?
For example, to make such calculations for a circle, I used the following formulas:
for (let y = 0; y < r*2; y++) {
P1=(x0-sqrt(r^2-(y-y0)^2), y);
P2=(x0+sqrt(r^2-(y-y0)^2), y;
}

Scan lines. Axis Aligned ellipse
The first example is simple and only handles axis aligned ellipses.
Call is scanEllipse(x, y, xRadius, yRadius);
const ctx = can.getContext("2d");
scanEllipse(102, 64, 100, 30);
scanEllipse(256, 64, 40, 60);
function scanEllipse(x, y, h, v) {
const hSqr = h * h;
const scale = h / v;
var i = -v;
while (i <= v) {
var ii = i * scale;
var p1 = (hSqr - ii * ii) ** 0.5;
ctx.fillStyle = i % 2 ? "#F00" : "#000";
ctx.fillRect(x - p1, y + i, p1 * 2, 1);
i++;
}
}
canvas { border: 1px solid black; }
<canvas id="can" width="300" height="128"></canvas>
Scan lines. Rotated ellipse
This gets messy. To make sure it covers as many cases as possible I animated the function. I could not see any glitches but there may be some cases (very big ellipse or ellipses with very large eccentricity) where the floating point error may cause artifacts.
Call is scanEllipse(x, y, xRadius, yRadius, ang); ang is in radians.
const ctx = can.getContext("2d");
const quadRoots = (a, b, c) => { // find quadratic roots
if (Math.abs(a) < 1e-6) { return b != 0 ? [-c / b] : [] }
b /= a;
var d = b * b - 4 * (c / a);
if (d > 0) {
d = d ** 0.5;
return [0.5 * (-b + d), 0.5 * (-b - d)]
}
return d === 0 ? [0.5 * -b] : [];
}
function drawHLine(x, y, w) {
ctx.fillStyle = y % 2 ? "#F00" : "#000";
ctx.fillRect(x, y, w, 1);
}
function scanEllipse(x, y, h, v, a) {
const C = Math.cos(a), C2 = C * C;
const S = Math.sin(a), S2 = S * S;
const v2 = v * v, h2 = h * h;
const A = v2 * C2 + h2 * S2;
var i = 0, a, b, scan = true;
function atY(y) {
const B = 2 * y * C * S * (v2 - h2);
const c = y * y *(v2 * S2 + h2 * C2 )- h2 * v2;
return quadRoots(A, B, c);
}
while (scan) {
[a, b] = atY(i);
if (a !== undefined && b !== undefined) {
drawHLine(x + a, y + i, b - a);
if (i > 0) {
[a, b] = atY(-i);
drawHLine(x + a, y - i, b - a);
}
} else { scan = false; }
i++;
}
}
requestAnimationFrame(renderLoop);
function renderLoop(time) {
ctx.clearRect(0, 0, can.width, can.height);
const h = Math.sin(time * 0.001) * 45 + 50;
const v = Math.sin(time * 0.00333) * 35 + 40;
scanEllipse(100, 100, h, v, time * 0.00077);
requestAnimationFrame(renderLoop);
}
canvas { border: 1px solid black; }
<canvas id="can" width="200" height="200"></canvas>
Scan lines. Rotated ellipse edge only
Addresses just the outside pixels. (to fit the rules of good pixel art line work).
The function uses the same method as above by uses each previous row to workout which pixels are edge pixels.
There is plenty of room for optimization and the animation is slowed just a little to let use see the pixels.
Not that this version calculates the left and right edge using the center of each pixel row (eg y + 0.5). Using the top or bottom of the row makes for a lesser quality ellipse IMHO.
Call is scanEllipse(x, y, xRadius, yRadius, ang); ang is in radians.
const ctx = can.getContext("2d");
const quadRoots = (a, b, c) => { // find quadratic roots
if (Math.abs(a) < 1e-6) { return b != 0 ? [-c / b] : [] }
b /= a;
var d = b * b - 4 * (c / a);
if (d > 0) {
d = d ** 0.5;
return [0.5 * (-b + d), 0.5 * (-b - d)]
}
return d === 0 ? [0.5 * -b] : [];
}
function drawHLine(x, y, w) {
ctx.fillStyle = y % 2 ? "#F00" : "#000";
ctx.fillRect(x, y, w, 1);
}
function scanEllipse(x, y, h, v, a) {
const C = Math.cos(a), C2 = C * C;
const S = Math.sin(a), S2 = S * S;
const v2 = v * v, h2 = h * h;
const A = v2 * C2 + h2 * S2;
var i = 0, a1, b1, a2, b2, scan = true;
var pa1, pb1, pa2, pb2; // p for previous
function atY(y) {
const B = 2 * y * C * S * (v2 - h2);
const c = y * y *(v2 * S2 + h2 * C2 )- h2 * v2;
return quadRoots(A, B, c);
}
const max = Math.max, min = Math.min;
const addPx = (x, y) => ctx.fillRect(x, y, 1, 1);
const addEdgeLine = (x1, x2, y) => {
[x1, x2] = [min(x1, x2) | 0, max(x1, x2) | 0];
if (x1 == x2) { addPx(x1++, y); }
while (x1 < x2) {addPx(x1++, y);}
}
while (scan) {
[a1, b1] = atY(i - 0.5);
if (a1 !== undefined && b1 !== undefined) {
[a2, b2] = atY(-i +0.5);
if (pa1) {
addEdgeLine(pa1 + x, a1 + x, y + i - 1);
addEdgeLine(pb1 + x, b1 + x, y + i - 1);
if (i > 1) {
addEdgeLine(pa2 + x, a2 + x, y - i + 1);
addEdgeLine(pb2 + x, b2 + x, y - i + 1);
}
pa2 = a2;
pb2 = b2;
} else {
pa2 = min(a1,a2);
pb2 = max(b1,b2);
}
pa1 = a1;
pb1 = b1;
} else {
// add last row (top bottom)
if (pa1) {
addEdgeLine(pa1 + x, pb1 + x, y + i - 1);
addEdgeLine(pa2 + x, pb2 + x, y - i + 1);
}
scan = false;
}
i++;
}
}
requestAnimationFrame(renderLoop);
var tick = 0;
function renderLoop(time) {
if (tick++ % 4 === 0) {
time /= 4;
ctx.clearRect(0, 0, can.width, can.height);
const h = Math.sin(time * 0.001) ** 2 * 34 + 10;
const v = Math.sin(time * 0.00333) ** 2 * 35 + 10;
scanEllipse(50, 50, h, v, time * 0.00077);
}
requestAnimationFrame(renderLoop);
}
canvas {
border: 1px solid black;
width: 400px;
height: 400px;
image-rendering: pixelated;
}
<canvas id="can" width="100" height="100"></canvas>

