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I would like to create an isometric 3D cube with fillRect whose 3 faces have the same dimensions as the image below:
Edit: I want to do it with fillRect. The reason for this is that I will draw images on the 3 faces of the cube afterwards. This will be very easy to do since I will use exactly the same transformations as for drawing the faces.
Edit 2: I didn't specify that I want to avoid using an external library so that the code is as optimized as possible. I know that it is possible to calculate the 3 matrices beforehand to draw the 3 faces and make a perfect isometric cube.
Edit 3: As my example code showed, I want to be able to set the size of the side of the isometric cube on the fly (const faceSize = 150).
I have a beginning of code but I have several problems:
The faces are not all the same dimensions
I don't know how to draw the top face
const faceSize = 150;
const canvas = document.querySelector('canvas');
const ctx = canvas.getContext('2d');
const centerX = canvas.width / 2;
const centerY = canvas.height / 2;
// Top Face (not big enough)
ctx.save();
ctx.translate(centerX, centerY);
ctx.scale(1, .5);
ctx.rotate(-45 * Math.PI / 180);
ctx.fillStyle = 'yellow';
ctx.fillRect(0, -faceSize, faceSize, faceSize);
ctx.restore();
// Left Face (not high enough)
ctx.save();
ctx.translate(centerX, centerY);
ctx.transform(1, .5, 0, 1, 0, 0);
ctx.fillStyle = 'red';
ctx.fillRect(-faceSize, 0, faceSize, faceSize);
ctx.restore();
// Right Face (not high enough)
ctx.save();
ctx.translate(centerX, centerY);
ctx.transform(1, -.5, 0, 1, 0, 0);
ctx.fillStyle = 'blue';
ctx.fillRect(0, 0, faceSize, faceSize);
ctx.restore();
<canvas width="400" height="400"></canvas>
I used a large part of #enhzflep's code which I adapted so that the width of the cube is dynamically changeable.
All the code seems mathematically correct, I just have a doubt about the value 1.22 given as a parameter to scaleSelf. Why was this precise value chosen?
Here is the code:
window.addEventListener('load', onLoad, false);
const canvas = document.createElement('canvas');
function onLoad() {
//canvas.width = cubeWidth;
//canvas.height = faceSize * 2;
canvas.width = 400;
canvas.height = 400;
document.body.appendChild(canvas);
drawCube(canvas);
}
function drawCube() {
const scale = Math.abs(Math.sin(Date.now() / 1000) * canvas.width / 200); // scale effect
const faceSize = 100 * scale;
const radians = 30 * Math.PI / 180;
const cubeWidth = faceSize * Math.cos(radians) * 2;
const centerPosition = {
x: canvas.width / 2,
y: canvas.height / 2
};
const ctx = canvas.getContext('2d');
ctx.save();
ctx.fillStyle = '#000';
ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
const defaultMat = [1, 0, 0, 1, 0, 0];
// Left (red) side
const leftMat = new DOMMatrix(defaultMat);
leftMat.translateSelf(centerPosition.x - cubeWidth / 2, centerPosition.y - faceSize / 2);
leftMat.skewYSelf(30);
ctx.setTransform(leftMat);
ctx.fillStyle = '#F00';
ctx.fillRect(0, 0, cubeWidth / 2, faceSize);
// Right (blue) side
const rightMat = new DOMMatrix(defaultMat);
rightMat.translateSelf(centerPosition.x, centerPosition.y);
rightMat.skewYSelf(-30);
ctx.setTransform(rightMat);
ctx.fillStyle = '#00F';
ctx.fillRect(0, 0, cubeWidth / 2, faceSize);
// Top (yellow) side
const topMat = new DOMMatrix(defaultMat);
const toOriginMat = new DOMMatrix(defaultMat);
const fromOriginMat = new DOMMatrix(defaultMat);
const rotMat = new DOMMatrix(defaultMat);
const scaleMat = new DOMMatrix(defaultMat);
toOriginMat.translateSelf(-faceSize / 2, -faceSize / 2);
fromOriginMat.translateSelf(centerPosition.x, centerPosition.y - faceSize / 2);
rotMat.rotateSelf(0, 0, -45);
scaleMat.scaleSelf(1.22, (faceSize / cubeWidth) * 1.22);
topMat.preMultiplySelf(toOriginMat);
topMat.preMultiplySelf(rotMat);
topMat.preMultiplySelf(scaleMat);
topMat.preMultiplySelf(fromOriginMat);
ctx.setTransform(topMat);
ctx.fillStyle = '#FF0';
ctx.fillRect(0, 0, faceSize, faceSize);
ctx.restore();
requestAnimationFrame(drawCube);
}
Here's a quick n dirty approach to the problem. It's too hot here for me to really think very clearly about this question. (I struggle with matrix maths too)
There's 2 things I think worth mentioning, each of which has an effect on the scaling operation.
width and height of the finished figure (and your posted example image) are different.
