Develop Reference

P5.js curveVertex function is closing at a point

I've created a noise function that pairs with a circle function to create a random noise circle thing that looks pretty cool. My problem is the curveVertex function in P5.js works correctly except for the connection of the first and last vertex. My code is:
let start = Array(50).fill(0); // dont change
let amount = 1; // amount of shapes
let gap = 30; // between shapes
let amplify = 50; // 0 -->
let colorSpeed = 1; // 1 - 9
let colorSeparation = 3; // 0 - 80 recomended 0 - 10
function setup() {
createCanvas(windowWidth, windowHeight);
for(let i = 0 ; i < start.length; i++){
start[i] = random(i);
}
}
function draw() {
background(0);
for(let dnc = (amount + 1) * gap; dnc > gap; dnc -= gap){
drawNoiseCircle(dnc, getNoise(start.length));
}
start = start.map( c => c + 0.01 );
}
function getNoise(amount){
let lengths = [];
for(let i = 1; i < amount + 1; i++){
let n1 = noise(start[i - 1]);
let noise1 = map(n1, 0, 1, -amplify, amplify);
lengths.push(abs(-noise1));
}
return lengths;
}
function drawNoiseCircle(radius, lengths){
colorMode(HSB);
fill(((frameCount + radius) * colorSeparation)/-map(colorSpeed, 1, 10, -10, -1) % 360, 100, 50);
noStroke()
let x;
let y;
beginShape();
for(let l = 0; l < lengths.length; l++){
x = Math.cos(radians(l * 360 / lengths.length)) * (radius + lengths[l]) + width/2;
y = Math.sin(radians(l * 360 / lengths.length)) * (radius + lengths[l]) + height/2;
curveVertex(x, y);
}
endShape(CLOSE);
stroke("black");
line(width/2, height/2, width, height/2);
line(width/2, height/2 + 9, width, height/2 + 9);
}
<script src="https://cdn.jsdelivr.net/npm/p5#1.4.1/lib/p5.js"></script>
I understand the endShape(CLOSED) closes the shape with a straight line, but I'm not sure any other way to close the shape.
You can see the pointed edge on the right side, directly in the middle of the shape.
!EDIT!
I've added lines to the shape to show the line segment that isn't affected by the curve vertex. Also, I understand it may not be a very significant problem, but if the amount of vertexes shrink, it becomes a much bigger problem (eg. a square or a triangle).

Unfortunately I won't have time to dive deep and debug the actual issue with curveVertex (or it's math) at the time, but it seems there's something interesting with curveVertex() in particular.
#Ouoborus point makes sense and the function "should" behave that way (and it was with vertex(), but not curveVertex()). For some reason curveVertex() requires looping over the not just the first point again, but the second and third.
Here's basic example:
function setup() {
createCanvas(300, 300);
background(220);
let numPoints = 6;
let angleIncrement = TWO_PI / numPoints;
let radius = 120;
beginShape();
for(let i = 0 ; i < numPoints + 3; i++){
let angle = angleIncrement * i;
let x = 150 + cos(angle) * radius;
let y = 150 + sin(angle) * radius;
curveVertex(x, y);
}
endShape();
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.4.1/p5.min.js"></script>
Try decreasing numPoints + 3 to numPoints + 2 or notice the behaviour you're describing.
(I could speculate it might have something to do with how curveVertex() (Catmull-Rom splines) are implemented in p5 and how many coordinates/points it requires, but this isn't accurate without reading the source code and debugging a bit)
Here's a version of your code using the above notes:
let start = Array(30).fill(0);
let colorSpeed = 1; // 1 - 9
let colorSeparation = 3; // 0 - 80 recomended 0 - 10
function setup() {
createCanvas(600, 600);
colorMode(HSB);
noStroke();
// init noise seeds
for(let i = 0 ; i < start.length; i++){
start[i] = random(i);
}
}
function getNoise(seeds, amplify = 50){
let amount = seeds.length;
let lengths = [];
for(let i = 1; i < amount + 1; i++){
let n1 = noise(seeds[i - 1]);
let noise1 = map(n1, 0, 1, -amplify, amplify);
lengths.push(abs(-noise1));
}
return lengths;
}
function drawNoiseCircle(radius, lengths){
let sides = lengths.length;
let ai = TWO_PI / sides;
let cx = width * 0.5;
let cy = height * 0.5;
fill(((frameCount + radius) * colorSeparation)/-map(colorSpeed, 1, 10, -10, -1) % 360, 100, 50);
beginShape();
for(let i = 0 ; i < sides + 3; i++){
let noiseRadius = radius + lengths[i % sides];
let a = ai * i;
let x = cx + cos(a) * noiseRadius;
let y = cy + sin(a) * noiseRadius;
curveVertex(x, y);
}
endShape();
}
function draw() {
background(0);
// draw with updated perlin noise values
drawNoiseCircle(120, getNoise(start));
// increment noise seed
start = start.map( c => c + 0.01 );
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.4.1/p5.min.js"></script>

How to visualize Fourier series / Fourier coefficients?

I'm currently having difficulties at visualizing Fourier series. I tried the same thing about three times in order to find errors but in vain.
Now I even don't know what is wrong with my code or understanding of Fourier series.
What I'm trying to make is a thing like shown in the following Youtube video: https://youtu.be/r6sGWTCMz2k
I think I know what is Fourier series a bit. I can prove this by showing my previous works:
(1) square wave approximation
(2) parameter
So now I would like to draw more complicated thing in a parametric way. Please let me show the process I've walked.
① From svg path, get coordinates. For example,
// svg path
const d = 'M 0 0 L 20 30 L 10 20 ... ... ... Z';
↓
↓ convert with some processing...
↓
const cx = [0, 20, 10, ...]; // function Fx(t)
const cy = [0, 30, 20, ...]; // function Fy(t)
② Get Fourier coefficients from Fx(t), Fy(t), respectively. After that, I can get approximated coordinates by calculating Fourier series respectively by using the coefficients I got. For example,
Let's say I have a0_x, an_x, bn_x, a0_y, an_y, bn_y.
Then, Fx(t) = a0_x + an_x[1] * cos(1wt) + bn_x[1] * cos(1wt)
+ an_x[2] * cos(2wt) + bn_x[2] * cos(2wt) + ...;
Fy(t) = a0_y + an_y[1] * cos(1wt) + bn_y[1] * cos(1wt)
+ an_y[2] * cos(2wt) + bn_y[2] * cos(2wt) + ...;
Therefore a set of points (Fx(t), Fy(t)) is an approximated path!
