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How to draw an irregular shaped polygon using the given angles

I am making a drawing application. I have created a class Polygon. Its constructor will receive three arguments and these will be its properties:
points(Number): Number of points the polygon will have.
rotation(Number): The angle the whole polygon will be rotated.
angles(Array Of number): The angles between two lines of the polygon.
I have been trying for the whole day, but I couldn't figure out the correct solution.
const canvas = document.querySelector('canvas');
const c = canvas.getContext('2d');
let isMouseDown = false;
let tool = 'polygon';
let savedImageData;
canvas.height = window.innerHeight;
canvas.width = window.innerWidth;
const mouse = {x:null,y:null}
let mousedown = {x:null,y:null}
const toDegree = val => val * 180 / Math.PI
class Polygon {
constructor(points, rotation, angles){
this.points = points;
this.rotation = rotation;
//if angles are given then convert them to radian
if(angles){
this.angles = angles.map(x => x * Math.PI/ 180);
}
//if angles array is not given
else{
/*get the angle for a regular polygon for given points.
3-points => 60
4-points => 90
5-points => 108
*/
let angle = (this.points - 2) * Math.PI/ this.points;
//fill the angles array with the same angle
this.angles = Array(points).fill(angle)
}
let sum = 0;
this.angles = this.angles.map(x => {
sum += x;
return sum;
})
}
draw(startx, starty, endx, endy){
c.beginPath();
let rx = (endx - startx) / 2;
let ry = (endy - starty) / 2;
let r = Math.max(rx, ry)
c.font = '35px cursive'
let cx = startx + r;
let cy = starty + r;
c.fillRect(cx - 2, cy - 2, 4, 4); //marking the center
c.moveTo(cx + r, cy);
c.strokeText(0, cx + r, cy);
for(let i = 1; i < this.points; i++){
//console.log(this.angles[i])
let dx = cx + r * Math.cos(this.angles[i] + this.rotation);
let dy = cy + r * Math.sin(this.angles[i] + this.rotation);
c.strokeStyle = 'red';
c.strokeText(i, dx, dy, 100);
c.strokeStyle ='black';
c.lineTo(dx, dy);
}
c.closePath();
c.stroke();
}
}
//update();
c.beginPath();
c.lineWidth = 1;
document.addEventListener('mousemove', function(e){
//Getting the mouse coords according to canvas
const canvasData = canvas.getBoundingClientRect();
mouse.x = (e.x - canvasData.left) * (canvas.width / canvasData.width);
mouse.y = (e.y - canvasData.top) * (canvas.height / canvasData.height);
if(tool === 'polygon' && isMouseDown){
drawImageData();
let pol = new Polygon(5, 0);
pol.draw(mousedown.x, mousedown.y, mouse.x, mouse.y);
}
})
function saveImageData(){
savedImageData = c.getImageData(0, 0, canvas.width, canvas.height);
}
function drawImageData(){
c.putImageData(savedImageData, 0, 0)
}
document.addEventListener('mousedown', () => {
isMouseDown = true;
mousedown = {...mouse};
if(tool === 'polygon'){
saveImageData();
}
});
document.addEventListener('mouseup', () => isMouseDown = false);
<canvas></canvas>
In the above code I am trying to make a pentagon but it doesn't work.