I think it's the ratio of the distance between (opposite) corners of the untransformed rectangle which fills 1/4 of the canvas, and the finished yellow side which affect the scaling.
Also, note that I'm drawing a square of canvas.height/2 sidelength for the yellow side, whereas I was drawing a rectangle for the red and blue sides.
In the scaling section, width/4 and height/4 are both shorthand for (width/2)/2 and (height/2)/2. width/2 and height/2 give you a rectangle filling 1/2 of the canvas, with a centre (middle of the square) located at (width/2)/2, (height/2)/2 - height/4 means something different in the translation section (even though it's the same number)
With that said, here's the sort of thing I was talking about earlier.
"use strict";
window.addEventListener('load', onLoaded, false);
function onLoaded(evt)
{
let width = 147;
let height = 171;
let canvas = document.createElement('canvas');
canvas.width = width;
canvas.height = height;
document.body.appendChild(canvas);
drawIsoDemo(canvas);
}
function drawIsoDemo(destCanvas)
{
let ctx = destCanvas.getContext('2d');
let width = destCanvas.width;
let height = destCanvas.height;
ctx.fillStyle = '#000';
ctx.fillRect(0,0,width,height);
var idMatVars = [1,0, 0,1, 0,0];
// left (red) side
let leftMat = new DOMMatrix( idMatVars );
leftMat.translateSelf( 0, 0.25*height );
leftMat.skewYSelf(30);
ctx.save();
ctx.transform( leftMat.a, leftMat.b, leftMat.c, leftMat.d, leftMat.e, leftMat.f);
ctx.fillStyle = '#F00';
ctx.fillRect(0,0,width/2,height/2);
ctx.restore();
// right (blue) side
let rightMat = new DOMMatrix( idMatVars );
rightMat.translateSelf( 0.5*width, 0.5*height );
rightMat.skewYSelf(-30);
ctx.save();
ctx.transform( rightMat.a, rightMat.b, rightMat.c, rightMat.d, rightMat.e, rightMat.f);
ctx.fillStyle = '#00F';
ctx.fillRect(0,0,width/2,height/2);
ctx.restore();
// top (yellow) side
let topMat = new DOMMatrix( idMatVars );
let toOriginMat = new DOMMatrix( idMatVars );
let fromOriginMat = new DOMMatrix(idMatVars);
let rotMat = new DOMMatrix(idMatVars);
let scaleMat = new DOMMatrix(idMatVars);
toOriginMat.translateSelf(-height/4, -height/4);
fromOriginMat.translateSelf(width/2,height/4);
rotMat.rotateSelf(0,0,-45);
scaleMat.scaleSelf(1.22,((height/2)/width)*1.22);
topMat.preMultiplySelf(toOriginMat);
topMat.preMultiplySelf(rotMat);
topMat.preMultiplySelf(scaleMat);
topMat.preMultiplySelf(fromOriginMat);
ctx.save();
ctx.transform( topMat.a, topMat.b, topMat.c, topMat.d, topMat.e, topMat.f);
ctx.fillStyle = '#FF0';
ctx.fillRect(0,0,height/2,height/2);
ctx.restore();
}
If we overlay a circle on your isometric cube, we can see that the outer vertices are spaced equally apart. In fact it's always 60°, which is no wonder as it's a hexagon.
So all we have to do is obtaining the coordinates for the outer vertices. This is quite easy as we can make a further assumption: if you look at the shape again, you'll notice that the length of each of the cube's sides seems to be the radius of the circle.
With the help of a little trigonometry and a for-loop which increments by 60 degrees, we can put calculate and put all those vertices into an array and finally connect those vertices to draw the cube.