This is all! Only thing left is just drawing!
Meanwhile, I processed the data in the following way:
const d = [svg path data];
const split = d.split(/[, ]/);
const points = get_points(split);
const normalized = normalize(points);
const populated = populate(normalized, 8);
const cx = populated.x; // Fx(t)
const cy = populated.y; // Fy(t)
/**
* This function does the below job.
* populate([0,3,6], 2) => output 0 12 3 45 6
* populate([0,4,8], 3) => output 0 123 4 567 8
*/
function populate(data, n) {
if (data.x.length <= 1) throw new Error('NotEnoughData');
if (n < 1) throw new Error('InvalidNValue');
const arr_x = new Array(data.x.length + (data.x.length - 1) * n);
const arr_y = new Array(data.y.length + (data.y.length - 1) * n);
for (let i = 0; i < data.x.length; i++) {
arr_x[i * (n + 1)] = data.x[i];
arr_y[i * (n + 1)] = data.y[i];
}
for (let i = 0; i <= arr_x.length - n - 1 - 1; i += (n + 1)) {
const x_interpolation = (arr_x[i + n + 1] - arr_x[i]) / (n + 1);
const y_interpolation = (arr_y[i + n + 1] - arr_y[i]) / (n + 1);
for (let j = 1; j <= n; j++) {
arr_x[i + j] = arr_x[i] + x_interpolation * j;
arr_y[i + j] = arr_y[i] + y_interpolation * j;
}
}
return { x: arr_x, y: arr_y };
}
// This function makes all values are in range of [-1, 1].
// I just did it... because I don't want to deal with big numbers (and not want numbers having different magnitude depending on data).
function normalize(obj) {
const _x = [];
const _y = [];
const biggest_x = Math.max(...obj.x);
const smallest_x = Math.min(...obj.x);
const final_x = Math.max(Math.abs(biggest_x), Math.abs(smallest_x));
const biggest_y = Math.max(...obj.y);
const smallest_y = Math.min(...obj.y);
const final_y = Math.max(Math.abs(biggest_y), Math.abs(smallest_y));
for (let i = 0; i < obj.x.length; i++) {
_x[i] = obj.x[i] / final_x;
_y[i] = obj.y[i] / final_y;
}
return { x: _x, y: _y };
}
// returns Fx(t) and Fy(t) from svg path data
function get_points(arr) {
const x = [];
const y = [];
let i = 0;
while (i < arr.length) {
const path_command = arr[i];
if (path_command === "M") {
x.push(Number(arr[i + 1]));
y.push(Number(arr[i + 2]));
i += 3;
} else if (path_command === 'm') {
if (i === 0) {
x.push(Number(arr[i + 1]));
y.push(Number(arr[i + 2]));
i += 3;
} else {
x.push(x.at(-1) + Number(arr[i + 1]));
y.push(y.at(-1) + Number(arr[i + 2]));
i += 3;
}
} else if (path_command === 'L') {
x.push(Number(arr[i + 1]));
y.push(Number(arr[i + 2]));
i += 3;
} else if (path_command === 'l') {
x.push(x.at(-1) + Number(arr[i + 1]));
y.push(y.at(-1) + Number(arr[i + 2]));
i += 3;
} else if (path_command === 'H') {
x.push(Number(arr[i + 1]));
y.push(y.at(-1));
i += 2;
} else if (path_command === 'h') {
x.push(x.at(-1) + Number(arr[i + 1]));
y.push(y.at(-1));
i += 2;
} else if (path_command === 'V') {
x.push(x.at(-1));
y.push(Number(arr[i + 1]));
i += 2;
} else if (path_command === 'v') {
x.push(x.at(-1));
y.push(y.at(-1) + Number(arr[i + 1]));
i += 2;
} else if (path_command === 'Z' || path_command === 'z') {
i++;
console.log('reached to z/Z, getting points done');
} else if (path_command === 'C' || path_command === 'c' || path_command === 'S' || path_command === 's' || path_command === 'Q' || path_command === 'q' || path_command === 'T' || path_command === 't' || path_command === 'A' || path_command === 'a') {
throw new Error('unsupported path command, getting points aborted');
} else {
x.push(x.at(-1) + Number(arr[i]));
y.push(y.at(-1) + Number(arr[i + 1]));
i += 2;
}
}
return { x, y };
}
Meanwhile, in order to calculate Fourier coefficients, I used numerical integration. This is the code.
/**
* This function calculates Riemann sum (area approximation using rectangles).
* #param {Number} div division number (= number of rectangles to be used)
* #param {Array | Function} subject subject of integration
* #param {Number} start where to start integration
* #param {Number} end where to end integration
* #param {Number} nth this parameter will be passed to 'subject'
* #param {Function} paramFn this parameter will be passed to 'subject'
* #returns {Number} numerical-integrated value
*/
function numerical_integration(div, subject, start, end, nth = null, paramFn = null) {
if (div < 1) throw new Error(`invalid div; it can't be 0 or 0.x`);
let sum = 0;
const STEP = 1 / div;
const isSubjectArray = Array.isArray(subject);
if (isSubjectArray) {
for (let t = start; t < end; t++) {
for (let u = 0; u < div; u++) {
sum += subject[t + 1] * STEP;
}
}
} else {
for (let t = start; t < end; t++) {
for (let u = 0; u < div; u++) {
const period = end - start;
const isParamFnArray = Array.isArray(paramFn);
if (isParamFnArray) sum += subject((t + 1), period, nth, paramFn) * STEP;
else sum += subject(((t + STEP) + STEP * u), period, nth, paramFn) * STEP;
}
}
}
return sum;
// console.log(numerical_integration(10, (x) => x ** 3, 0, 2));
}
The approximation is near. For (x) => x, division 10, from 0 to 2, the approximation is 2.1 while actual answer is 2. For (x) => x ** 2, division 10, from 0 to 2, the approximation is 2.87, while actual answer is 2.67. For (x) => x ** 3, division 10, from 0 to 2, the approximation is 4.41, while actual answer is 4.
And I found a0, an, bn by the following: (※ You can find Fourier coefficients formulas in my previous question)
/**
* This function will be passed to 'getAn' function.