Unit polygon
The following snippet contains a function polygonFromSidesOrAngles that returns the set of points defining a unit polygon as defined by the input arguments. sides, or angles
Both arguments are optional but must have one argument
If only sides given then angles are calculated to make the complete polygon with all side lengths equal
If only angles given then the number of sides is assumed to be the number of angles. Angles are in degrees 0-360
If the arguments can not define a polygon then there are several exceptions throw.
The return is a set of points on a unit circle that define the points of the polygon. The first point is at coordinate {x : 1, y: 0} from the origin.
The returned points are not rotated as that is assumed to be a function of the rendering function.
All points on the polygon are 1 unit distance from the origin (0,0)
Points are in the form of an object containing x and y properties as defined by the function point and polarPoint
Method used
I did not lookup an algorithm, rather I worked it out from the assumption that a line from (1,0) on the unit circle at the desired angle will intercept the circle at the correct distance from (1,0). The intercept point is used to calculate the angle in radians from the origin. That angle is then used to calculate the ratio of the total angles that angle represents.
The function that does this is calcRatioOfAngle(angle, sides) returning the angle as a ratio (0-1) of Math.PI * 2
It is a rather long handed method and likely can be significantly reduced
As it is unclear in your question what should be done with invalid arguments the function will throw a range error if it can not proceed.
Polygon function
Math.PI2 = Math.PI * 2;
Math.TAU = Math.PI2;
Math.deg2Rad = Math.PI / 180;
const point = (x, y) => ({x, y});
const polarPoint = (ang, dist) => ({x: Math.cos(ang) * dist, y: Math.sin(ang) * dist});
function polygonFromSidesOrAngles(sides, angles) {
function calcRatioOfAngle(ang, sides) {
const v1 = point(Math.cos(ang) - 1, Math.sin(ang));
const len2 = v1.x * v1.x + v1.y * v1.y;
const u = -v1.x / len2;
const v2 = point(v1.x * u + 1, v1.y * u);
const d = (1 - (v2.y * v2.y + v2.x * v2.x)) ** 0.5 / (len2 ** 0.5);
return Math.atan2(v2.y + v1.y * d, v2.x + 1 + v1.x * d) / (Math.PI * (sides - 2) / 2);
}
const vetAngles = angles => angles.reduce((sum, ang) => sum += ang, 0) === (angles.length - 2) * 180;
var ratios = [];
if(angles === undefined) {
if (sides < 3) { throw new RangeError("Polygon must have more than 2 side") }
const rat = 1 / sides;
while (sides--) { ratios.push(rat) }
} else {
if (sides === undefined) { sides = angles.length }
else if (sides !== angles.length) { throw new RangeError("Numbers of sides does not match number of angles") }
if (sides < 3) { throw new RangeError("Polygon must have more than 2 side") }
if (!vetAngles(angles)) { throw new RangeError("Set of angles can not create a "+sides+" sided polygon") }
ratios = angles.map(ang => calcRatioOfAngle(ang * Math.deg2Rad, sides));
ratios.unshift(ratios.pop()); // rotate right to get first angle at start
}
var ang = 0;
const points = [];
for (const rat of ratios) {
ang += rat;
points.push(polarPoint(ang * Math.TAU, 1));
}
return points;
}
Render function
Function to render the polygon. It includes the rotation so you don't need to create a separate set of points for each angle you want to render the polygon at.
The radius is the distance from the center point x,y to any of the polygons vertices.
function drawPolygon(ctx, poly, x, y, radius, rotate) {
ctx.setTransform(radius, 0, 0, radius, x, y);
ctx.rotate(rotate);
ctx.beginPath();
for(const p of poly.points) { ctx.lineTo(p.x, p.y) }
ctx.closePath();
ctx.setTransform(1, 0, 0, 1, 0, 0);
ctx.stroke();
}
Example
The following renders a set of test polygons to ensure that the code is working as expected.
Polygons are rotated to start at the top and then rendered clock wise.
The example has had the vetting of input arguments removed.
const ctx = can.getContext("2d");
can.height = can.width = 512;
Math.PI2 = Math.PI * 2;
Math.TAU = Math.PI2;
Math.deg2Rad = Math.PI / 180;
const point = (x, y) => ({x, y});
const polarPoint = (ang, dist) => ({x: Math.cos(ang) * dist, y: Math.sin(ang) * dist});
function polygonFromAngles(sides, angles) {
function calcRatioOfAngle(ang, sides) {
const x = Math.cos(ang) - 1, y = Math.sin(ang);
const len2 = x * x + y * y;
const u = -x / len2;
const x1 = x * u + 1, y1 = y * u;
const d = (1 - (y1 * y1 + x1 * x1)) ** 0.5 / (len2 ** 0.5);
return Math.atan2(y1 + y * d, x1 + 1 + x * d) / (Math.PI * (sides - 2) / 2);
}
var ratios = [];
if (angles === undefined) {
const rat = 1 / sides;
while (sides--) { ratios.push(rat) }
} else {
ratios = angles.map(ang => calcRatioOfAngle(ang * Math.deg2Rad, angles.length));
ratios.unshift(ratios.pop());
}
var ang = 0;
const points = [];
for(const rat of ratios) {
ang += rat;
points.push(polarPoint(ang * Math.TAU, 1));
}
return points;
}
function drawPolygon(poly, x, y, radius, rot) {
const xdx = Math.cos(rot) * radius;
const xdy = Math.sin(rot) * radius;
ctx.setTransform(xdx, xdy, -xdy, xdx, x, y);
ctx.beginPath();
for (const p of poly) { ctx.lineTo(p.x, p.y) }
ctx.closePath();
ctx.setTransform(1, 0, 0, 1, 0, 0);
ctx.stroke();
}
const segs = 4;
const tests = [
[3], [, [45, 90, 45]], [, [90, 10, 80]], [, [60, 50, 70]], [, [40, 90, 50]],
[4], [, [90, 90, 90, 90]], [, [90, 60, 90, 120]],
[5], [, [108, 108, 108, 108, 108]], [, [58, 100, 166, 100, 116]],
[6], [, [120, 120, 120, 120, 120, 120]], [, [140, 100, 180, 100, 100, 100]],
[7], [8],
];
var angOffset = -Math.PI / 2; // rotation of poly
const w = ctx.canvas.width;
const h = ctx.canvas.height;
const wStep = w / segs;
const hStep = h / segs;
const radius = Math.min(w / segs, h / segs) / 2.2;
var x,y, idx = 0;
for (y = 0; y < segs && idx < tests.length; y ++) {
for (x = 0; x < segs && idx < tests.length; x ++) {
drawPolygon(polygonFromAngles(...tests[idx++]), (x + 0.5) * wStep , (y + 0.5) * hStep, radius, angOffset);
}
}
canvas {
border: 1px solid black;
}
<canvas id="can"></canvas>