Here's an example:
let canvas = document.getElementById("canvas");
let ctx = canvas.getContext("2d");
function drawCube(x, y, sideLength) {
let vertices = [new Point(x, y)];
for (let a = 0; a < 6; a++) {
vertices.push(new Point(x + Math.cos(((a * 60) - 30) * Math.PI / 180) * sideLength, y + Math.sin(((a * 60) - 30) * Math.PI / 180) * sideLength));
}
ctx.fillStyle = "#ffffff";
ctx.beginPath();
ctx.moveTo(vertices[0].x, vertices[0].y);
ctx.lineTo(vertices[5].x, vertices[5].y);
ctx.lineTo(vertices[6].x, vertices[6].y);
ctx.lineTo(vertices[1].x, vertices[1].y);
ctx.lineTo(vertices[0].x, vertices[0].y);
ctx.fill();
ctx.fillStyle = "#a0a0a0";
ctx.beginPath();
ctx.moveTo(vertices[0].x, vertices[0].y);
ctx.lineTo(vertices[1].x, vertices[1].y);
ctx.lineTo(vertices[2].x, vertices[2].y);
ctx.lineTo(vertices[3].x, vertices[3].y);
ctx.lineTo(vertices[0].x, vertices[0].y);
ctx.fill();
ctx.fillStyle = "#efefef";
ctx.beginPath();
ctx.moveTo(vertices[0].x, vertices[0].y);
ctx.lineTo(vertices[3].x, vertices[3].y);
ctx.lineTo(vertices[4].x, vertices[4].y);
ctx.lineTo(vertices[5].x, vertices[5].y);
ctx.lineTo(vertices[0].x, vertices[0].y);
ctx.fill();
}
class Point {
constructor(x, y) {
this.x = x;
this.y = y;
}
}
drawCube(200, 150, 85);
canvas {
background: #401fc1;
}
<canvas id="canvas" width="400" height="300"></canvas>
EDIT
What you want to achieve is ain't that easily simply because the CanvasRenderingContext2D API actually does not offer a skewing/shearing transform.
Nevertheless with the help of a third-party library we're able to transform the three sides in an orthographic way. It's called perspective.js
Still we need to calculate the outer vertices but instead of using the moveTo/lineTo commands, we forward the coordinates to perspective.js to actually do the perspective distortion of some source images.
Here's another example:
let canvas = document.getElementById("canvas");
let ctx = canvas.getContext("2d");
class Point {
constructor(x, y) {
this.x = x;
this.y = y;
}
}
function drawCube(x, y, sideLength) {
let vertices = [new Point(x, y)];
for (let a = 0; a < 6; a++) {
vertices.push(new Point(x + Math.cos(((a * 60) - 30) * Math.PI / 180) * sideLength, y + Math.sin(((a * 60) - 30) * Math.PI / 180) * sideLength));
}
let p = new Perspective(ctx, images[0]);
p.draw([
[vertices[5].x, vertices[5].y],
[vertices[6].x, vertices[6].y],
[vertices[1].x, vertices[1].y],
[vertices[0].x, vertices[0].y]
]);
p = new Perspective(ctx, images[1]);
p.draw([
[vertices[0].x, vertices[0].y],
[vertices[1].x, vertices[1].y],
[vertices[2].x, vertices[2].y],
[vertices[3].x, vertices[3].y]
]);
p = new Perspective(ctx, images[2]);
p.draw([
[vertices[4].x, vertices[4].y],
[vertices[5].x, vertices[5].y],
[vertices[0].x, vertices[0].y],
[vertices[3].x, vertices[3].y]
]);
}
function loadImages(index) {
let image = new Image();
image.onload = function(e) {
images.push(e.target);
if (index + 1 < sources.length) {
loadImages(index + 1);
} else {
drawCube(200, 150, 125, e.target);
}
}
image.src = sources[index];
}
let sources = ["https://picsum.photos/id/1079/200/300", "https://picsum.photos/id/76/200/300", "https://picsum.photos/id/79/200/300"];
let images = [];
loadImages(0);
canvas {
background: #401fc1;
}
<script src="https://cdn.rawgit.com/wanadev/perspective.js/master/dist/perspective.min.js"></script>
<canvas id="canvas" width="400" height="300"></canvas>
I would like to be able to simulate the movement of the body on a "carousel" with respect to physics. (centripetal, centrifugal force, angular speed). Below is some sample code.
