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Build a pyramid of balls using the canvas

I'm having difficulties replicating the pyramid below on the canvas.
I'm struggling with the math portion on how to draw a new ball on each new line. Here is my code so far.
<canvas id="testCanvas" width="300" height="300" style="border:1px solid #d3d3d3;"></canvas>
<script>
// Access canvas element and its context
const canvas = document.getElementById('testCanvas');
const context = canvas.getContext("2d");
const x = canvas.width;
const y = canvas.height;
const radius = 10;
const diamater = radius * 2;
const numOfRows = canvas.width / diamater;
function ball(x, y) {
context.arc(x, y, radius, 0, 2 * Math.PI, true);
context.fillStyle = "#FF0000"; // red
context.fill();
}
function draw() {
for (let i = 0; i < numOfRows; i++) {
for (let j = 0; j < i + 1; j++) {
ball(
//Pos X
(x / 2),
//Pos Y
diamater * (i + 1)
);
}
}
ball(x / 2, y);
context.restore();
}
draw();
</script>
I've been stuck on this problem for a while. I appreciate any assistance you can provide.
Thank you.

I noticed that the circle do not touch. I am not sure if you need or want them to but as this presented an interesting problem I create this answer.
Distance between stacked circles.
The distance between rows can be calculated using the right triangle as shown in the following image
Where R is the radius of the circle and D is the distance between rows.
D = ((R + R) ** 2 - R ** 2) ** 0.5;
With that we can get the number of rows we can fit given a radius as
S = (H - R * 2) / D;
Where H is the height of the canvas and S is the number of rows.
Example
Given a radius fits as many rows as possible into the give canvas height.
const ctx = canvas.getContext("2d");
const W = canvas.width, H = canvas.height, CENTER = W / 2;
const cols = ["#E80", "#0B0"];
draw();
function fillPath(path, x, y, color) {
ctx.fillStyle = color;
ctx.setTransform(1, 0, 0, 1, x, y);
ctx.fill(path);
}
function draw() {
const R = 10;
const D = ((R * 2) ** 2 - R ** 2) ** 0.5;
const S = (H - R * 2) / D | 0;
const TOP = R + (H - (R * 2 + D * S)) / 2; // center horizontal
const circle = new Path2D();
circle.arc(0, 0, R, 0, Math.PI * 2);
var y = 0, x;
while (y <= S) {
x = 0;
const LEFT = CENTER - (y * R);
while (x <= y) {
fillPath(circle, LEFT + (x++) * R * 2, TOP + y * D, cols[y % 2]);
}
y ++;
}
}
canvas {
border:1px solid #ddd;
}
<canvas id="canvas" width="300" height="180"></canvas>
Radius to fit n rows of stacked circles
Or if you have the height H and the number of rows S you want to fit. As shown in next image.
We want to find R given H and S we rearrange for H and solve the resulting quadratic with
ss = S * S - 2 * S + 1;
a = 4 / ss;
b = -4 * H / ss;
c = H * H / ss;
R = (-b-(b*b - 4 * a * c) ** 0.5) / (2 * a); // the radius
Example
Given the number of rows (number input) calculates the radius that will fit that number of rows
const ctx = canvas.getContext("2d");
const W = canvas.width, H = canvas.height, CENTER = W / 2;
rowsIn.addEventListener("input", draw)
const cols = ["#DD0", "#0A0"];
draw();
function fillPath(path, x, y, color) {
ctx.fillStyle = color;
ctx.setTransform(1, 0, 0, 1, x, y);
ctx.fill(path);
}
function draw() {
ctx.setTransform(1, 0, 0, 1, 0, 0);
ctx.clearRect(0,0,W,H);
const S = Number(rowsIn.value);
const ss = S * S - 2 * S + 1;
const a = 4 / ss - 3, b = -4 * H / ss, c = H * H / ss;
const R = (- b - ((b * b - 4 * a * c) ** 0.5)) / (2 * a); // the radius
const TOP = R;
const D = ((R * 2) ** 2 - R ** 2) ** 0.5;
//const S = (H - R * 2) / D;
const circle = new Path2D();
circle.arc(0, 0, R, 0, Math.PI * 2);
var y = 0, x;
while (y < S) {
x = 0;
const LEFT = CENTER - (y * R);
while (x <= y) {
fillPath(circle, LEFT + (x++) * R * 2, TOP + y * D, cols[y % 2]);
}
y ++;
}
}
canvas {
border:1px solid #ddd;
}
<canvas id="canvas" width="300" height="180"></canvas>
<input type="number" id="rowsIn" min="3" max="12" value="3">Rows