I do just a few modification.
Constructor take angles on degree
When map angles to radian complement 180 because canvas use angles like counterclockwise. We wan to be clockwise
First point start using the passed rotation
const canvas = document.querySelector('canvas');
const c = canvas.getContext('2d');
let isMouseDown = false;
let tool = 'polygon';
let savedImageData;
canvas.height = window.innerHeight;
canvas.width = window.innerWidth;
const mouse = {x:null,y:null}
let mousedown = {x:null,y:null}
const toDegree = val => val * 180 / Math.PI;
const toRadian = val => val * Math.PI / 180;
class Polygon {
constructor(points, rotation, angles){
this.points = points;
this.rotation = toRadian(rotation);
//if angles array is not given
if(!angles){
/*get the angle for a regular polygon for given points.
3-points => 60
4-points => 90
5-points => 108
*/
let angle = (this.points - 2) * 180 / this.points;
//fill the angles array with the same angle
angles = Array(points).fill(angle);
}
this.angles = angles;
let sum = 0;
console.clear();
// To radians
this.angles = this.angles.map(x => {
x = 180 - x;
x = toRadian(x);
return x;
})
}
draw(startx, starty, endx, endy){
c.beginPath();
let rx = (endx - startx) / 2;
let ry = (endy - starty) / 2;
let r = Math.max(rx, ry)
c.font = '35px cursive'
let cx = startx + r;
let cy = starty + r;
c.fillRect(cx - 2, cy - 2, 4, 4); //marking the center
c.moveTo(cx + r, cy);
let sumAngle = 0;
let dx = cx + r * Math.cos(this.rotation);
let dy = cy + r * Math.sin(this.rotation);
c.moveTo(dx, dy);
for(let i = 0; i < this.points; i++){
sumAngle += this.angles[i];
dx = dx + r * Math.cos((sumAngle + this.rotation));
dy = dy + r * Math.sin((sumAngle + this.rotation));
c.strokeStyle = 'red';
c.strokeText(i, dx, dy, 100);
c.strokeStyle ='black';
c.lineTo(dx, dy);
}
c.closePath();
c.stroke();
}
}
//update();
c.beginPath();
c.lineWidth = 1;
document.addEventListener('mousemove', function(e){
//Getting the mouse coords according to canvas
const canvasData = canvas.getBoundingClientRect();
mouse.x = (e.x - canvasData.left) * (canvas.width / canvasData.width);
mouse.y = (e.y - canvasData.top) * (canvas.height / canvasData.height);
if(tool === 'polygon' && isMouseDown){
drawImageData();
let elRotation = document.getElementById("elRotation").value;
let rotation = elRotation.length == 0 ? 0 : parseInt(elRotation);
let elPoints = document.getElementById("elPoints").value;
let points = elPoints.length == 0 ? 3 : parseInt(elPoints);
let elAngles = document.getElementById("elAngles").value;
let angles = elAngles.length == 0 ? null : JSON.parse(elAngles);
let pol = new Polygon(points, rotation, angles);
pol.draw(mousedown.x, mousedown.y, mouse.x, mouse.y);
}
})
function saveImageData(){
savedImageData = c.getImageData(0, 0, canvas.width, canvas.height);
}
function drawImageData(){
c.putImageData(savedImageData, 0, 0)
}
document.addEventListener('mousedown', () => {
isMouseDown = true;
mousedown = {...mouse};
if(tool === 'polygon'){
saveImageData();
}
});
document.addEventListener('mouseup', () => isMouseDown = false);
<!DOCTYPE html>
<html lang="en">
<body>
Points: <input id="elPoints" style="width:30px" type="text" value="3" />
Rotation: <input id="elRotation" style="width:30px" type="text" value="0" />
Angles: <input id="elAngles" style="width:100px" type="text" value="[45, 45, 90]" />
<canvas></canvas>
</body>
</html>