<!DOCTYPE html>
<html>
<head>
<script>
var rotate = Math.PI / 180;
var ballRotation = 1;
function drawthis() {
var friction = 0.5;
context.setTransform(1, 0, 0, 1, 0, 0);
context.clearRect(0, 0, cvs.width, cvs.height);
context.translate(350, 350);
context.rotate(rotate);
context.beginPath();
context.arc(1, 1, 12, 0, 2 * Math.PI, false);
context.fill();
context.beginPath();
context.arc(0, 0, 150, 0, Math.PI * 2, false);
context.lineWidth = 6;
context.stroke();
motion = ballRotation - friction;
rotate += motion;
requestAnimationFrame(drawthis);
}
function init() {
cvs = document.getElementById("canvas");
context = cvs.getContext("2d");
context.clearRect(0, 0, context.width, context.height);
context.fillStyle = "#ff0000";
requestAnimationFrame(drawthis);
}
</script>
</head>
<body onload="init()">
<canvas id="canvas" width="800" height="800"></canvas>
</body>
</html>
I mean something like this
Ball on a turn table
Below you will find a simple simulation of a point sliding on a turning wheel. The point represents the contact point of a ball.
The simulation ignores the fact that the ball can roll, or has mass.
The ball slides via a simple friction model, where friction is a scalar value applied to the difference between the balls speed vector, and the speed of the wheel at the point under the ball.
There is only 1 force involved. It is the force tangential to the vector from the ball to the wheel center, subtracted by the ball movement vector and then multiplied by the friction coefficient.
For details on how this is calculated see comments in the function ball.update()
Notes
That if the ball starts at the dead center of the wheel nothing will happen.
I could not workout if it was the path of the ball you wanted or just the simulation of the ball, so I added both.
The ball resets after it leaves the wheel.
The wheel is marked with text and center cross so its rotation can be seen.
const ROTATE = Math.PI / 50;
const WHEEL_SIZE = 0.6;
Math.rand = (min, max) => Math.random() * (max - min) + min;
Math.randPow = (min, max, p) => Math.random() ** p * (max - min) + min;
var friction = 0.35;
const ctx = canvas.getContext("2d");
requestAnimationFrame(mainLoop);
ctx.font = "30px arial";
ctx.textAlign = "center";
scrollBy(0, canvas.height / 2 - canvas.height / 2 * WHEEL_SIZE);
function mainLoop() {
ctx.setTransform(1, 0, 0, 1, 0, 0);
ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
wheel.update();
ball.update(wheel, arrow);
wheel.draw();
path.draw();
ball.draw();
arrow.draw(ball);
requestAnimationFrame(mainLoop);
}
const path = Object.assign([],{
draw() {
ctx.setTransform(1, 0, 0, 1, 0, 0);
ctx.strokeStyle = "#F00";
ctx.lineWidth = 1;
ctx.beginPath();
for (const p of this) { ctx.lineTo(p.x, p.y) }
ctx.stroke();
},
reset() { this.length = 0 },
add(point) {
this.push({x: point.x, y: point.y});
if (this.length > 1000) { // prevent long lines from slowing render
this.shift()
}
}
});
const arrow = {
dx: 0,dy: 0,
draw(ball) {
if (this.dx || this.dy) {
const dir = Math.atan2(this.dy, this.dx);
// len is converted from frame 1/60th second to seconds
const len = Math.hypot(this.dy, this.dx) * 60;
const aXx = Math.cos(dir);
const aXy = Math.sin(dir);
ctx.setTransform(aXx, aXy, -aXy, aXx, ball.x, ball.y);
ctx.beginPath();
ctx.lineTo(0,0);
ctx.lineTo(len, 0);
ctx.moveTo(len - 4, -2);
ctx.lineTo(len, 0);
ctx.lineTo(len - 4, 2);
ctx.strokeStyle = "#FFF";
ctx.lineWidth = 2;
ctx.stroke();
}
}
};
const ball = {
x: canvas.width / 2 + 4,
y: canvas.height / 2,
dx: 0, // delta pos Movement vector
dy: 0,
update(wheel, arrow) {
// get distance from center
const dist = Math.hypot(wheel.x - this.x, wheel.y - this.y);
// zero force arrow
arrow.dx = 0;
arrow.dy = 0;
// check if on wheel
if (dist < wheel.radius) {
// get tangent vector direction
const tangent = Math.atan2(this.y - wheel.y, this.x - wheel.x) + Math.PI * 0.5 * Math.sign(wheel.dr);
// get tangent as vector
// which is distance times wheel rotation in radians.