* #param {Number} t this function is a function of time
* #param {Number} period period of a function to be integrated
* #param {Number} nth integer multiple
* #param {Array | Function} paramFn
* #returns {Number} computed value
*/
function fc(t, period, nth, paramFn) {
const isParamFnArray = Array.isArray(paramFn);
const w = 2 * Math.PI / period;
if (isParamFnArray) return paramFn[t] * Math.cos(nth * w * t);
else return paramFn(t) * Math.cos(nth * w * t);
}
// This function will be passed to 'getBn' function.
function fs(t, period, nth, paramFn) {
const isParamFnArray = Array.isArray(paramFn);
const w = 2 * Math.PI / period;
if (isParamFnArray) return paramFn[t] * Math.sin(nth * w * t);
else return paramFn(t) * Math.sin(nth * w * t);
}
/**
* This function returns a0 value.
* #param {Number} period period of a function to be integrated
* #param {Array | Function} intgFn function to be intergrated
* #param {Number} div number of rectangles to use
* #returns {Number} a0 value
*/
// Why * 30? in order to scale up
// Why - 1? because arr[arr.length] is undefined.
function getA0(period, intgFn, div) {
return 30 * numerical_integration(div, intgFn, 0, period - 1) / period;
}
/**
* This function returns an values.
* #param {Number} period period of a function to be integrated
* #param {Number} div number of rectangles to use
* #param {Number} howMany number of an values to be calculated
* #param {Array | Function} paramFn function to be integrated
* #returns {Array} an values
*/
function getAn(period, div, howMany, paramFn) {
const an = [];
for (let n = 1; n <= howMany; n++) {
const value = 30 * numerical_integration(div, fc, 0, period - 1, n, paramFn) * 2 / period;
an.push(value);
}
return an;
}
// This function returns bn values.
function getBn(period, div, howMany, paramFn) {
const bn = [];
for (let n = 1; n <= howMany; n++) {
const value = 30 * numerical_integration(div, fs, 0, period - 1, n, paramFn) * 2 / period;
bn.push(value);
}
return bn;
}
const xa0 = getA0(cx.length, cx, 10);
const xan = getAn(cx.length, 10, 100, cx);
const xbn = getBn(cx.length, 10, 100, cx);
const ya0 = getA0(cy.length, cy, 10);
const yan = getAn(cy.length, 10, 100, cy);
const ybn = getBn(cy.length, 10, 100, cy);
However, the result was not a thing I wanted... It was a weird shape... Maybe this is life...
The below is the canvas drawing code:
const $cvs = document.createElement('canvas');
const cctx = $cvs.getContext('2d');
$cvs.setAttribute('width', 1000);
$cvs.setAttribute('height', 800);
$cvs.setAttribute('style', 'border: 1px solid black;');
document.body.appendChild($cvs);
window.requestAnimationFrame(draw_tick);
// offset
const xoo = { x: 200, y: 600 }; // x oscillator offset
const yoo = { x: 600, y: 200 }; // y ~
// path
const path = [];
// drawing function
let deg = 0;
function draw_tick() {
const rAF = window.requestAnimationFrame(draw_tick);
// initialize
cctx.clearRect(0, 0, 1000, 800);
// y oscillator
const py = { x: 0, y: 0 };
// a0
// a0 circle
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.arc(yoo.x + py.x, yoo.y + py.y, Math.abs(ya0), 0, 2 * Math.PI);
cctx.stroke();
// a0 line
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.moveTo(yoo.x + py.x, yoo.y + py.y);
py.x += ya0 * Math.cos(0 * deg * Math.PI / 180);
py.y += ya0 * Math.sin(0 * deg * Math.PI / 180);
cctx.lineTo(yoo.x + py.x, yoo.y + py.y);
cctx.stroke();
// an
for (let i = 0; i < yan.length; i++) {
const radius = yan[i];
// an circles
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.arc(yoo.x + py.x, yoo.y + py.y, Math.abs(radius), 0, 2 * Math.PI);
cctx.stroke();
// an lines
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.moveTo(yoo.x + py.x, yoo.y + py.y);
py.x += radius * Math.cos((i+1) * deg * Math.PI / 180);
py.y += radius * Math.sin((i+1) * deg * Math.PI / 180);
cctx.lineTo(yoo.x + py.x, yoo.y + py.y);
cctx.stroke();
}
// bn
for (let i = 0; i < ybn.length; i++) {
const radius = ybn[i];
// bn circles
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.arc(yoo.x + py.x, yoo.y + py.y, Math.abs(radius), 0, 2 * Math.PI);
cctx.stroke();
// bn lines
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.moveTo(yoo.x + py.x, yoo.y + py.y);
py.x += radius * Math.cos((i+1) * deg * Math.PI / 180);
py.y += radius * Math.sin((i+1) * deg * Math.PI / 180);
cctx.lineTo(yoo.x + py.x, yoo.y + py.y);
cctx.stroke();
}
// x oscillator
const px = { x: 0, y: 0 };
// a0
// a0 circle
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.arc(yoo.x + py.x, yoo.y + py.y, Math.abs(xa0), 0, 2 * Math.PI);
cctx.stroke();
// a0 line
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.moveTo(yoo.x + py.x, yoo.y + py.y);
py.x += xa0 * Math.cos(0 * deg * Math.PI / 180);
py.y += xa0 * Math.sin(0 * deg * Math.PI / 180);
cctx.lineTo(yoo.x + py.x, yoo.y + py.y);
cctx.stroke();
// an
for (let i = 0; i < xan.length; i++) {
const radius = xan[i];
// an circles
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.arc(xoo.x + px.x, xoo.y + px.y, Math.abs(radius), 0, 2 * Math.PI);
cctx.stroke();
// an lines
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.moveTo(xoo.x + px.x, xoo.y + px.y);
px.x += radius * Math.cos((i+1) * deg * Math.PI / 180);
px.y += radius * Math.sin((i+1) * deg * Math.PI / 180);
cctx.lineTo(xoo.x + px.x, xoo.y + px.y);
cctx.stroke();
}
// bn
for (let i = 0; i < xbn.length; i++) {
const radius = xbn[i];
// bn circles
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.arc(xoo.x + px.x, xoo.y + px.y, Math.abs(radius), 0, 2 * Math.PI);
cctx.stroke();
// bn lines
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.moveTo(xoo.x + px.x, xoo.y + px.y);
px.x += radius * Math.cos((i+1) * deg * Math.PI / 180);
px.y += radius * Math.sin((i+1) * deg * Math.PI / 180);
cctx.lineTo(xoo.x + px.x, xoo.y + px.y);
cctx.stroke();
}
// y oscillator line
cctx.strokeStyle = 'black';
cctx.beginPath();
cctx.moveTo(yoo.x + py.x, yoo.y + py.y);
cctx.lineTo(xoo.x + px.x, yoo.y + py.y);
cctx.stroke();
// x oscillator line
cctx.strokeStyle = 'black';
cctx.beginPath();
cctx.moveTo(xoo.x + px.x, xoo.y + px.y);
cctx.lineTo(xoo.x + px.x, yoo.y + py.y);
cctx.stroke();
// path
path.push({ x: px.x, y: py.y });
cctx.beginPath();
cctx.strokeStyle = 'black';
cctx.moveTo(200 + path[0].x, 200 + path[0].y);
for (let i = 0; i < path.length; i++) {
cctx.lineTo(200 + path[i].x, 200 + path[i].y);
}
cctx.stroke();
// degree update
if (deg === 359) {
window.cancelAnimationFrame(rAF);
} else {
deg++;
}
}
So! I decided to be logical. First, I checked whether the converted path data is correct by drawing it at canvas. The below is the canvas code and the data.