How to stop canvas jumping animation

I have a canvas animation which you can see here.
I've noticed that once you have watched the animation after a while (approximately 25 seconds) the animation starts to jump around. I'm struggling to figure out how to make it so that it is one constant fluid motion?
Code below:
<canvas id="canvas"></canvas>
var canvas = document.querySelector("#canvas");
var ctx = canvas.getContext("2d");
canvas.width = parseInt(getComputedStyle(canvas).width);
canvas.height = parseInt(getComputedStyle(canvas).height);
var P = 4;
var A = 4;
function draw(shift) {
var w = canvas.width;
var h = canvas.height;
shift = shift >= 500*Math.PI ? shift - 100*Math.PI : shift;
ctx.clearRect(0, 0, w, h);
var grd = ctx.createLinearGradient(0, 0, w, h);
grd.addColorStop(0, "#4a8bf5");
grd.addColorStop(1, "#f16b55");
ctx.strokeStyle = grd;
ctx.lineCap = "round";
for (var i = 0; i < w; ) {
var _A = Math.abs(A*Math.cos(2*i));
ctx.beginPath();
var pos = Math.exp(-_A * i / w) * Math.sin(P * Math.PI * (i + shift) / w);
pos *= h / 2;
var lw = Math.exp(-_A * i / w) * Math.sin(3 * Math.PI * (i - shift) / w) * 2;
ctx.lineWidth = (lw)+1;
ctx.lineTo(i, h / 2 - pos);
ctx.closePath();
ctx.stroke();
i += 1;
}
window.requestAnimationFrame(function(){
draw(shift + 1);
});
}
draw(0);