const tx = Math.cos(tangent) * dist * wheel.dr;
const ty = Math.sin(tangent) * dist * wheel.dr;
// get difference between ball vector and tangent vector scaling by friction
const fx = arrow.dx = (tx - this.dx) * friction;
const fy = arrow.dy = (ty - this.dy) * friction;
// Add the force vector
this.dx += fx;
this.dy += fy;
} else if (dist > wheel.radius * 1.7) { // reset ball
// to ensure ball is off center use random polar coord
const dir = Math.rand(0, Math.PI * 2);
const dist = Math.randPow(1, 20, 2); // add bias to be close to center
this.x = canvas.width / 2 + Math.cos(dir) * dist;
this.y = canvas.height / 2 + Math.sin(dir) * dist;
this.dx = 0;
this.dy = 0;
path.reset();
}
// move the ball
this.x += this.dx;
this.y += this.dy;
path.add(ball);
},
draw() {
ctx.fillStyle = "#0004";
ctx.setTransform(1, 0, 0, 1, this.x + 5, this.y + 5);
ctx.beginPath();
ctx.arc(0, 0, 10, 0, 2 * Math.PI);
ctx.fill();
ctx.fillStyle = "#f00";
ctx.setTransform(1, 0, 0, 1, this.x, this.y);
ctx.beginPath();
ctx.arc(0, 0, 12, 0, 2 * Math.PI);
ctx.fill();
ctx.fillStyle = "#FFF8";
ctx.setTransform(1, 0, 0, 1, this.x - 5, this.y - 5);
ctx.beginPath();
ctx.ellipse(0, 0, 2, 3, -Math.PI * 0.75, 0, 2 * Math.PI);
ctx.fill();
},
}
const wheel = {
x: canvas.width / 2, y: canvas.height / 2, r: 0,
dr: ROTATE, // delta rotate
radius: Math.min(canvas.height, canvas.width) / 2 * WHEEL_SIZE,
text: "wheel",
update() { this.r += this.dr },
draw() {
const aXx = Math.cos(this.r);
const aXy = Math.sin(this.r);
ctx.setTransform(aXx, aXy, -aXy, aXx, this.x, this.y);
ctx.fillStyle = "#CCC";
ctx.strokeStyle = "#000";
ctx.lineWidth = 6;
ctx.beginPath();
ctx.arc(0, 0, this.radius, 0, 2 * Math.PI);
ctx.stroke();
ctx.fill();
ctx.strokeStyle = ctx.fillStyle = "#aaa";
ctx.lineWidth = 2;
ctx.beginPath();
ctx.lineTo(-20,0);
ctx.lineTo(20,0);
ctx.moveTo(0,-20);
ctx.lineTo(0,20);
ctx.stroke();
ctx.fillText(this.text, 0, this.radius - 16);
},
}
<canvas id="canvas" width="300" height="300"></canvas>
Centripetal force
Centripetal is the force towards the center of the turning wheel. However because the ball is sliding the force calculated is not a centripetal force.
You can calculate the centripetal force by scaling the vector from the ball to the center by the dot product of the "vector to center" dot "force vector"
The force vector on the ball is shown as a white arrow. The arrows size is the force as acceleration in pixels per second.
The vector is towards the center but will never point directly at the center of the wheel.
Approximation
This simulation is an approximation. You will need an understanding of calculus and differential equations to get closer to reality.
Using a more complex simulation would only be noticeable if the friction was very close or at 1 and it is easier then to just fix the ball to the wheel, scaling the position from center by an inverse power of the friction coefficient.
How can you add multiple balls to this code ?