let count = 0;
function draw_tick2() {
const rAF = window.requestAnimationFrame(draw_tick2);
const s = 100; // scale up
// initialize
cctx.clearRect(0, 0, 1000, 800);
cctx.beginPath();
// 200 has no meaning I just added it to move the path.
for (let i = 0; i < count; i++) {
if (i === 0) cctx.moveTo(200 + s * cx[i], 200 + s * cy[i]);
else cctx.lineTo(200 + s * cx[i], 200 + s * cy[i]);
}
cctx.stroke();
if (count < cx.length - 1) {
count++;
} else {
window.cancelAnimationFrame(rAF);
}
}
const paimon = 'm 0,0 -2.38235,-2.87867 -1.58823,-1.29045 -1.9853,-0.893384 -3.17647,-0.39706 1.58824,-1.98529 1.09191,-2.08456 v -2.38235 l -0.79412,-2.87868 1.88603,2.18383 1.6875,1.88602 1.78677,0.99265 1.78676,0.39706 1.78676,-0.19853 -1.6875,1.58824 -0.69485,1.68749 -0.0993,2.084564 0.39706,2.18383 9.62867,3.87132 2.77941,1.9853 4.66544,-1.09192 3.07721,-1.88603 1.9853,-2.58088 -3.97059,0.49633 -3.375,-0.79412 -2.87868,-2.58088 -2.08456,-3.077214 2.38235,1.48897 2.08456,0.19853 3.57353,-0.89338 2.58089,-2.48162 -3.07721,0.39706 -3.87132,-1.88603 -2.97794,-2.08456 -2.48162,-2.87868 -3.87133,-4.06985 -4.06985,-2.68015 -5.95588,-2.58088 -5.85662,-0.79412 -5.45956,0.99265 0.59559,1.6875 -0.99265,1.09191 -0.79412,3.47427 -1.29044,-2.97794 -0.89338,-1.19118 0.79412,-1.48897 1.6875,-0.79412 0.39706,-3.772057 1.48897,1.290441 1.78676,0.09926 -2.08456,-1.985293 1.78677,-0.893382 4.36765,-0.19853 4.86397,0.992648 1.19117,1.091912 -2.38235,1.985301 3.17647,-0.49633 2.87868,-2.680149 -3.57353,-2.580881 -5.45956,-1.488972 h -4.46691 l -3.6728,-3.176471 -0.79412,1.389706 -0.79411,-1.488969 0.69485,-0.595588 -1.58824,-3.871325 -0.39706,3.672795 -0.69485,0.297794 0.89338,1.091911 v 1.091912 h -1.19113 l -0.59559,-0.992648 -1.98529,2.878677 -4.06986,1.588236 -4.26838,1.985293 3.27574,3.871329 2.87867,1.88603 2.58088,0.29779 -2.58088,-1.58823 -0.89338,-2.084566 4.86397,-0.992645 -1.19118,2.382351 h 1.58824 l 1.48897,-1.88603 0.29779,2.77942 -2.38235,2.38235 -3.57353,2.87868 -3.97059,4.86397 -2.08456,3.67279 -2.58088,2.58088 -2.68015,1.09192 -3.17647,0.0993 -1.3897,-0.69485 1.09191,3.17647 2.18382,3.573534 3.375,2.38235 -1.78676,5.85662 -1.38971,6.05514 0.39706,4.36765 1.38971,4.66544 3.87132,4.46691 -0.79412,-3.57352 -0.49632,-4.06986 v -2.48162 l 1.78676,5.85662 3.07721,3.17647 3.07721,1.29044 3.37499,0.79412 2.28309,-0.89338 0.69486,-1.48897 -1.19118,0.49632 -2.48162,-1.98529 -2.28309,-2.87868 2.28309,2.48162 h 0.99265 l 0.69485,-0.49632 0.2978,-1.19118 0.0993,-0.79412 -0.89339,0.59559 -1.58823,-0.99265 -1.29044,-1.3897 -1.19118,-2.38236 -0.89338,-4.86397 -0.0993,-4.56617 0.29779,-4.96324 0.39706,0.89338 1.19118,-0.44669 0.0496,-0.89338 1.09191,0.69485 1.48897,0.2978 1.53861,0.89338 0.99264,0.64522 h -0.79411 l 0.49632,2.43199 -0.44669,1.58823 -1.78676,0.39706 -1.24081,-1.24081 -0.24817,-1.43934 0.84375,-0.94301 1.19118,-0.49633 1.14154,0.94302 0.24816,1.14154 -0.0993,1.48897 -1.83639,0.64523 -1.58824,-1.53861 -0.44669,-1.48897 -0.24816,-2.18382 -1.43934,0.99264 0.0496,-0.99264 -0.44669,1.78676 0.69485,3.12684 1.09192,4.26838 1.78676,1.78677 6.89889,3.02757 -2.53124,0.99265 -3.17647,1.3897 -0.79412,0.39706 0.59559,0.39706 1.34007,-0.69485 0.0496,1.19117 1.98529,-0.39705 2.68015,-0.44669 -0.2978,-1.93567 0.79412,1.58824 2.82905,-0.44669 4.06985,-1.34008 1.04229,-0.59559 -0.2978,-1.78676 -0.34743,-1.73713 -4.9136,2.48162 -2.58088,0.94301 -3.17648,-4.81434 1.53861,0.49633 1.3897,0.0496 1.43935,-0.24816 -1.34008,0.24816 h -1.58824 l -1.41452,-0.54596 3.12684,4.78953 2.63052,-0.89339 4.86397,-2.4568 2.65533,-2.08456 0.39706,-5.90625 -0.84375,1.5386 -1.14155,0.54596 -1.5386,0.19853 -1.29044,-0.89338 -0.59559,-1.09191 -0.24816,-1.73714 0.24816,-1.3897 -2.08456,0.54595 -0.29779,-0.34742 0.34743,-0.49633 0.64522,-0.39706 1.5386,-0.39705 2.18382,-0.19853 1.24081,0.0993 1.14154,0.54596 0.4467,1.43934 -0.19853,1.63786 -0.59559,1.29044 -1.24081,0.89339 -1.43934,-0.39706 -0.99264,-1.09191 -0.0496,-1.19118 0.79412,-0.89338 0.89338,-0.44669 1.19118,-0.0496 0.64522,1.04228 0.34742,0.79412 -0.14889,1.14155 0.99265,-0.4467 0.29779,-1.34007 -0.19853,-4.06985 -1.93566,-0.44669 -2.53125,-1.6875 -2.23346,-1.88603 -2.23345,-4.069864 -0.44669,3.920964 0.64522,4.21875 1.5386,3.92096 0.74448,0.44669 h -1.73713 l -2.18383,-0.54596 -3.12684,-2.08456 -1.58823,-2.28309 -1.14154,-2.08456 -1.29044,-3.871324 -1.38971,2.481624 -1.48897,2.63051 -0.94302,1.9853 3.8217,-6.948534 1.29044,3.672794 2.33272,3.92096 2.9283,2.13419 0.49633,0.44669 2.28309,0.49632 h 1.63787 l -0.69485,-0.69485 -0.84375,-1.93566 -1.34008,-5.80698 0.44669,-3.970594 2.33273,4.069854 4.56617,3.47426 2.08456,0.59559 0.19853,2.82905 -0.0496,3.97058 -0.0993,6.00552 -0.54595,3.02757 -1.58824,2.77941 -1.5386,0.89339 -1.19118,0.24816 -1.48897,-0.69485 -0.69485,-0.1489 0.69485,1.24081 1.43934,1.6875 2.68015,1.19117 3.17647,0.2978 3.77206,-2.23346 1.3897,-2.77941 0.89339,-3.82169 0.0496,-3.375 0.14889,6.25368 -1.14154,5.11213 -2.08456,3.27573 -2.08456,1.6875 -1.88603,0.59559 -2.28308,-0.79412 1.78676,1.6875 4.9136,1.88603 2.43199,0.2978 2.68015,-0.39706 2.72977,-1.09191 3.62317,-3.27574 0.89338,-3.97059 0.49632,-3.57353 -0.0993,-2.87867 -0.39706,-3.17647 -0.49632,-3.07721 1.98529,3.47427 1.19117,2.18382 0.39706,1.29044 0.39706,-2.28309 -0.39706,-3.0772 -1.29044,-3.77206 -1.29044,-2.87868 -1.6875,-3.27573 -10.125,-4.16912 z';
This is ★Paimon chan★ from a computer game 'Genshin Impact'. Thus it is proved that there are no flaws at the data, since all the data is plotted correctly.
Next, I plotted the approximated (Fx(t), Fy(t)) points so that I can check whether there is a problem. And It turned out that there was a problem. But I don't understand what is the problem. At the same time this path is interesting; The beginning part of the path seems like the hairpin.
This is the drawing code:
function approxFn(t) {
let x = xa0;
let y = ya0;
for (let i = 0; i < xan.length; i++) {
x += xan[i] * Math.cos(2 * Math.PI * i * t / cx.length);
x += xbn[i] * Math.sin(2 * Math.PI * i * t / cx.length);
y += yan[i] * Math.cos(2 * Math.PI * i * t / cx.length);
y += ybn[i] * Math.sin(2 * Math.PI * i * t / cx.length);
}
return { x, y };
}
function draw_tick3() {
const rAF = window.requestAnimationFrame(draw_tick3);
const s = 5;
// initialize
cctx.clearRect(0, 0, 1000, 800);
cctx.beginPath();
for (let t = 0; t < count; t++) {
if (count === 0) cctx.moveTo(200 + s * approxFn(t).x, 200 + s * approxFn(t).y);
else cctx.lineTo(200 + s * approxFn(t).x, 200 + s * approxFn(t).y);
}
cctx.stroke();
if (count < cx.length - 1) {
count++;
} else {
window.cancelAnimationFrame(rAF);
}
}
The above is all the code in my js file. In where I made a mistake? It's a mystery! I know this question is exceptionally seriously long question. But please help me! I want to realize Paimon chan! ㅠwㅠ
※ (This section is irrelevant with the question) Meanwhile I made a success to draw the path in a complex number plane. If you're interested, please see my work... I would like to add circle things to this but I have no idea what is 'radius' in this case.
// You can see that I used real part for x and imaginary part for y.
for (let i = 0; i <= count; i++) {
if (i === 0) {
cctx.moveTo(coords[i].real * scaler + paimonPosition, coords[i].imag * scaler + paimonPosition);
} else {
cctx.lineTo(coords[i].real * scaler + paimonPosition, coords[i].imag * scaler + paimonPosition);
}
}
And this is the result. But what makes me confused is a case of cn = -5000 ~ 5000. As far as I understand, more cn, more accurate as original wave. But why it crashes when cn is so big?
Anyways, thank you very much for reading this long question!

(the character shown: Paimon from Genshin Impact)
Hello myself!
First, errors in your code...
You did not consider a case where sequence of values come after drawing command. For example, your get_points function can't handle a case like h 0 1 2.
Current get_points function can't handle second m drawing command. You need to manually join strings if you have multiple paths.
You need to manually set m x y to m 0 0. Otherwise you can't see canvas drawing. (Maybe values are too too small to draw)
Second, in brief, you can't draw a shape with rotating vectors having fixed magnitude, if you approximate f(t) in a xy plane. It's because what you approximated is not a shape itself, but shape's coordinates.
Third, the reason you got weird shape when you tried to plot approximated data is at your approxFn() function.
x += xan[i] * Math.cos(2 * Math.PI * i * t / cx.length);
x += xbn[i] * Math.sin(2 * Math.PI * i * t / cx.length);
y += yan[i] * Math.cos(2 * Math.PI * i * t / cx.length);
y += ybn[i] * Math.sin(2 * Math.PI * i * t / cx.length);
not t, (t + 1) is correct. Your approximated data has no problem.
Fourth, so you need to take a complex plane approach if you want rotating vectors. In this case, the radius of circles are the magnitude of a sum vector of a real part vector and an imaginary part vector (Pythagorean theorem).
Fifth, In Cn formula, you missed 1 / T.