The solution is to make sure that the change in shift results in the sin() argument changing by a multiple of 2π.
Given
Math.sin((i + shift) / (w / P))
this can be done using something like
if (shift > 500) shift -= 2 * Math.PI * (w / P);
There will still be a jump in the 2nd sin() argument here, the line width. To avoid this, shift has to be reduced by a number that causes both arguments to change by multiples of 2π, the LCM if you will.
var canvas = document.querySelector("#canvas");
var ctx = canvas.getContext("2d");
canvas.width = parseInt(getComputedStyle(canvas).width);
canvas.height = parseInt(getComputedStyle(canvas).height);
var P = 10;
var A = 4;
var shift = 0;
function draw() {
var w = canvas.width;
var h = canvas.height;
shift += 1;
if (shift > 500) shift -= 2 * Math.PI * (w / P);
shift_el.innerHTML = shift;
ctx.clearRect(0, 0, w, h);
var grd = ctx.createLinearGradient(0, 0, w, h);
grd.addColorStop(0, "#4a8bf5");
grd.addColorStop(1, "#f16b55");
ctx.strokeStyle = grd;
ctx.lineCap = "round";
for (var i = 0; i < w;) {
var _A = Math.abs(A * Math.cos(2 * i));
ctx.beginPath();
var pos = Math.exp(-_A * i / w) * Math.sin((i + shift) / (w / P));
pos *= h / 2;
var lw = Math.exp(-_A * i / w) * Math.sin(3 * Math.PI * (i - shift) / w) * 2;
ctx.lineWidth = (lw) + 1;
ctx.lineTo(i, h / 2 - pos);
ctx.closePath();
ctx.stroke();
i += 1;
}
window.requestAnimationFrame(draw);
}
draw();
body {
background: #ffffff;
padding: 0;
margin: 0;
}
canvas {
height: 200px;
width: 100%;
}
#shift_el {
position: absolute;
top: 0
}
<canvas id="canvas"></canvas>
<div id="shift_el"></div>

How to draw/Form circle with two points?

I need to draw a circle and i have only two points.Now i need to find center point and radius of the circle? You can form the circle in clock wise direction.
Thanks in advance

Here is a Brute Force approach to the problem.
EDIT
Added a max iterations limit to cut off calculations if the line between the two points is almost straight along x (meaning a radius would be nearing Infinity)
Also animations, because that makes everything better :)
var canvas = document.body.appendChild(document.createElement("canvas"));
var ctx = canvas.getContext("2d");
canvas.width = 1000;
canvas.height = 1000;
var points = [
{ x: parseInt(prompt("x1", "110")), y: parseInt(prompt("y1", "120")), r: 5 },
{ x: parseInt(prompt("x2", "110")), y: parseInt(prompt("y2", "60")), r: 5 },
];
function calculateRemainingPoint(points, x, precision, maxIteration) {
if (x === void 0) { x = 0; }
if (precision === void 0) { precision = 0.001; }
if (maxIteration === void 0) { maxIteration = 100000; }
var newPoint = {
x: x,
y: (points[0].y + points[1].y) / 2,
r: 50
};
var d0 = distance(points[0].x, points[0].y, x, newPoint.y);
var d1 = distance(points[1].x, points[1].y, x, newPoint.y);
var iteration = 0;
//Bruteforce approach
while (Math.abs(d0 - d1) > precision && iteration < maxIteration) {
var oldDiff = Math.abs(d0 - d1);
var oldY = newPoint.y;
iteration++;
newPoint.y += oldDiff / 10;
d0 = distance(points[0].x, points[0].y, x, newPoint.y);
d1 = distance(points[1].x, points[1].y, x, newPoint.y);
var diff_1 = Math.abs(d0 - d1);
if (diff_1 > oldDiff) {
newPoint.y = oldY - oldDiff / 10;
d0 = distance(points[0].x, points[0].y, x, newPoint.y);
d1 = distance(points[1].x, points[1].y, x, newPoint.y);
}
}
var diff = (points[0].x + points[1].x) / points[0].x;
newPoint.r = d0;
return newPoint;
}
points.push(calculateRemainingPoint(points));
function distance(x1, y1, x2, y2) {
var a = x1 - x2;
var b = y1 - y2;
return Math.sqrt(a * a + b * b);
}
function draw() {
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.beginPath();
ctx.moveTo(-canvas.width, canvas.height / 2);
ctx.lineTo(canvas.width, canvas.height / 2);
ctx.stroke();
ctx.closePath();
ctx.beginPath();
ctx.moveTo(canvas.width / 2, -canvas.height);
ctx.lineTo(canvas.width / 2, canvas.height);
ctx.stroke();
ctx.closePath();
for (var pointIndex = 0; pointIndex < points.length; pointIndex++) {
var point = points[pointIndex];
ctx.beginPath();
ctx.arc(point.x + canvas.width / 2, canvas.height / 2 - point.y, point.r, 0, Math.PI * 2);
ctx.arc(point.x + canvas.width / 2, canvas.height / 2 - point.y, 2, 0, Math.PI * 2);
ctx.stroke();
ctx.closePath();
}
}
setInterval(function () {
points = points.slice(0, 2);
points[Math.floor(Math.random() * points.length) % points.length][Math.random() > 0.5 ? 'x' : 'y'] = Math.random() * canvas.width - canvas.width / 2;
setTimeout(function () {
points.push(calculateRemainingPoint(points));
requestAnimationFrame(draw);
}, 1000 / 60);
}, 1000);
draw();