Using a repeater instead of a canvas to curve text

Instead of using a canvas to curve the text to fit on the image. Is it possible instead to use a Repeater to achieve the same effect? Currently my code does what I need it to do with a Canvas. But I'm curious and it also might be better for me to use a Repeater to accomplish what I ultimately want. How can I modify my existing code to achieve this?
import QtQuick 2.15
import QtQuick.Window 2.15
Window {
id: root
visible: true
width: 640
height: 480
title: qsTr("Hello World")
property string letters: "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
Image {
id: abcBar
source: "alphabetBar.png"
visible: false
anchors.right: parent.right
anchors.top: parent.top
anchors.rightMargin: -10
}
// Rectangle {
// id: body
// anchors.fill: parent
// readonly property real dx: 12
// function midpoint(idx) {
// return 10 + idx * body.dx;
// }
// Repeater {
// anchors.fill: parent
// model: root.letters.length
// Text {
// anchors.horizontalCenter: parent.left
// anchors.horizontalCenterOffset: body.midpoint(index)
// anchors.verticalCenter: parent.verticalCenter
// text: root.letters[index]
// }
// }
// }
Canvas {
anchors.fill: parent
onPaint: {
var ctx = getContext('2d');
ctx.save();
ctx.canvas.width = 160;
ctx.canvas.height = 432;
ctx.font = "18px Roboto";
ctx.textAlign = "center";
ctx.fillStyle = "#000000"
const centerX = 10;
const centerY = ctx.canvas.height / 2;
const angle = Math.PI;
const radius = 130
ctx.fillStyle = "#000000"
ctx.restore();
ctx.save();
ctx.drawImage(abcBar, 0, 0, abcBar.width, abcBar.height);
console.log('loaded')
ctx.restore();
const args = {
ctx,
// text: "A • D • G • J • M • P • S • V • Z",
text: root.letters,
offset: 0,
G1: {
x: 20,
y: 80,
},
G2: {
x: 190,
y: 230,
},
G3: {
x: 0,
y: 372
},
}
textOnCurve(args);
}
}
function textOnCurve({ ctx, text, offset, G1, G2, G3, G4}){
const x1 = G1.x;
const y1 = G1.y;
const x2 = G2.x;
const y2 = G2.y;
const x3 = G3.x;
const y3 = G3.y;
const x4 = G3.x;
const y4 = G3.y;
ctx.save();
ctx.textAlign = "center";
var widths = [];
for (var i = 0; i < text.length; i++)
{
widths[widths.length] = ctx.measureText(text[i]).width;
}
ctx.beginPath();
var ch = curveHelper(x1, y1, x2, y2, x3, y3, x4, y4);
ctx.stroke();
var pos = offset;
var cpos = 0;
for (var j = 0; j < text.length; j++)
{
pos += widths[j] / 2;
cpos = ch.forward(pos);
ch.tangent(cpos);
ctx.setTransform(ch.vect.x, ch.vect.y, -ch.vect.y, ch.vect.x, ch.vec.x, ch.vec.y);
ctx.fillText(text[j], 0, 0);
pos += widths[j] / 2;
}
ctx.restore();
}
function curveHelper(x1, y1, x2, y2, x3, y3, x4, y4)
{
var tx1, ty1, tx2, ty2, tx3, ty3, tx4, ty4;
var a, b, c, u;
var vec, currentPos, vec1, vect, quad, currentDist;
vec = { x: 0, y: 0 } ;
vec1 = { x: 0, y: 0 } ;
vect = { x: 0, y: 0 } ;
quad = false;
currentPos = 0;
currentDist = 0;
if (x4 === undefined || x4 === null)
{
quad = true;
x4 = x3;
y4 = y3;
}
var estLen = Math.sqrt((x4 - x1)* (x4 - x1)+ (y4 - y1)* (y4 - y1));
var onePix = 1 / estLen;
function posAtC(c)
{
tx1 = x1; ty1 = y1;
tx2 = x2; ty2 = y2;
tx3 = x3; ty3 = y3;
tx1 += (tx2 - tx1)* c;
ty1 += (ty2 - ty1)* c;
tx2 += (tx3 - tx2)* c;
ty2 += (ty3 - ty2)* c;
tx3 += (x4 - tx3)* c;
ty3 += (y4 - ty3)* c;
tx1 += (tx2 - tx1)* c;
ty1 += (ty2 - ty1)* c;
tx2 += (tx3 - tx2)* c;
ty2 += (ty3 - ty2)* c;
vec.x = tx1 + (tx2 - tx1)* c;
vec.y = ty1 + (ty2 - ty1)* c;
return vec;
}
function posAtQ(c)
{
tx1 = x1; ty1 = y1;
tx2 = x2; ty2 = y2;
tx1 += (tx2 - tx1)* c;
ty1 += (ty2 - ty1)* c;
tx2 += (x3 - tx2)* c;
ty2 += (y3 - ty2)* c;
vec.x = tx1 + (tx2 - tx1)* c;
vec.y = ty1 + (ty2 - ty1)* c;
return vec;
}
function forward(dist)
{
var step;
helper.posAt(currentPos);
while (currentDist < dist)
{
vec1.x = vec.x;
vec1.y = vec.y;
currentPos += onePix;
helper.posAt(currentPos);
currentDist += step = Math.sqrt((vec.x - vec1.x)* (vec.x - vec1.x)+ (vec.y - vec1.y)* (vec.y - vec1.y));
}
currentPos -= ((currentDist - dist)/ step)* onePix
currentDist -= step;
helper.posAt(currentPos);
currentDist += Math.sqrt((vec.x - vec1.x)* (vec.x - vec1.x)+ (vec.y - vec1.y)* (vec.y - vec1.y));
return currentPos;
}
function tangentQ(pos)
{
a = (1 - pos)* 2;
b = pos * 2;
vect.x = a * (x2 - x1)+ b * (x3 - x2);
vect.y = a * (y2 - y1)+ b * (y3 - y2);
u = Math.sqrt(vect.x * vect.x + vect.y * vect.y);
vect.x /= u;
vect.y /= u;
}
function tangentC(pos)
{
a = (1 - pos)
b = 6 * a * pos;
a *= 3 * a;
c = 3 * pos * pos;
vect.x = -x1 * a + x2 * (a - b)+ x3 * (b - c)+ x4 * c;
vect.y = -y1 * a + y2 * (a - b)+ y3 * (b - c)+ y4 * c;
u = Math.sqrt(vect.x * vect.x + vect.y * vect.y);
vect.x /= u;
vect.y /= u;
}
var helper = {
vec: vec,
vect: vect,
forward: forward,
}
if (quad)
{
helper.posAt = posAtQ;
helper.tangent = tangentQ;
} else
{
helper.posAt = posAtC;
helper.tangent = tangentC;
}
return helper
}
}

That is certainly possible:
Rectangle {
id: control
width: Math.min(parent.height, parent.width)
height: width
anchors.centerIn: parent
color: "#40ff0000" //to see where it is going, which helps in positioning
property double startAngle: -45
property double endAngle: 45
Repeater {
model: 26
Text {
property double angle: control.startAngle + (control.endAngle - control.startAngle) * (index / 26)
x: (control.width / 2) * (1 + 0.9 * Math.cos(Math.PI * angle / 180)) - width * 0.5
y: (control.height / 2) * (1 + 0.9 * Math.sin(Math.PI * angle / 180)) - height * 0.5
text: String.fromCharCode(index + 65)
//rotation: angle
}
}
}
In the occasion you want to add a MouseArea to each text or change it to a button, this would also be a wise route to go.
Note that you will have to position the rectangle a bit with respect to your image.