Sixth, The reason it crashed is... I don't know the exact reason but I think numerical integration and/or finding Cn is wrong. The new code I wrote don't crash at high Cn.
p.s. I wrote some writings about Fourier series. Please see if you are interested: https://logic-finder.github.io/memory/FourierSeriesExploration/opening/opening-en.html

Canvas problems. Not able to reproduce design

I need to build canvas animation like design requires. I spend almost 3 days but I'm not able to do anything like in design. Here a REQUESTED design!. And here - what I've got for now: current implementation which definitely not what requested from design .I need only animation of planet from particles at background (also whole process of animation changes in time, it starts from few particles but then amount growing and movings directions of particles changes)
here my current code:
export class CanvasComponent implements OnInit {
sphereRad = 280;
radius_sp = 1;
distance = 600;
particle_size = 0.7;
constructor() { }
ngOnInit() {
this.canvasApp();
}
canvasApp () {
const canvas = document.querySelector('canvas');
const context = canvas.getContext('2d');
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
let displayWidth;
let displayHeight;
let wait;
let count;
let numToAddEachFrame;
let particleList;
let recycleBin;
let particleAlpha;
let r, g, b;
let fLen;
let m;
let projCenterX;
let projCenterY;
let zMax;
let turnAngle;
let turnSpeed;
let sphereCenterX, sphereCenterY, sphereCenterZ;
let particleRad;
let zeroAlphaDepth;
let randAccelX, randAccelY, randAccelZ;
let gravity;
let rgbString;
// we are defining a lot of letiables used in the screen update functions globally so that they don't have to be redefined every frame.
let p;
let outsideTest;
let nextParticle;
let sinAngle;
let cosAngle;
let rotX, rotZ;
let depthAlphaFactor;
let i;
let theta, phi;
let x0, y0, z0;
// INITIALLI
const init = () => {
wait = 1;
count = wait - 1;
numToAddEachFrame = 30;
// particle color
r = 255;
g = 255;
b = 255;
rgbString = 'rgba(' + r + ',' + g + ',' + b + ','; // partial string for color which will be completed by appending alpha value.
particleAlpha = 1; // maximum alpha
displayWidth = canvas.width;
displayHeight = canvas.height;
fLen = this.distance; // represents the distance from the viewer to z=0 depth.
// projection center coordinates sets location of origin
projCenterX = displayWidth / 2;
projCenterY = displayHeight / 2;
// we will not draw coordinates if they have too large of a z-coordinate (which means they are very close to the observer).
zMax = fLen - 2;
particleList = {};
recycleBin = {};
// random acceleration factors - causes some random motion
randAccelX = 0.1;
randAccelY = 0.1;
randAccelZ = 0.1;
gravity = -0; // try changing to a positive number (not too large, for example 0.3), or negative for floating upwards.
particleRad = this.particle_size;
sphereCenterX = 0;
sphereCenterY = 0;
sphereCenterZ = -3 - this.sphereRad;
// alpha values will lessen as particles move further back, causing depth-based darkening:
zeroAlphaDepth = 0;
turnSpeed = 2 * Math.PI / 1200; // the sphere will rotate at this speed (one complete rotation every 1600 frames).
turnAngle = 0; // initial angle
// timer = setInterval(onTimer, 10 / 24);
onTimer();
}
const onTimer = () => {
// if enough time has elapsed, we will add new particles.
count++;
if (count >= wait) {
count = 0;
for (i = 0; i < numToAddEachFrame; i++) {
theta = Math.random() * 2 * Math.PI;
phi = Math.acos(Math.random() * 2 - 1);
x0 = this.sphereRad * Math.sin(phi) * Math.cos(theta);
y0 = this.sphereRad * Math.sin(phi) * Math.sin(theta);
z0 = this.sphereRad * Math.cos(phi);
// We use the addParticle function to add a new particle. The parameters set the position and velocity components.
// Note that the velocity parameters will cause the particle to initially fly outwards away from the sphere center (after
// it becomes unstuck).
const p = addParticle(x0, sphereCenterY + y0, sphereCenterZ + z0, 0.002 * x0, 0.002 * y0, 0.002 * z0);
// we set some 'envelope' parameters which will control the evolving alpha of the particles.
p.attack = 50;
p.hold = 50;
p.decay = 100;
p.initValue = 0;
p.holdValue = particleAlpha;
p.lastValue = 0;
// the particle will be stuck in one place until this time has elapsed:
p.stuckTime = 90 + Math.random() * 20;
p.accelX = 0;
p.accelY = gravity;
p.accelZ = 0;
}
}
// update viewing angle
turnAngle = (turnAngle + turnSpeed) % (2 * Math.PI);
sinAngle = Math.sin(turnAngle);
cosAngle = Math.cos(turnAngle);
// background fill
context.fillStyle = '#000000';
context.fillRect(0, 0, displayWidth, displayHeight);
// update and draw particles
p = particleList.first;
while (p != null) {
// before list is altered record next particle
nextParticle = p.next;
// update age
p.age++;
// if the particle is past its 'stuck' time, it will begin to move.
if (p.age > p.stuckTime) {
p.velX += p.accelX + randAccelX * (Math.random() * 2 - 1);
p.velY += p.accelY + randAccelY * (Math.random() * 2 - 1);
p.velZ += p.accelZ + randAccelZ * (Math.random() * 2 - 1);
p.x += p.velX;
p.y += p.velY;
p.z += p.velZ;
}
/*
We are doing two things here to calculate display coordinates.
The whole display is being rotated around a vertical axis, so we first calculate rotated coordinates for
x and z (but the y coordinate will not change).
Then, we take the new coordinates (rotX, y, rotZ), and project these onto the 2D view plane.