No that is impossible.
Create two circles with the same radius at centerpoints A + B. At the intersection of these two circles create an circle with the same radius....
Then make the same with an other radius....

Rectangle Coordinate Projection into another Rectangle

So I would like to project coordinates from one rectangle in javascript to another, in essence, scaling coordinates from one rectangle to another. How would I do that?
function Rectangle(maxX, minX, maxY, minY) {
this.maxX = maxX;
this.minX = minX;
this.maxY = maxY;
this.minY = minY;
}
So 2 Rectangles with different size and coordinates. I want to draw into one rectangle and scale that proportionally into the other rectangle.

Something like this?
var src = new Rectangle(6, 0, 6, 2);
var dst = new Rectangle(4, 2, 8, 0);
function Rectangle(maxX, minX, maxY, minY) {
this.maxX = maxX;
this.minX = minX;
this.maxY = maxY;
this.minY = minY;
}
var canvas = document.querySelector("canvas");
var width = canvas.width, height = canvas.height;
var w = width / 2 + 0.5, h = height / 2 + 0.5;
var sx = width / 20, sy = height / 20;
var context = canvas.getContext("2d");
context.strokeStyle = "#808080";
context.fillStyle = "#000080";
tween(src, dst, 25, 1, 1000);
function tween(src, dst, fps, seconds, delay) {
var frames = fps * seconds;
var srcMaxX = src.maxX;
var srcMinX = src.minX;
var srcMaxY = src.maxY;
var srcMinY = src.minY;
var maxX = dst.maxX - srcMaxX;
var minX = dst.minX - srcMinX;
var maxY = dst.maxY - srcMaxY;
var minY = dst.minY - srcMinY;
drawRectangle(srcMaxX, srcMinX, srcMaxY, srcMinY);
setTimeout(function loop(frame, delay) {
var dstMaxX = srcMaxX + maxX * frame / frames;
var dstMinX = srcMinX + minX * frame / frames;
var dstMaxY = srcMaxY + maxY * frame / frames;
var dstMinY = srcMinY + minY * frame / frames;
drawRectangle(dstMaxX, dstMinX, dstMaxY, dstMinY);
if (frame < frames) setTimeout(loop, delay, frame + 1, delay);
}, delay, 1, 1000 / fps);
}
function drawRectangle(maxX, minX, maxY, minY) {
context.clearRect(0, 0, width, height);
drawLine(0, h, width, h);
drawLine(w, 0, w, height);
var x = w + sx * minX;
var y = h - sy * maxY;
var wth = sx * (maxX - minX);
var hgt = sy * (maxY - minY);
context.fillRect(x, y, wth, hgt);
}
function drawLine(x1, y1, x2, y2) {
context.beginPath();
context.moveTo(x1, y1);
context.lineTo(x2, y2);
context.stroke();
}
canvas {
border: 1px solid #000000;
}
<canvas width="400" height="400"></canvas>
Hope this helps.