Properly inject JavaScript functions inside of the QT project

I created the below image in html and JavaScript where the alphabets curve around the arc of the image. I am trying to convert the code I wrote and properly inject the functions inside of a QT project. However, my current implementation does not work due TypeError: Type errors. Can someone help with this?
Also if possible: I would like to rotate the alphabets to be vertical to the arc instead of horizontal.
import QtQuick 2.15
import QtQuick.Window 2.15
Window {
visible: true
width: 640
height: 480
title: qsTr("Hello World")
Canvas {
anchors.fill: parent
Image {
id: abcBar
source: "alphabetBar.png"
visible: false
}
onPaint: {
var ctx = getContext('2d');
ctx.save();
ctx.canvas.width = 160;
ctx.canvas.height = 432;
ctx.font = "18px Roboto";
ctx.textAlign = "center";
ctx.fillStyle = "#000000"
const centerX = 10;
const centerY = ctx.canvas.height / 2;
const angle = Math.PI;
const radius = 130
ctx.fillStyle = "#000000"
ctx.restore();
ctx.save();
ctx.drawImage(abcBar, 0, 0, ctx.canvas.width, ctx.canvas.height);
console.log('loaded')
ctx.restore();
const args = {
ctx,
text: "A • D • G • J • M • P • S • V • Z",
offset: 0,
G1: {
x: 20,
y: 80,
},
G2: {
x: 190,
y: 230,
},
G3: {
x: 0,
y: 372
},
}
textOnCurve(args);
}
}
function textOnCurve({ ctx, text, offset, G1, G2, G3, G4}){
const x1 = G1.x;
const y1 = G1.y;
const x2 = G2.x;
const y2 = G2.y;
const x3 = G3.x;
const y3 = G3.y;
const x4 = G3.x;
const y4 = G3.y;
ctx.save();
ctx.textAlign = "center";
var widths = [];
for (var i = 0; i < text.length; i++)
{
widths[widths.length] = ctx.measureText(text[i]).width;
}
ctx.beginPath();
var ch = curveHelper(x1, y1, x2, y2, x3, y3, x4, y4);
ctx.stroke();
var pos = offset;
var cpos = 0;
for (var j = 0; j < text.length; j++)
{
pos += widths[j] / 2;
cpos = ch.forward(pos);
ch.tangent(cpos);
ctx.setTransform(ch.vect.x, ch.vect.y, -ch.vect.y, ch.vect.x, ch.vec.x, ch.vec.y);
ctx.fillText(text[j], 0, 0);
pos += widths[j] / 2;
}
ctx.restore();
}
function curveHelper(x1, y1, x2, y2, x3, y3, x4, y4)
{
var tx1, ty1, tx2, ty2, tx3, ty3, tx4, ty4;
var a, b, c, u;
var vec, currentPos, vec1, vect, quad, currentDist;
vec = { x: 0, y: 0 } ;
vec1 = { x: 0, y: 0 } ;
vect = { x: 0, y: 0 } ;
quad = false;
currentPos = 0;
currentDist = 0;
if (x4 === undefined || x4 === null)
{
quad = true;
x4 = x3;
y4 = y3;
}
var estLen = Math.sqrt((x4 - x1)* (x4 - x1)+ (y4 - y1)* (y4 - y1));
var onePix = 1 / estLen;
function posAtC(c)
{
tx1 = x1; ty1 = y1;
tx2 = x2; ty2 = y2;
tx3 = x3; ty3 = y3;
tx1 += (tx2 - tx1)* c;
ty1 += (ty2 - ty1)* c;
tx2 += (tx3 - tx2)* c;
ty2 += (ty3 - ty2)* c;
tx3 += (x4 - tx3)* c;
ty3 += (y4 - ty3)* c;
tx1 += (tx2 - tx1)* c;
ty1 += (ty2 - ty1)* c;
tx2 += (tx3 - tx2)* c;
ty2 += (ty3 - ty2)* c;
vec.x = tx1 + (tx2 - tx1)* c;
vec.y = ty1 + (ty2 - ty1)* c;
return vec;
}
function posAtQ(c)
{
tx1 = x1; ty1 = y1;
tx2 = x2; ty2 = y2;
tx1 += (tx2 - tx1)* c;
ty1 += (ty2 - ty1)* c;
tx2 += (x3 - tx2)* c;
ty2 += (y3 - ty2)* c;
vec.x = tx1 + (tx2 - tx1)* c;
vec.y = ty1 + (ty2 - ty1)* c;
return vec;
}
function forward(dist)
{
var step;
helper.posAt(currentPos);
while (currentDist < dist)
{
vec1.x = vec.x;
vec1.y = vec.y;
currentPos += onePix;
helper.posAt(currentPos);
currentDist += step = Math.sqrt((vec.x - vec1.x)* (vec.x - vec1.x)+ (vec.y - vec1.y)* (vec.y - vec1.y));
}
currentPos -= ((currentDist - dist)/ step)* onePix
currentDist -= step;
helper.posAt(currentPos);
currentDist += Math.sqrt((vec.x - vec1.x)* (vec.x - vec1.x)+ (vec.y - vec1.y)* (vec.y - vec1.y));
return currentPos;
}
function tangentQ(pos)
{
a = (1 - pos)* 2;
b = pos * 2;
vect.x = a * (x2 - x1)+ b * (x3 - x2);
vect.y = a * (y2 - y1)+ b * (y3 - y2);
u = Math.sqrt(vect.x * vect.x + vect.y * vect.y);
vect.x /= u;
vect.y /= u;
}
function tangentC(pos)
{
a = (1 - pos)
b = 6 * a * pos;
a *= 3 * a;
c = 3 * pos * pos;
vect.x = -x1 * a + x2 * (a - b)+ x3 * (b - c)+ x4 * c;
vect.y = -y1 * a + y2 * (a - b)+ y3 * (b - c)+ y4 * c;
u = Math.sqrt(vect.x * vect.x + vect.y * vect.y);
vect.x /= u;
vect.y /= u;
}
var helper = {
vec: vec,
vect: vect,
forward: forward,
}
if (quad)
{
helper.posAt = posAtQ;
helper.tangent = tangentQ;
} else
{
helper.posAt = posAtC;
helper.tangent = tangentC;
}
return helper
}
}