*/
rotX = cosAngle * p.x + sinAngle * (p.z - sphereCenterZ);
rotZ = -sinAngle * p.x + cosAngle * (p.z - sphereCenterZ) + sphereCenterZ;
// m = this.radius_sp * fLen / (fLen - rotZ);
m = this.radius_sp;
p.projX = rotX * m + projCenterX;
p.projY = p.y * m + projCenterY;
p.projZ = rotZ * m + projCenterX;
// update alpha according to envelope parameters.
if (p.age < p.attack + p.hold + p.decay) {
if (p.age < p.attack) {
p.alpha = (p.holdValue - p.initValue) / p.attack * p.age + p.initValue;
} else if (p.age < p.attack + p.hold) {
p.alpha = p.holdValue;
} else if (p.age < p.attack + p.hold + p.decay) {
p.alpha = (p.lastValue - p.holdValue) / p.decay * (p.age - p.attack - p.hold) + p.holdValue;
}
} else {
p.dead = true;
}
// see if the particle is still within the viewable range.
if ((p.projX > displayWidth) || (p.projX < 0) || (p.projY < 0) || (p.projY > displayHeight) || (rotZ > zMax)) {
outsideTest = true;
} else {
outsideTest = false;
}
if (outsideTest || p.dead ||
(p.projX > displayWidth / (2 + (1 - Math.random())) && p.projZ + displayWidth * 0.1 > displayWidth / 2) ||
(p.projX < displayWidth / (2 - (1 - Math.random())) && p.projZ + displayWidth * 0.25 < displayWidth / 2)
) {
recycle(p);
} else {
// depth-dependent darkening
// console.log(turnAngle, rotZ)
depthAlphaFactor = 1;
// depthAlphaFactor = (1 - (1.5 + rotZ / 100));
depthAlphaFactor = (depthAlphaFactor > 1) ? 1 : ((depthAlphaFactor < 0) ? 0 : depthAlphaFactor);
context.fillStyle = rgbString + depthAlphaFactor * p.alpha + ')';
// draw
context.beginPath();
context.arc(p.projX, p.projY, m * particleRad, 0, 2 * Math.PI, false);
context.closePath();
context.fill();
}
p = nextParticle;
}
window.requestAnimationFrame(onTimer);
}
const addParticle = (x0, y0, z0, vx0, vy0, vz0) => {
let newParticle;
// const color;
// check recycle bin for available drop:
if (recycleBin.first != null) {
newParticle = recycleBin.first;
// remove from bin
if (newParticle.next != null) {
recycleBin.first = newParticle.next;
newParticle.next.prev = null;
} else {
recycleBin.first = null;
}
} else {
newParticle = {};
}
// if the recycle bin is empty, create a new particle (a new empty object):
// add to beginning of particle list
if (particleList.first == null) {
particleList.first = newParticle;
newParticle.prev = null;
newParticle.next = null;
} else {
newParticle.next = particleList.first;
particleList.first.prev = newParticle;
particleList.first = newParticle;
newParticle.prev = null;
}
// initialize
newParticle.x = x0;
newParticle.y = y0;
newParticle.z = z0;
newParticle.velX = vx0;
newParticle.velY = vy0;
newParticle.velZ = vz0;
newParticle.age = 0;
newParticle.dead = false;
if (Math.random() < 0.5) {
newParticle.right = true;
} else {
newParticle.right = false;
}
return newParticle;
}
const recycle = (p) => {
// remove from particleList
if (particleList.first === p) {
if (p.next != null) {
p.next.prev = null;
particleList.first = p.next;
} else {
particleList.first = null;
}
} else {
if (p.next == null) {
p.prev.next = null;
} else {
p.prev.next = p.next;
p.next.prev = p.prev;
}
}
// add to recycle bin
if (recycleBin.first == null) {
recycleBin.first = p;
p.prev = null;
p.next = null;
} else {
p.next = recycleBin.first;
recycleBin.first.prev = p;
recycleBin.first = p;
p.prev = null;
}
};
init();
}
}
So I will be happy with any help also REWARD(for full implementation) is possible (ETH, BTC any currency you wish).

Filtering specific range of numbers from an array

I'm creating an algorithm that will blur the border of a canvas(image). Before applying the blur effect, I am creating an array filtered that includes all pixel values that needs to be blurred.
I've created an example with a 10×10px image.
function compute(w, h, bW) {
w *= 4;
var ignored = [];
for (y = bW; y < (h - bW); y++) {
for (x = 0; x < (w - (bW * 4 * 2)); x++) {
ignored.push(w * y + x + bW * 4);
}
}
console.log(ignored);
function range(limit) {
return Array.apply(null, Array(limit)).map(function(_, i) {
return i;
})
}
Array.prototype.diff = function(array) {
return this.filter(function(elem) {
return array.indexOf(elem) === -1;
})
}
var filtered = range(w * h).diff(ignored);
console.log(filtered);
return filtered;
}
compute(10, 10, 2);
//////////////////////////////////////////////////////////////////
// Below is just to display the numbers that are being filtered //
// Here, the size is 100 x 100 px with 10px border width //
//////////////////////////////////////////////////////////////////
var pixels = compute(100, 100, 10);
var c = document.getElementsByTagName('canvas')[0];
var ctx = c.getContext('2d');
var imgD = ctx.createImageData(100, 100);
for (var i = 0; i < imgD.data.length; i += 4) {
if (pixels.indexOf(i) > 0) {
imgD.data[i + 0] = 0;
imgD.data[i + 1] = 0;
imgD.data[i + 2] = 0;
imgD.data[i + 3] = 255;
} else {
imgD.data[i + 0] = 255;
imgD.data[i + 1] = 0;
imgD.data[i + 2] = 0;
imgD.data[i + 3] = 255;
}
}
ctx.putImageData(imgD, 10, 10);
<canvas></canvas>
The array filtered contains all the numbers that has the background color and ignored contains all the numbers that has the background color and in the image.
My question is:
How do I change my code so that the array filtered will have the numbers with background color and and not ?
An Example on a bit high resolution(65×65px):

FIDDLEJS : http://jsfiddle.net/t14gr6pL/2/
Explanation:
It depends on the width of your triangles (the second color). In the 64*64 example, this width is 7.
Let's assume that this width (tw) is calculate like this (you can change) :
var tw = (2 * bW) - 1;
So your code would be:
function compute(w, h, bW) {
var filtered = [];
var WIDTH_MULTIPLICATOR = 4;
var bH = bW;
w *= WIDTH_MULTIPLICATOR;
bW *= WIDTH_MULTIPLICATOR;
var triangleWidth = (2 * bW) - 1;
for (y = 0; y < h; y++) {
for (x = 0; x < w; x++) {
if (
// Borders
(Math.min(x, w - x) < bW) ||
(Math.min(y, h - y) < bH) ||
// Adding "Triangles"
(Math.min(x, w - x) < bW + triangleWidth - Math.max(0, Math.min(y, h - y) - bH) * WIDTH_MULTIPLICATOR)
) {
filtered.push(w * y + x);
}
}
}
return filtered;
}

2d collision weird freeze on collide

I have this weird problem. I'm trying to code some 2d collision and stumbled across a collision detection program. I decided to try translate it into javascript and maybe learn something along the way.
The thing is that when I run it in my browser, all circles freeze in place as soon as two of them collide, but the program don't crash and I get no errors in the console.