Ideally I would like to send to a function X amount of balls to be displayed on the canvas.
var canvas = document.getElementById("mycanvas");
var ctx = canvas.getContext("2d");
var p = { x: 25, y: 25 };
var velo = 3,
corner = 50,
rad = 20;
var ball = { x: p.x, y: p.y };
var moveX = Math.cos((Math.PI / 180) * corner) * velo;
var moveY = Math.sin((Math.PI / 180) * corner) * velo;
function DrawMe() {
ctx.clearRect(0, 0, 400, 300);
if (ball.x > canvas.width - rad || ball.x < rad) moveX = -moveX;
if (ball.y > canvas.height - rad || ball.y < rad) moveY = -moveY;
ball.x += moveX;
ball.y += moveY;
ctx.beginPath();
ctx.fillStyle = "red";
ctx.arc(ball.x, ball.y, rad, 0, Math.PI * 2, false);
ctx.fill();
ctx.closePath();
}
setInterval(DrawMe, 10);
You could have the "DrawMe" function take in the "ball" as a parameter, and instead of just having 1 ball, you could have an array of balls, and on each tick of the "setInterval" call, you could update all of the different balls by looping through the array and calling "DrawMe" for each ball. Just one way :)
I want to spin a circle around a triangle using canvas. Have this code from earlier, but here is the circle in the middle, and a rectangle spinning, i want the circle to spin and have a triangle in the middle. Can someone help?
Here is the JS code i have:
var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");
var cx = 100;
var cy = 100;
var rectWidth = 15;
var rectHeight = 10;
var rotation = 0;
requestAnimationFrame(animate);
function animate() {
requestAnimationFrame(animate);
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.beginPath();
ctx.arc(cx, cy, 10, 0, Math.PI * 2);
ctx.closePath();
ctx.fill();
ctx.save();
ctx.translate(cx, cy);
ctx.rotate(rotation);
ctx.strokeRect(-rectWidth / 2 + 20, -rectHeight / 2, rectWidth, rectHeight);
ctx.restore();
rotation += Math.PI / 180;
}
<canvas id="canvas"></canvas>
I have edited your code to draw the requested shapes and added comments to describe, what i am doing in the snippet below.
var canvas = document.body.appendChild(document.createElement("canvas"));
var ctx = canvas.getContext("2d");
var cx = 100;
var cy = 100;
var rotation = 0;
requestAnimationFrame(animate);
function animate() {
//Clear canvas
ctx.clearRect(0, 0, canvas.width, canvas.height);
//Draw center figure
/*
ctx.beginPath();
ctx.arc(cx, cy, 10, 0, Math.PI * 2);
ctx.closePath();
ctx.fill();
*/
ctx.beginPath();
ctx.moveTo(cx - 10, cy - 10);
ctx.lineTo(cx, cy + 10);
ctx.lineTo(cx + 10, cy - 10);
ctx.closePath();
ctx.fill();
//Rotate canvas
ctx.save();
ctx.translate(cx, cy);
ctx.rotate(rotation);
//Draw rotating object
/*ctx.strokeRect(-rectWidth / 2 + 20, -rectHeight / 2, rectWidth, rectHeight);*/
ctx.beginPath();
ctx.arc(20, 0, 5, 0, Math.PI * 2);
ctx.closePath();
ctx.fill();
//Rotate canvas back
ctx.restore();
//Save rotation
rotation += Math.PI / 180;
//Request next frame
requestAnimationFrame(animate);
}
It sounds like you lack experience with HTML Canvas manipulation, so i would like to recommend some MDN's official canvas tutorial.
If you have further questions feel free to open new questions with more code-specific problems in the future.
Here is an alternative to moving objects without using the ctx.translate or the ctx.rotate
We can use Math.sin and Math.cos to move around in a circular or elliptical motion.
Once you understand this approach you open the door for many possibilities, for example you can make the spins relative to other objects.
var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");
var rotation = 0;
setInterval(animate, 10);
function animate(rx, ry, speed) {
ctx.clearRect(0, 0, canvas.width, canvas.height);
draw(120, 80, 1)
draw(240, 80, 10/3)
}
function draw(rx, ry, speed) {
var x = Math.cos(rotation) * 50 + rx
var y = Math.sin(rotation) * 50 + ry
ctx.beginPath()
ctx.arc(x, y, 20, 0, Math.PI * 2);
ctx.stroke();
for (var i = 1; i < 8; i++) {
x += Math.sin(rotation * i/speed) * 20
y += Math.cos(rotation * i/speed) * 20/i
ctx.beginPath()
ctx.arc(x, y, 8/i, 0, Math.PI * 2);
ctx.stroke();
}
rotation += Math.PI / 180;
}
<canvas id="canvas" height=170 width=400></canvas>
Try the following:
<code>
var canvas=document.getElementById("canvas");
var ctx=canvas.getContext("2d");
var cx=100;
var cy=100;
var rectWidth=15;
var rectHeight=10;
var rotation=0;
requestAnimationFrame(animate);
function animate(){
requestAnimationFrame(animate);
ctx.clearRect(0,0,canvas.width,canvas.height);
ctx.beginPath();
var radius = 8;
ctx.moveTo(cx - radius, cy + radius);
ctx.lineTo(cx, cy - radius);
ctx.lineTo(cx + radius , cy + radius);
ctx.lineTo(cx - radius, cy + radius);
ctx.fill();
ctx.save();
ctx.translate(cx,cy);
ctx.rotate(rotation);
ctx.strokeRect(-rectWidth/2+20,-rectHeight/2,rectWidth,rectHeight);
ctx.restore();
rotation+=Math.PI/180;
}
</code>
I have a basic JSFiddle whereby I want to have random points plotted inside a circle.