The reference to Image on line 35 is not going to work because it is a browser-specific JavaScript class which is not available in the QML JavaScript runtime. Even though it seems like the QML Image class you have commented out should be referencable in the runtime, no QML components are directly referencable in JavaScript as classes like this.
You will need to port your code to use Canvas::loadImage() as documented here:
https://doc.qt.io/qt-5/qml-qtquick-canvas.html#loadImage-method
Or you can uncomment your QML Image object and call Context2d::drawImage() with its id as the first argument as documented here:
https://doc.qt.io/qt-5/qml-qtquick-context2d.html#drawImage-method-2
Note, if you do that, the Image will appear twice in the window unless you set visible: false on the QML one.

Adding gravity to billiard physics in JS canvas animation

I am trying to write aa small physics demo using Javascript. I have multiple balls that bounce off each other just fine, but things go wrong when I try to add gravity.
I am trying to conserve the momentum once they hit, but when I add constant gravity to each one, the physics start to break down.
Here is what I have in terms of code:
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; }
As you can see, I have checkCollision helper method, which calculates the kinetic energy and new velocities of a ball once it has collided with another ball. My update loop looks like this:
// 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)
}
How do I calculate aa gravity, while preventing the physics from exploding when the balls start stacking on top of each other?
It seems that the gravity force is colliding with the "checkCollision" method. The checkCollision method tries to move them back in place, but the constant gravity overwrites it and continues pulling them down.
EDIT: After some reading I understand some Verlet integration is in order, but am having difficulties with wrapping my head around it.
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)
}

Balls do not overlap
There is a fundamental flaw in the collision testing due to the fact that the collisions are calculated only when 2 balls overlap. In the real world this never happens.
The result of "collide on overlap" when many balls are interacting, will result in behavior that does not conserve the total energy of the system.
Resolve by order of collision
You can resolve collisions such that balls never overlap however the amount of processing is indeterminate per frame, growing exponentially as the density of balls increases.
The approach is to locate the first collision between balls in the time between frames. Resolve that collision and then with the new position of that collision find the next collision closest in time forward from the last. Do that until there are no pending collisions for that frame. (There is more to it than that) The result is that the simulation will never be in the impossible state where balls overlap.
Check out my Pool simulator on CodePen that uses this method to simulate pool balls. The balls can have any speed and always resolve correctly.
Verlet integration.
However you can reduce the noise using the overlapping collisions by using verlet integration which will keep the total energy of the balls at a more stable level.
To do that we introduce 2 new properties of the ball, px, py that hold the previous position of the ball.
Each frame we calculate the balls velocity as the difference between the current position and the new position. That velocity is used to do the calculations for the frame.
When a ball changes direction (hits wall or another ball) we also need to change the balls previous position to match where it would have been on the new trajectory.
Use constant time steps.
Using time steps based on time since last frame will also introduce noise and should not be used in the overlap collision method.
Reduce time, increase iteration
To further combat the noise you need to slow the overall speed of the balls to reduce the amount they overlay and thus more closely behave as if they collided at the point ballA.radius + ballB.radius apart. Also you should test every ball against every other ball, not just ball against balls above it in the balls array.
To keep the animation speed up you solve the ball V ball V wall collisions a few times per frame. The example does 5. The best value depends on the total energy of the balls, the level of noise that is acceptable, and the CPU power of the device its running on.
Accuracy matters
Your collision function is also way out there. I had a quick look and it did not look right. I added an alternative in the example.
When a ball hits a wall it does so at some time between the frames. You must move the ball away from the wall by the correct distance. Not doing so is like simulating a ball that sticks to a wall a tiny bit each time it hits, further diverging from what really happens.
Example
This is a rewrite of your original code. Click canvas to add some energy.
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>

How to change color of circle when collision detection occurs?