With these functions:
function Point(x, y) {
this.x = x;
this.y = y;
}
function Rect(xMin, xMax, yMin, yMax) {
this.xMin = xMin;
this.xMax = xMax;
this.yMin = yMin;
this.yMax = yMax;
}
Rect.prototype.width = function() {
return this.xMax - this.xMin;
};
Rect.prototype.height = function() {
return this.yMax - this.yMin;
};
function RectProjection(a, b) {
var xScale = b.width() / a.width();
var yScale = b.height() / a.height();
var xOffset = b.xMin - xScale * a.xMin;
var yOffset = b.yMin - yScale * a.yMin;
return function (p) {
return Point(xScale * p.x + xOffset, yScale * p.y + yOffset);
};
}
You can then do something like this:
var proj = projection(new Rectangle(0, 2, 0, 3), new Rectangle(2, 6, 2, 8));
var q = proj(new Point(1, 2));
Where q is Point(4, 6).

How to constrain movement within the area of a circle

This might be more a geometry related question, but I'm trying to constrain a controller within an area of a circle. I know I have to touch the Math.sin() and Math.cos() methods, but my attemps so far have been fruitless so far.
Here is the jsfiddle:
So far I've been able to constrain it to an invisible square. http://jsfiddle.net/maGVK/

So I finally was able to complete this with a bit of everyone's help.
var pointerEl = document.getElementById("pointer");
var canvasEl = document.getElementById("canvas");
var canvas = {
width: canvasEl.offsetWidth,
height: canvasEl.offsetHeight,
top: canvasEl.offsetTop,
left: canvasEl.offsetLeft
};
canvas.center = [canvas.left + canvas.width / 2, canvas.top + canvas.height / 2];
canvas.radius = canvas.width / 2;
window.onmousemove = function(e) {
var result = limit(e.x, e.y);
pointer.style.left = result.x + "px";
pointer.style.top = result.y + "px";
}
function limit(x, y) {
var dist = distance([x, y], canvas.center);
if (dist <= canvas.radius) {
return {x: x, y: y};
}
else {
x = x - canvas.center[0];
y = y - canvas.center[1];
var radians = Math.atan2(y, x)
return {
x: Math.cos(radians) * canvas.radius + canvas.center[0],
y: Math.sin(radians) * canvas.radius + canvas.center[1]
}
}
}
function distance(dot1, dot2) {
var x1 = dot1[0],
y1 = dot1[1],
x2 = dot2[0],
y2 = dot2[1];
return Math.sqrt(Math.pow(x1 - x2, 2) + Math.pow(y1 - y2, 2));
}
You can see the result here:
http://jsfiddle.net/7Asn6/

var pointerEl = document.getElementById("pointer");
var canvasEl = document.getElementById("canvas");
var canvas = {
width: canvasEl.offsetWidth,
height: canvasEl.offsetHeight,
top: canvasEl.offsetTop,
left: canvasEl.offsetLeft
};
canvas.center = [canvas.left + canvas.width / 2, canvas.top + canvas.height / 2];
canvas.radius = canvas.width / 2;
window.onmousemove = function(e) {
var result = limit(e.x, e.y);
if (!result.limit) {
pointer.style.left = result.x + "px";
pointer.style.top = result.y + "px";
}
}
function limit(x, y) {
var dist = distance([x, y], canvas.center);
if (dist <= canvas.radius) {
return {x: x, y: y};
} else {
return {limit: true};
}
}
function distance(dot1, dot2) {
var x1 = dot1[0],
y1 = dot1[1],
x2 = dot2[0],
y2 = dot2[1];
return Math.sqrt(Math.pow(x1 - x2, 2) + Math.pow(y1 - y2, 2));
}
this could do the work, though the movement is not smooth....that will need more geometry knowledge...
fiddle: http://jsfiddle.net/cRxMa/