How you can approach this problem is by breaking it down into one step at a time.
On (1)st row draw 1 circle
On (2)nd row draw 2 circles
On (3)rd row draw 3 circles
And so on...
Then you have to figure out where to draw each circle. That also you can break down into steps.
1st-row 1st circle in the center (width)
2nd-row 1st circle in the center minus diameter
2nd-row 2nd circle in the center plus diameter
and so on.
Doing this way you will find a pattern to convert into 2 for loops.
Something like this:
//1st row 1st circle
ball(w/2,radius * 1, red);
//2nd row 1st circle
ball(w/2 - radius,radius * 3, blue);
//2nd row 2nd circle
ball(w/2 + radius,radius * 3, blue);
The code below shows each step how each ball is drawn. I have also done few corrections to take care of the numberOfRows.
const canvas = document.getElementById('testCanvas');
const context = canvas.getContext("2d");
const w = canvas.width;
const h = canvas.height;
const radius = 10;
const diamater = radius * 2;
const numOfRows = Math.min(h / diamater, w / diamater);
const red = "#FF0000";
const blue = "#0000FF";
var k = 1;
function ball(x, y, color) {
setTimeout(function() {
context.beginPath();
context.arc(x, y, radius, 0, 2 * Math.PI, true);
context.fillStyle = color;
context.fill();
}, (k++) * 250);
}
for (var i = 1; i <= numOfRows; i++) {
for (var j = 1; j <= i; j++) {
var y = (i * radius * 2) - radius;
var x = (w / 2) - ((i * radius) + radius) + (j * diamater);
ball(x, y, i % 2 ? red : blue);
}
}
<canvas id="testCanvas"
width="300" height="180"
style="border:1px solid #d3d3d3;"></canvas>

How can i get random colors for each object in canvas with JS?

I would like to get random colors for each object in canvas how can i do that, I have tried this:
for (var i = 0; i < 100; i++) {
var raza = (Math.random() - 0.001) * 30;
var x = Math.random() * (innerWidth - raza * 2) + raza;
var y = Math.random() * (innerHeight - raza * 2) + raza;
var dx = (Math.random() - 0.5) * 4; //calcul viteza X
var dy = (Math.random() - 0.5) * 4; //calcul viteza Y
var color = c.strokeStyle = "#" + ((1 << 24) * Math.random() | 0).toString(12);
cercArray.push(new Circle(x, y, dx, dy, raza, color));
}

Lots of different ways to do this, here is an example using HSL.
const canvas = document.querySelector('canvas');
const ctx = canvas.getContext('2d');
let lastDate = Date.now() - 500;
function draw() {
requestAnimationFrame(draw);
const color = {
h: Math.floor(Math.random() * 360),
s: Math.floor(Math.random() * 100),
v: Math.floor(Math.random() * 100)
};
if (lastDate + 500 < Date.now()) {
lastDate = Date.now();
ctx.fillStyle = `hsl(${color.h},${color.s}% ,${color.v}%)`;
ctx.fillRect(0, 0, 100, 100);
}
}
draw();
<canvas></canvas>