As far as I understood it seems that even after changing the color when the collision is detected it reverts back to blue due to the else statement when it is compared between other circle and they are not colliding. So how would you solve this so that that the instance when the collision between any circle occurs it changes to red
collision detection
this.update = function() {
for (let i = 0; i < circles.length; i++) {
if (this !== circles[i] && getDistance(this.x, this.y, circles[i].x, circles[i].y) <= 200 * 200) {
this.c = 'red';
circles[i].c = 'red';
resolveCollision(this, circles[i]);
} else {
this.c = 'blue';
circles[i].c = 'blue';
}
}
//wall deflection
if (this.x - this.r <= 0 || this.x + this.r >= innerWidth)
this.v.x *= -1
if (this.y - this.r <= 0 || this.y + this.r >= innerHeight)
this.v.y *= -1
this.x += this.v.x;
this.y += this.v.y;
this.draw();
};
//deflection amongst other circles
function resolveCollision(circle, othercircle) {
const xVelocityDiff = circle.v.x - othercircle.v.x;
const yVelocityDiff = circle.v.y - othercircle.v.y;
const xDist = othercircle.x - circle.x;
const yDist = othercircle.y - circle.y;
if (xVelocityDiff * xDist + yVelocityDiff * yDist >= 0) {
const angle = -Math.atan2(othercircle.y - circle.y, othercircle.x - circle.x);
const m1 = circle.m;
const m2 = othercircle.m;
const u1 = rotate(circle.v, angle);
const u2 = rotate(othercircle.v, angle);
const v1 = {
x: u1.x * (m1 - m2) / (m1 + m2) + u2.x * 2 * m2 / (m1 + m2),
y: u1.y
}
const v2 = {
x: u2.x * (m1 - m2) / (m1 + m2) + u1.x * 2 * m2 / (m1 + m2),
y: u2.y
}
const vFinal1 = rotate(v1, -angle);
const vFinal2 = rotate(v2, -angle);
circle.v.x = vFinal1.x;
circle.v.y = vFinal1.y;
othercircle.v.x = vFinal2.x;
othercircle.v.y = vFinal2.y;
}
}