I've tried to debug it and I think the problem lays within the first if-statement in the checkForCollision-function. Like it's always false.
Here's a link to the original version (Scroll down to "Listing 3" for complete code):
http://compsci.ca/v3/viewtopic.php?t=14897&postdays=0&postorder=asc&start=0
And here is my translation:
var canvas = document.getElementById('canvas01');
var drawFps = document.getElementById('fps');
var context = canvas.getContext('2d');
// The amount of delay between frames
var delay = 50;
// The maximum distance two circles can be apart and still be considered colliding
var epsilon = 10^-9;
// The number of circles
var numCircles = 5;
// We anticipate many circles so we create an array
var circles = new Array();
// Stores the amount of time untill a collision occurs
var t;
// Initialize the circles
createCircle();
function createCircle() {
for(var i = 0; i < numCircles; i++) {
var velX = Math.floor(Math.random() * 5) + 1; // this will get a number between 1 and 5;
velX *= Math.floor(Math.random() * 2) == 1 ? 1 : -1; // this will add minus sign in 50% of cases
var velY = Math.floor(Math.random() * 5) + 1;
velY *= Math.floor(Math.random() * 2) == 1 ? 1 : -1;
var radius = Math.floor(Math.random() * 30) + 15;
var mass = Math.PI * Math.pow(radius, 2);
circleData = {
x : Math.floor(Math.random() * canvas.width),
y : Math.floor(Math.random() * canvas.height),
vx : velX,
vy : velY,
vxp : velX,
vyp : velY,
r : radius,
m : mass
}
circles.push(circleData);
}
}
setInterval(loop, 17);
// Returns the amount of frames untill a collision will occur
function timeToCollision() {
var t = Number.MAX_VALUE;
var A;
var B;
var C;
var D;
var DISC;
// Loop through every pair of circles and calculate when they will collide
for(var i = 0; i < circles.length; i++) {
for(var j = 0; j < circles.length; j++) {
if(movingToCircle (circles[i], circles[j])) {
// Breaking down the formula for t
A = Math.pow(circles[i].vx, 2) + Math.pow(circles[i].vy, 2) - 2 * circles[i].vx * circles[j].vx + Math.pow(circles[j].vx, 2) - 2 * circles[i].vy * circles[j].vy + Math.pow(circles[j].vy, 2);
B = -circles[i].x * circles[i].vx - circles[i].y * circles[i].vy + circles[i].vx * circles[j].x + circles[i].vy * circles[j].y + circles[i].x * circles[j].vx - circles[j].x * circles[j].vx + circles[i].y * circles[j].vy - circles[j].y * circles[j].vy;
C = Math.pow(circles[i].vx, 2) + Math.pow(circles[i].vy, 2) - 2 * circles[i].vx * circles[j].vx + Math.pow(circles[j].vx, 2) - 2 * circles[i].vy * circles[j].vy + Math.pow(circles[j].vy, 2);
D = Math.pow(circles[i].x, 2) + Math.pow(circles[i].y, 2) - Math.pow(circles[i].r, 2) - 2 * circles[i].x * circles[j].x + Math.pow(circles[j].x, 2) - 2 * circles[i].y * circles[j].y + Math.pow(circles[j].y, 2) - 2 * circles[i].r * circles[j].r - Math.pow(circles[j].r, 2);
DISC = Math.pow((-2 * B), 2) - 4 * C * D;
// If the discriminent if non negative, a collision will occur and
// we must compare the time to our current time of collision. We
// udate the time if we find a collision that has occurd earlier
// than the previous one.
if(DISC >= 0) {
// We want the smallest time
t = Math.min(Math.min(t, 0.5 * (2 * B - Math.sqrt(DISC)) / A), 0.5 * (2 * B + Math.sqrt(DISC)) / A)
}
}
}
}
return t;
}
// Draws all the circles to the screen
function drawCircles() {
for(var i = 0; i < circles.length; i++) {
context.fillStyle = '#000000';
context.beginPath();
context.arc(circles[i].x, circles[i].y, circles[i].r, 0, 2 * Math.PI, true);
context.closePath();
context.fill();
}
}
// Updates all the circles attributes. If a collision Occures in between frames,
// the circles will be updated to the point of the collision. We return when the
// collision occurs so that we can adjust the delay in the main loop.
function updateCircles() {
// We want to increment by at most one frame
var t = Math.min(1, timeToCollision());
for(var i = 0; i < circles.length; i++) {
circles[i].x += circles[i].vx * t;
circles[i].y += circles[i].vy * t;
}
return t;
}
// Collision reaction function
function collide(c1, c2) {
var nx = (c1.x - c2.x) / (c1.r + c2.r);
var ny = (c1.y - c2.y) / (c1.r + c2.r);
var a1 = c1.vx * nx + c1.vy * ny;
var a2 = c2.vx * nx + c2.vy * ny;
var p = 2 * (a1 - a2) / (c1.m + c2.m);
c1.vxp = c1.vx - p * nx * c2.m;
c1.vyp = c1.vy - p * ny * c2.m;
c2.vxp = c2.vx + p * nx * c1.m;
c2.vyp = c2.vy + p * ny * c1.m;
}
// Checks if a collision has occured between any of the circles
function checkForCollision() {
for(var i = 0; i < circles.length; i++) {
for(var j = 0; j < circles.length; j++) {
if(movingToCircle(circles[i], circles[j]) && Math.pow((circles[j].x - circles[i].x), 2) + Math.pow((circles[j].y - circles[i].y), 2) <= Math.pow((circles[i].r + circles[j].r + epsilon), 2)) {
collide(circles[i], circles[j]);
}
}
if(circles[i].x < 1 || circles[i].x > canvas.width) {
circles[i].vxp *= -1;
}
if(circles[i].y < 1 || circles[i].y > canvas.height) {
circles[i].vyp *= -1;
}
}
for(var i = 0; i < circles.length; i++) {
circles[i].vx = circles[i].vxp;
circles[i].vy = circles[i].vyp;
}
}
// Tells us if two circles are moving towards each other
function movingToCircle(c1, c2) {
// Position Vector dotted with the Relative Velocity Vector
return (c2.x - c1.x) * (c1.vx - c2.vx) + (c2.y - c1.y) * (c1.vy - c2.vy) > 0;
}
// Main animation loop
function loop() {
// Clear Canvas
context.fillStyle = '#ffffff';
context.fillRect( 0, 0, canvas.width, canvas.height );
drawCircles();
checkForCollision();
t = updateCircles();
}
Note that I've changed balls to circles just because I find it fits better for 2d.
Thank you in advance.