How to Convert an Array into an Object

I'm trying to make a circle from a radius and x,y coordinate. I have it all done except the array is not the correct format for my use.
I get:
[
"X_PROPS:40,Y_PROPS:0",
"X_PROPS:39.99390780625565,Y_PROPS:0.6980962574913405",
"X_PROPS:39.97563308076383,Y_PROPS:1.3959798681000388",
"X_PROPS:39.94518139018295,Y_PROPS:2.093438249717753"
]
but I need:
[
{X_PROPS:40,Y_PROPS:0},
{X_PROPS:39.99390780625565,Y_PROPS:0.6980962574913405},
{X_PROPS:39.97563308076383,Y_PROPS:1.3959798681000388},
{X_PROPS:39.94518139018295,Y_PROPS:2.093438249717753}
]
I tried this:
function spec(radius, steps, centerX, centerY){
var xValues = [centerX];
var yValues = [centerY];
var result = [];
for (var i = 0; i < steps; i++) {
xValues[i] = (centerX + radius * Math.cos(2 * Math.PI * i / steps));
yValues[i] = (centerY + radius * Math.sin(2 * Math.PI * i / steps));
result.push('X_PROPS:'+ xValues[i]+','+'Y_PROPS:'+ yValues[i]);
}
return result;
}
console.log(spec(40,360,0,0))

This expression 'X_PROPS:'+ xValues[i]+','+'Y_PROPS:'+ yValues[i] creates a string. Create an object literal instead:
function spec(radius, steps, centerX, centerY) {
var result = [];
for (var i = 0; i < steps; i++) {
result.push({
X_PROPS: (centerX + radius * Math.cos(2 * Math.PI * i / steps)),
Y_PROPS: (centerY + radius * Math.sin(2 * Math.PI * i / steps))
});
}
return result;
}
console.log(spec(40, 360, 0, 0))