But I do not know how to limit the points to be inside the circle.
This is what I currently have:
var ctx = canvas.getContext('2d'),
count = 1000, // number of random points
cx = 150,
cy = 150,
radius = 148;
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.arc(canvas.width/2, canvas.height/2, radius, 0, 2*Math.PI);
ctx.closePath();
ctx.fillStyle = '#00000';
ctx.fill();
// create random points
ctx.fillStyle = '#ffffff';
while(count) {
// randomise x:y
ctx.fillRect(x + canvas.width/2, y + canvas.height/2, 2, 2);
count--;
}
How would i go about generating random (x,y) coordinates to plot random points inside the circle?
My current fiddle: http://jsfiddle.net/e8jqdxp3/
To plot points randomly in a circle, you can pick a random value from the radius squared, then square root it, pick a random angle, and convert the polar coordinate to rectangular. The square / square root step ensures that we get a uniform distribution (otherwise most points would be near the center of the circle).
So the formula to plot a random point in the circle is the following, where r' is a random value between 0 and r2, and θ is a random value between 0 and 2π:
Screenshot of result:
Live Demo:
var canvas = document.getElementById("thecanvas");
var ctx = canvas.getContext('2d'),
count = 1000, // number of random points
cx = 150,
cy = 150,
radius = 148;
ctx.fillStyle = '#CCCCCC';
ctx.fillRect(0, 0, canvas.width, canvas.height);
ctx.fillStyle = '#000000';
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.arc(canvas.width / 2, canvas.height / 2, radius, 0, 2 * Math.PI);
ctx.closePath();
ctx.fill();
// create random points
ctx.fillStyle = '#ffffff';
while (count) {
var pt_angle = Math.random() * 2 * Math.PI;
var pt_radius_sq = Math.random() * radius * radius;
var pt_x = Math.sqrt(pt_radius_sq) * Math.cos(pt_angle);
var pt_y = Math.sqrt(pt_radius_sq) * Math.sin(pt_angle);
ctx.fillRect(pt_x + canvas.width / 2, pt_y + canvas.width / 2, 2, 2);
count--;
}
<canvas id="thecanvas" width="400" height="400"></canvas>
JSFiddle Version: https://jsfiddle.net/qc735bqw/
Randomly pick dSquared (0..radius^2) and theta (0..2pi), then
x = sqrt(dSquared) cos(theta)
y = sqrt(dSquared) sin(theta)
JSFiddle
var ctx = canvas.getContext('2d'),
count = 1000, // number of random points
cx = canvas.width/2,
cy = canvas.height/2,
radius = 148;
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.arc(0+canvas.width/2, 0+canvas.height/2, radius, 0, 2*Math.PI);
ctx.closePath();
ctx.fillStyle = '#00000';
ctx.fill();
ctx.fillStyle = '#ffffff';
while(count) {
var x = Math.random() * canvas.width;
var y = Math.random() * canvas.height;
var xDiff = cx - x;
var yDiff = cy - y;
if(Math.sqrt(xDiff*xDiff+yDiff*yDiff)<radius)
{
ctx.fillRect(x, y, 2, 2);
count--;
}
}
This worked for me:
const getRandomCoordinateInCircle = radius => {
var angle = Math.random() * Math.PI * 2;
const x = Math.cos(angle) * radius * Math.random();
const y = Math.sin(angle) * radius * Math.random();
return { x, y };
};
console.log(getRandomCoordinateInCircle(1000);
// { x: 118.35662725763385, y: -52.60516556856313 }
Returns a random point with { x: 0, y: 0} as the centre of the circle.