Semaphores
Use a semaphore that holds the collision state of the circle.
Thus in your Circle.prototype would have something like these functions and properties
Circle.prototype = {
collided: false, // when true change color
draw() {
ctx.strokeStyle = this.collided ? "red" : "blue";
ctx.lineWidth = 3;
ctx.beginPath();
ctx.arc(this.x, this.y, this.r - 1.5, 0, Math.PI * 2);
ctx.stroke();
},
...
...
// in update
update() {
// when collision is detected set semaphore
if (collision) {
this.collided = true;
}
}
}
Counters
Or you may want to only have the color change last for some time. You can modify the semaphore and use it as a counter. On collision set it to the number of frames to change color for.
Circle.prototype = {
collided: 0,
draw() {
ctx.strokeStyle = this.collided ? (this.collided--, "red") : "blue";
ctx.lineWidth = 3;
ctx.beginPath();
ctx.arc(this.x, this.y, this.r - 1.5, 0, Math.PI * 2);
ctx.stroke();
},
...
...
// in update
update() {
// when collision is detected set semaphore
if (collision) {
this.collided = 60; // 1 second at 60FPS
}
}
}
Example
This example is taken from another answer I did earlier this year.
As there is a lot of code I have highlighted the relevant code with
/*= ANSWER CODE ==============================================================
...
=============================================================================*/
The example uses counters and changes color for 30 frames after a collision with another ball or wall.
I did not use a semaphore as all the balls would be red within a second.
canvas.width = innerWidth -20;
canvas.height = innerHeight -20;
mathExt(); // creates some additional math functions
const ctx = canvas.getContext("2d");
const GRAVITY = 0;
const WALL_LOSS = 1;
const BALL_COUNT = 10; // approx as will not add ball if space can not be found
const MIN_BALL_SIZE = 6;
const MAX_BALL_SIZE = 30;
const VEL_MIN = 1;
const VEL_MAX = 5;
const MAX_RESOLUTION_CYCLES = 100; // Put too many balls (or too large) in the scene and the
// number of collisions per frame can grow so large that
// it could block the page.
// If the number of resolution steps is above this value
// simulation will break and balls can pass through lines,
// get trapped, or worse. LOL
const SHOW_COLLISION_TIME = 30;
const balls = [];
const lines = [];
function Line(x1,y1,x2,y2) {
this.x1 = x1;
this.y1 = y1;
this.x2 = x2;
this.y2 = y2;
}
Line.prototype = {
draw() {
ctx.moveTo(this.x1, this.y1);
ctx.lineTo(this.x2, this.y2);
},
reverse() {
const x = this.x1;
const y = this.y1;
this.x1 = this.x2;
this.y1 = this.y2;
this.x2 = x;
this.y2 = y;
return this;
}
}
function Ball(x, y, vx, vy, r = 45, m = 4 / 3 * Math.PI * (r ** 3)) {
this.r = r;
this.m = m
this.x = x;
this.y = y;
this.vx = vx;
this.vy = vy;
/*= ANSWER CODE ==============================================================*/
this.collided = 0;
/*============================================================================*/
}
Ball.prototype = {
update() {
this.x += this.vx;
this.y += this.vy;
this.vy += GRAVITY;
},
draw() {
/*= ANSWER CODE ==============================================================*/
ctx.strokeStyle = this.collided ? (this.collided--, "#F00") : "#00F";
ctx.lineWidth = 3;
ctx.beginPath();
ctx.arc(this.x, this.y, this.r - 1.5, 0, Math.PI * 2);
ctx.stroke();
/* ============================================================================*/
},
interceptLineTime(l, time) {
const u = Math.interceptLineBallTime(this.x, this.y, this.vx, this.vy, l.x1, l.y1, l.x2, l.y2, this.r);
if (u >= time && u <= 1) {
return u;
}
},
checkBallBallTime(t, minTime) {
return t > minTime && t <= 1;
},
interceptBallTime(b, time) {
const x = this.x - b.x;
const y = this.y - b.y;
const d = (x * x + y * y) ** 0.5;