Make a JavaScript canvas background transparent

Am trying to make the background of this Codepen transparent https://codepen.io/scorch/pen/BZjbmW. I would like to have the Swirls on the a different backgrounds, instead of the colored background that is on the stated Codepen.
I have tried add css code but that did not seem to do anything. I tried messing with the Canvas RGB and that did not seem to do anything either.
// create a canvas element
var canvas = document.createElement("canvas")
// attach element to DOM
document.getElementsByTagName("body")[0].appendChild(canvas)
// background color [r, g, b]
var bg = [20, 0, 30]
var wh = window.innerHeight
// get the canvas context (this is the part we draw to)
var ctx = canvas.getContext("2d")
function setup() {
// setup the canvas size to match the window
canvas.width = window.innerWidth
canvas.height = window.innerHeight
wh = window.innerWidth < window.innerHeight ? window.innerWidth : window.innerHeight
// set the 0,0 point to the middle of the canvas, this is not necessary but it can be handy
ctx.translate(canvas.width / 2, canvas.height / 2)
fill(bg, 1)
}
// fill entire canvas with a preset color
function fill(rgb, amt) {
ctx.beginPath(); // start path
ctx.rect(-canvas.width / 2, -canvas.height / 2, canvas.width, canvas.height) // set rectangle to be the same size as the window
ctx.fillStyle = `rgba(${rgb[0]}, ${rgb[1]}, ${rgb[2]}, ${amt})` // use the rgb array/color for fill, and amt for opacity
ctx.fill() // do the drawing
}
function drawCircle(x, y, r, color) {
ctx.beginPath()
ctx.arc(x, y, r, 0, 2 * Math.PI)
ctx.fillStyle = color || 'white'
ctx.fill()
ctx.closePath()
}
function Particle() {
// initialize loopers with random trange and offset
this.loop1 = new Looper(500 + 200 * Math.random(), 860 * Math.random())
this.loop2 = new Looper(320 + 70 * Math.random(), 20 * Math.random())
this.loop3 = new Looper(120 + 20 * Math.random(), 140 * Math.random())
this.history = []
this.history_max = 40
// this.x = null
// this.y = null
this.offset = Math.random() // some color offset for the color
this.draw = function() {
// set x,y, radius, and color params
var x = this.loop1.sin * (wh / 4 - 10) + this.loop2.sin * (wh / 6 - 10) + this.loop3.sin * 60
var y = this.loop1.cos * (wh / 4 - 10) + this.loop2.cos * (wh / 6 - 10) + this.loop3.cos * 10
var r = 0.2 + 3 * this.loop3.sinNorm * this.loop3.cosNorm // set the radius
var c = `hsla(${280 + 60 * (this.loop3.cosNorm + this.offset) * this.loop2.sinNorm}, ${100}%, ${50 + 10 * this.loop3.sin}%, ${1})`
ctx.beginPath()
ctx.strokeStyle = c
ctx.lineCap = 'round'
ctx.lineWidth = r
var tx = x
var ty = y
for (var i = 0; i < Math.min(this.history_max * this.loop3.cosNorm, this.history.length); i++) {
ctx.moveTo(tx, ty)
tx = this.history[i][0]
ty = this.history[i][1]
ctx.lineTo(tx, ty)
}
ctx.stroke()
drawCircle(x, y, r * 2 + 3, c); // draw the circle
this.loop1.update() // update looper
this.loop2.update() // update looper
this.loop3.update() // update looper
this.history.unshift([x, y])
if (this.history.length > this.history_max) {
this.history.pop()
}
}
}
// initialize a set of particle
var particles = []
for (var i = 0; i < 90; i++) {
particles.push(new Particle())
}
function draw() {
// fill context with background color
fill(bg, 0.36)
// update all the particles
for (var i = 0; i < particles.length; i++) {
particles[i].draw() // do it once
}
// this is a draw loop, this will execute frequently and is comparable to EnterFrame on other platform
window.requestAnimationFrame(function() {
draw()
})
}
// start enterFrame loop
window.requestAnimationFrame(draw);
// force running setup
setup()
// re-setup canvas when the size of the window changes
window.addEventListener("resize", setup)
// create a class to hold value and have built in incrementing functionality
function Looper(steps, start) {
this.val = start || 0 // set value to start value if defined, or 1
this.steps = steps || 100 // set steps to passed value or default to 100
this.norm = this.val / this.range // initialize normalized value (between 0 and 1)
this.sin = Math.sin(this.norm * Math.PI * 2) // get sine value from norm normalized to [0, 2PI]
this.sinNorm = (this.sin + 1) / 2 // normalize sin to [0,1]
this.cos = Math.cos(this.norm * Math.PI * 2) // get cosine value from norm normalized to [0, 2PI]
this.cosNorm = (this.cos + 1) / 2 // normalize cos to [0,1]
this.update = function() {
this.val = (this.val + 1) % this.steps // update value
this.norm = this.val / this.steps // update normalize value (between 0 and 1)
this.sin = Math.sin(this.norm * Math.PI * 2) // get sine value from norm normalized to [0, 2PI]
this.sinNorm = (this.sin + 1) / 2 // normalize sine to [0,1]
this.cos = Math.cos(this.norm * Math.PI * 2) // get cosine value from norm normalized to [0, 2PI]
this.cosNorm = (this.cos + 1) / 2 // normalize cos to [0,1]
}
}