This arithmetic is trivial as long as you normalize each data point (prospective position), which i have tried to do in the function below:
function locatePoint(canvas_size, next_position) {
// canvas_size & next_position are both 2-element arrays
// (w, h) & (x, y)
dist = function(x, y) {
return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
};
x = next_position[0];
y = next_position[1];
rescaledX = x/(canvas_size[0]/2);
rescaledY = y/(canvas_size[1]/2);
if (distance(x, y) <= 1) {
// the base case; position is w/in the circle
}
else {
// position is outside the circle, so perhaps
// do something like random select a new position, then
// call this function again (recursively) passing in
// that new position
}
}
so in the simple diagram below, i have just inscribed a unit circle (r=1) inside a square whose sides are r*2. Your canvas dimensions do not have to be square though. To further simplify the calculation, you only need to consider one of the four quadrants--the upper right quadrant, let's say. The reason is that the Euclidean distance formula squares each coordinate value, so negative values become positive.
Put another way, the simplest way is to imagine a circle inscribed in your canvas and whose center is also the center of your canvas (so (0, 0) is the center not the upper left-hand corner); next, both canvas and circle are shrunk until the circle has radius = 1. Hopefully i have captured this in the function above.

Hi and thanks for sharing your solution.
Your jsfiddle helps me a lot to constraint the movement of a rotation handle.
Here's my solution using jQuery :
function getBall(xVal, yVal, dxVal, dyVal, rVal, colorVal) {
var ball = {
x: xVal,
lastX: xVal,
y: yVal,
lastY: yVal,
dx: dxVal,
dy: dyVal,
r: rVal,
color: colorVal,
normX: 0,
normY: 0
};
return ball;
}
var canvas = document.getElementById("myCanvas");
var xLabel = document.getElementById("x");
var yLabel = document.getElementById("y");
var dxLabel = document.getElementById("dx");
var dyLabel = document.getElementById("dy");
var ctx = canvas.getContext("2d");
var containerR = 200;
canvas.width = containerR * 2;
canvas.height = containerR * 2;
canvas.style["border-radius"] = containerR + "px";
var balls = [
getBall(containerR, containerR * 2 - 30, 2, -2, 20, "#0095DD"),
getBall(containerR, containerR * 2 - 50, 3, -3, 30, "#DD9500"),
getBall(containerR, containerR * 2 - 60, -3, 4, 10, "#00DD95"),
getBall(containerR, containerR * 2 / 5, -1.5, 3, 40, "#DD0095")
];
function draw() {
ctx.clearRect(0, 0, canvas.width, canvas.height);
for (var i = 0; i < balls.length; i++) {
var curBall = balls[i];
ctx.beginPath();
ctx.arc(curBall.x, curBall.y, curBall.r, 0, Math.PI * 2);
ctx.fillStyle = curBall.color;
ctx.fill();
ctx.closePath();
curBall.lastX = curBall.x;
curBall.lastY = curBall.y;
curBall.x += curBall.dx;
curBall.y += curBall.dy;
var dx = curBall.x - containerR;
var dy = curBall.y - containerR;
var distanceFromCenter = Math.sqrt(dx * dx + dy * dy);
if (distanceFromCenter >= containerR - curBall.r) {
var normalMagnitude = distanceFromCenter;
var normalX = dx / normalMagnitude;
var normalY = dy / normalMagnitude;
var tangentX = -normalY;
var tangentY = normalX;
var normalSpeed = -(normalX * curBall.dx + normalY * curBall.dy);
var tangentSpeed = tangentX * curBall.dx + tangentY * curBall.dy;
curBall.dx = normalSpeed * normalX + tangentSpeed * tangentX;
curBall.dy = normalSpeed * normalY + tangentSpeed * tangentY;
}
xLabel.innerText = "x: " + curBall.x;
yLabel.innerText = "y: " + curBall.y;
dxLabel.innerText = "dx: " + curBall.dx;
dyLabel.innerText = "dy: " + curBall.dy;
}
requestAnimationFrame(draw);
}
draw();
canvas { background: #eee; }
<div id="x"></div>
<div id="y"></div>
<div id="dx"></div>
<div id="dy"></div>
<canvas id="myCanvas"></canvas>
Hope this help someone.