if (d > this.r + b.r) {
const times = Math.circlesInterceptUnitTime(
this.x, this.y,
this.x + this.vx, this.y + this.vy,
b.x, b.y,
b.x + b.vx, b.y + b.vy,
this.r, b.r
);
if (times.length) {
if (times.length === 1) {
if(this.checkBallBallTime(times[0], time)) { return times[0] }
return;
}
if (times[0] <= times[1]) {
if(this.checkBallBallTime(times[0], time)) { return times[0] }
if(this.checkBallBallTime(times[1], time)) { return times[1] }
return
}
if(this.checkBallBallTime(times[1], time)) { return times[1] }
if(this.checkBallBallTime(times[0], time)) { return times[0] }
}
}
},
collideLine(l, time) {
/*= ANSWER CODE ==============================================================*/
this.collided = SHOW_COLLISION_TIME;
/*============================================================================*/
const x1 = l.x2 - l.x1;
const y1 = l.y2 - l.y1;
const d = (x1 * x1 + y1 * y1) ** 0.5;
const nx = x1 / d;
const ny = y1 / d;
const u = (this.vx * nx + this.vy * ny) * 2;
this.x += this.vx * time;
this.y += this.vy * time;
this.vx = (nx * u - this.vx) * WALL_LOSS;
this.vy = (ny * u - this.vy) * WALL_LOSS;
this.x -= this.vx * time;
this.y -= this.vy * time;
},
collide(b, time) { // b is second ball
/*= ANSWER CODE ==============================================================*/
this.collided = SHOW_COLLISION_TIME;
b.collided = SHOW_COLLISION_TIME;
/*============================================================================*/
const a = this;
const m1 = a.m;
const m2 = b.m;
a.x = a.x + a.vx * time;
a.y = a.y + a.vy * time;
b.x = b.x + b.vx * time;
b.y = b.y + b.vy * time;
const x = a.x - b.x
const y = a.y - b.y
const d = (x * x + y * y);
const u1 = (a.vx * x + a.vy * y) / d
const u2 = (x * a.vy - y * a.vx ) / d
const u3 = (b.vx * x + b.vy * y) / d
const u4 = (x * b.vy - y * b.vx ) / d
const mm = m1 + m2;
const vu3 = (m1 - m2) / mm * u1 + (2 * m2) / mm * u3;
const vu1 = (m2 - m1) / mm * u3 + (2 * m1) / mm * u1;
b.vx = x * vu1 - y * u4;
b.vy = y * vu1 + x * u4;
a.vx = x * vu3 - y * u2;
a.vy = y * vu3 + x * u2;
a.x = a.x - a.vx * time;
a.y = a.y - a.vy * time;
b.x = b.x - b.vx * time;
b.y = b.y - b.vy * time;
},
doesOverlap(ball) {
const x = this.x - ball.x;
const y = this.y - ball.y;
return (this.r + ball.r) > ((x * x + y * y) ** 0.5);
}
}
function canAdd(ball) {
for(const b of balls) {
if (ball.doesOverlap(b)) { return false }
}
return true;
}
function create(bCount) {
lines.push(new Line(-10, 20, ctx.canvas.width + 10, 5));
lines.push((new Line(-10, ctx.canvas.height - 2, ctx.canvas.width + 10, ctx.canvas.height - 30)).reverse());
lines.push((new Line(30, -10, 4, ctx.canvas.height + 10)).reverse());
lines.push(new Line(ctx.canvas.width - 3, -10, ctx.canvas.width - 30, ctx.canvas.height + 10));
while (bCount--) {
let tries = 100;
while (tries--) {
const dir = Math.rand(0, Math.TAU);
const vel = Math.rand(VEL_MIN, VEL_MAX);
const ball = new Ball(
Math.rand(MAX_BALL_SIZE + 30, canvas.width - MAX_BALL_SIZE - 30),
Math.rand(MAX_BALL_SIZE + 30, canvas.height - MAX_BALL_SIZE - 30),
Math.cos(dir) * vel,
Math.sin(dir) * vel,
Math.rand(MIN_BALL_SIZE, MAX_BALL_SIZE),
);
if (canAdd(ball)) {
balls.push(ball);
break;
}
}
}
}
function resolveCollisions() {
var minTime = 0, minObj, minBall, resolving = true, idx = 0, idx1, after = 0, e = 0;
while (resolving && e++ < MAX_RESOLUTION_CYCLES) { // too main ball may create very lone resolution cycle. e limits this
resolving = false;
minObj = undefined;
minBall = undefined;
minTime = 1;
idx = 0;
for (const b of balls) {
idx1 = idx + 1;
while (idx1 < balls.length) {
const b1 = balls[idx1++];
const time = b.interceptBallTime(b1, after);
if (time !== undefined) {
if (time <= minTime) {
minTime = time;
minObj = b1;
minBall = b;
resolving = true;
}
}
}