ctx.fillStyle = rgba(255,255,255,0)
// create a canvas element
var canvas = document.createElement("canvas")
// attach element to DOM
document.getElementsByTagName("body")[0].appendChild(canvas)
// background color [r, g, b]
var bg = [20, 0, 30]
var wh = window.innerHeight
// get the canvas context (this is the part we draw to)
var ctx = canvas.getContext("2d")
function setup() {
// setup the canvas size to match the window
canvas.width = window.innerWidth
canvas.height = window.innerHeight
wh = window.innerWidth < window.innerHeight ? window.innerWidth : window.innerHeight
// set the 0,0 point to the middle of the canvas, this is not necessary but it can be handy
ctx.translate(canvas.width / 2, canvas.height / 2)
fill(bg, 1)
}
// fill entire canvas with a preset color
function fill(rgb, amt) {
ctx.beginPath(); // start path
ctx.rect(-canvas.width / 2, -canvas.height / 2, canvas.width, canvas.height) // set rectangle to be the same size as the window
ctx.fillStyle = `rgba(255,255,255,0)` // use the rgb array/color for fill, and amt for opacity
ctx.fill() // do the drawing
}
function drawCircle(x, y, r, color) {
ctx.beginPath()
ctx.arc(x, y, r, 0, 2 * Math.PI)
ctx.fillStyle = color || 'white'
ctx.fill()
ctx.closePath()
}
function Particle() {
// initialize loopers with random trange and offset
this.loop1 = new Looper(500 + 200 * Math.random(), 860 * Math.random())
this.loop2 = new Looper(320 + 70 * Math.random(), 20 * Math.random())
this.loop3 = new Looper(120 + 20 * Math.random(), 140 * Math.random())
this.history = []
this.history_max = 40
// this.x = null
// this.y = null
this.offset = Math.random() // some color offset for the color
this.draw = function() {
// set x,y, radius, and color params
var x = this.loop1.sin * (wh / 4 - 10) + this.loop2.sin * (wh / 6 - 10) + this.loop3.sin * 60
var y = this.loop1.cos * (wh / 4 - 10) + this.loop2.cos * (wh / 6 - 10) + this.loop3.cos * 10
var r = 0.2 + 3 * this.loop3.sinNorm * this.loop3.cosNorm // set the radius
var c = `hsla(${280 + 60 * (this.loop3.cosNorm + this.offset) * this.loop2.sinNorm}, ${100}%, ${50 + 10 * this.loop3.sin}%, ${1})`
ctx.beginPath()
ctx.strokeStyle = c
ctx.lineCap = 'round'
ctx.lineWidth = r
var tx = x
var ty = y
for (var i = 0; i < Math.min(this.history_max * this.loop3.cosNorm, this.history.length); i++) {
ctx.moveTo(tx, ty)
tx = this.history[i][0]
ty = this.history[i][1]
ctx.lineTo(tx, ty)
}
ctx.stroke()
drawCircle(x, y, r * 2 + 3, c); // draw the circle
this.loop1.update() // update looper
this.loop2.update() // update looper
this.loop3.update() // update looper
this.history.unshift([x, y])
if (this.history.length > this.history_max) {
this.history.pop()
}
}
}
// initialize a set of particle
var particles = []
for (var i = 0; i < 90; i++) {
particles.push(new Particle())
}
function draw() {
// fill context with background color
fill(bg, 0.36)
// update all the particles
for (var i = 0; i < particles.length; i++) {
particles[i].draw() // do it once
}
// this is a draw loop, this will execute frequently and is comparable to EnterFrame on other platform
window.requestAnimationFrame(function() {
draw()
})
}
// start enterFrame loop
window.requestAnimationFrame(draw);
// force running setup
setup()
// re-setup canvas when the size of the window changes
window.addEventListener("resize", setup)
// create a class to hold value and have built in incrementing functionality
function Looper(steps, start) {
this.val = start || 0 // set value to start value if defined, or 1
this.steps = steps || 100 // set steps to passed value or default to 100
this.norm = this.val / this.range // initialize normalized value (between 0 and 1)
this.sin = Math.sin(this.norm * Math.PI * 2) // get sine value from norm normalized to [0, 2PI]
this.sinNorm = (this.sin + 1) / 2 // normalize sin to [0,1]
this.cos = Math.cos(this.norm * Math.PI * 2) // get cosine value from norm normalized to [0, 2PI]
this.cosNorm = (this.cos + 1) / 2 // normalize cos to [0,1]
this.update = function() {
this.val = (this.val + 1) % this.steps // update value
this.norm = this.val / this.steps // update normalize value (between 0 and 1)
this.sin = Math.sin(this.norm * Math.PI * 2) // get sine value from norm normalized to [0, 2PI]
this.sinNorm = (this.sin + 1) / 2 // normalize sine to [0,1]
this.cos = Math.cos(this.norm * Math.PI * 2) // get cosine value from norm normalized to [0, 2PI]
this.cosNorm = (this.cos + 1) / 2 // normalize cos to [0,1]
}
}