for (const l of lines) {
const time = b.interceptLineTime(l, after);
if (time !== undefined) {
if (time <= minTime) {
minTime = time;
minObj = l;
minBall = b;
resolving = true;
}
}
}
idx ++;
}
if (resolving) {
if (minObj instanceof Ball) {
minBall.collide(minObj, minTime);
} else {
minBall.collideLine(minObj, minTime);
}
after = minTime;
}
}
}
create(BALL_COUNT);
mainLoop();
function mainLoop() {
ctx.clearRect(0,0,ctx.canvas.width, ctx.canvas.height);
resolveCollisions();
for (const b of balls) { b.update() }
for (const b of balls) { b.draw() }
ctx.lineWidth = 1;
ctx.strokeStyle = "#000";
ctx.beginPath();
for(const l of lines) { l.draw() }
ctx.stroke();
requestAnimationFrame(mainLoop);
}
function mathExt() {
Math.TAU = Math.PI * 2;
Math.rand = (min, max) => Math.random() * (max - min) + min;
Math.randI = (min, max) => Math.random() * (max - min) + min | 0; // only for positive numbers 32bit signed int
Math.randItem = arr => arr[Math.random() * arr.length | 0]; // only for arrays with length < 2 ** 31 - 1
// contact points of two circles radius r1, r2 moving along two lines (a,e)-(b,f) and (c,g)-(d,h) [where (,) is coord (x,y)]
Math.circlesInterceptUnitTime = (a, e, b, f, c, g, d, h, r1, r2) => { // args (x1, y1, x2, y2, x3, y3, x4, y4, r1, r2)
const A = a * a, B = b * b, C = c * c, D = d * d;
const E = e * e, F = f * f, G = g * g, H = h * h;
var R = (r1 + r2) ** 2;
const AA = A + B + C + F + G + H + D + E + b * c + c * b + f * g + g * f + 2 * (a * d - a * b - a * c - b * d - c * d - e * f + e * h - e * g - f * h - g * h);
const BB = 2 * (-A + a * b + 2 * a * c - a * d - c * b - C + c * d - E + e * f + 2 * e * g - e * h - g * f - G + g * h);
const CC = A - 2 * a * c + C + E - 2 * e * g + G - R;
return Math.quadRoots(AA, BB, CC);
}
Math.quadRoots = (a, b, c) => { // find roots for quadratic
if (Math.abs(a) < 1e-6) { return b != 0 ? [-c / b] : [] }
b /= a;
var d = b * b - 4 * (c / a);
if (d > 0) {
d = d ** 0.5;
return [0.5 * (-b + d), 0.5 * (-b - d)]
}
return d === 0 ? [0.5 * -b] : [];
}
Math.interceptLineBallTime = (x, y, vx, vy, x1, y1, x2, y2, r) => {
const xx = x2 - x1;
const yy = y2 - y1;
const d = vx * yy - vy * xx;
if (d > 0) { // only if moving towards the line
const dd = r / (xx * xx + yy * yy) ** 0.5;
const nx = xx * dd;
const ny = yy * dd;
return (xx * (y - (y1 + nx)) - yy * (x -(x1 - ny))) / d;
}
}
}
<canvas id="canvas"></canvas>

const collided = {
color: 'red',
get current() {
return this.color
},
set current(clr) {
if (this.color === 'red') {
this.color = 'blue'
} else {
this.color = 'red'
}
}
}
this.update= function(){
for(let i=0;i<circles.length;i++){
if(this!==circles[i] && getDistance(this.x,this.y,circles[i].x,circles[i].y)<=200*200){
this.c=collided.current
collided.current = this.c
circles[i].c=collided.current
resolveCollision(this,circles[i]);
}
// ...
}
}
The trick is to use use getters and setters to ensure that the most recently used color value is never reapplied

First, split the if:
// psudo-code
if this is not circles[i], then
if overlapping, then
do something
else
do something else
else
do nothing
Then, fix if this is not circles[i]:
{x:100,y:100}!={x:100,y:100}, so
either add id to circles and compare ids (my recommendation), or,
compare .xs and .ys (less desired - what if they are equal but not same circle?), or,
use JSON.stringify(a)==JSON.stringify(b).
I would add .overlapping and before the loop, I'd add another loop setting all .overlapping to false, then, withing the modified original loop, I'd check if .overlapping is false, and then if there is a collision, I'd set .overlapping to true for both.
Another way would be to create an array to hole overlapping circles' .ids and check if that array includes the current loop item's .id.