Drawing parallel equidistant lines inside a circle

I'm trying to draw parallel equidistant lines inside a circle. I've got to the stage that if i connect points from their opposite angles on the circumference I get parallel lines... but they're not equidistant...
Here's some code:
var num_lines = 8;
var num_points = num_lines * 2;
var start_angle = 100;
var points = [];
var radius = 200;
ctx.strokeCircle(w/2, h/2, radius, radius); // shorthand for ctx.arc( x, y, 5, 0, Math.PI * 2, true );
for (var i = 0; i < num_points; i++) {
var angle = 360/num_points * i;
ctx.fillStyle = "red";
if (i %2 == 0 ) ctx.fillStyle = "blue";
var x = w/2 + Math.cos(angle) * radius/2;
var y = h/2 + Math.sin(angle) * radius/2;
ctx.circle(x, y, 10, 10); // shorthand for ctx.arc( x, y, 5, 0, Math.PI * 2, true );
points.push({x: x, y: y});
}
for (var i = 0; i < num_lines; i++) {
ctx.line(points[i].x, points[i].y, points[points.length-i-1].x, points[points.length-i-1].y)
}

Use Pythagoras' theorem.
The ...
y: vertical position of the line relative to the center
x: horizontal distance of its endpoints from the center
r: radius of the circle
... must satisfy y^2 + x^2 = r^2.
Code:
var radius = 200;
var num_lines = 8;
// vertical spacing
var delta_y = (2.0 * radius) / (num_lines + 1);
ctx.strokeCircle(w/2, h/2, radius, radius);
for (var i = 0; i < num_lines; i++)
{
// applying pythagoras
var y = delta_y * (i + 1) - radius / 2;
var x = Math.sqrt(radius * radius - y * y);
// calculating endpoints
var left_x = w / 2 - x;
var right_x = w / 2 + x;
var end_y = h / 2 + y;
ctx.fillStyle = (i % 2 == 0) ? "blue" : "red";
ctx.circle(left_x, end_y, 10, 10);
ctx.circle(right_x, end_y, 10, 10);
ctx.line(left_x, end_y, right_x, end_y);
}
EDIT: rotation
To rotate a vector by angle a clockwise:
x' = x * cos(a) + y * sin(a)
y' = y * cos(a) - x * sin(a)
Code:
var radius = 200;
var num_lines = 50;
var angle = 60;
// temporary variables
var delta_y = (2.0 * radius) / (num_lines);
var cos_a = Math.cos(angle * Math.PI / 180.0);
var sin_a = Math.sin(angle * Math.PI / 180.0);
ctx.strokeCircle(w / 2, h / 2, radius * 2, radius * 2);
for (var i = 0; i < num_lines; i++)
{
// applying pythagoras
var y = delta_y * i - radius;
var x = Math.sqrt(radius * radius - y * y);
// rotating the displacement vector
var left_x = y * sin_a + x * cos_a;
var right_x = y * sin_a - x * cos_a;
var left_y = y * cos_a - x * sin_a;
var right_y = y * cos_a + x * sin_a;
ctx.fillStyle = (i % 2 == 0) ? "blue" : "red";
ctx.line(w / 2 + left_x , h / 2 + left_y ,
w / 2 + right_x, h / 2 + right_y);
}

got it to work like so... wondering how I can rotate the lines at an angle (mathematically, not using ctx.translate and ctx.rotate ):
var radius = 200;
var num_lines = 50;
// vertical spacing
var delta_y = (2.0 * radius) / (num_lines);
ctx.strokeCircle(w/2, h/2, radius * 2, radius * 2);
for (var i = 0; i < num_lines; i++)
{
// applying pythagoras
var y = delta_y * (i) - radius;
var x = Math.sqrt(radius * radius - y * y);
// calculating endpoints
var left_x = w / 2 - x;
var right_x = w / 2 + x;
var end_y = h / 2 + y;
ctx.fillStyle = (i % 2 == 0) ? "blue" : "red";
ctx.line(left_x, end_y, right_x, end_y);
}