Develop Reference

How to get axis-aligned bounding box of an ellipse with all given parameters?

void ctx.ellipse(x, y, radiusX, radiusY, rotation, startAngle, endAngle [, anticlockwise]);
The canvas context 2D API ellipse() method creates an elliptical arc centered at (x, y) with the radii radiusX and radiusY. The path starts at startAngle and ends at endAngle, and travels in the direction given by anticlockwise.
How to get the axis-aligned bounding box of a ellipse with the given parameters:x, y, radiusX, radiusY, rotation, startAngle, endAngle , anticlockwise?

Two solutions
This answer contains two exact solutions it is not an approximation.
The solutions are
boundEllipseAll will find the bounds of the full ellipse. If is a lot less complex than the full solution but you need to ensure that the x radius is greater than the y radius (eg rotate the ellipse 90 deg and swap the x, y radius)
boundEllipse Will find the bounds for a segment of an ellipse. It will work for all ellipses however I have not included the CCW flag. To get the bounds for CCW ellipse swap the start and end angles.
It works by first finding the x, y coords at the start and end points calculating the min and max along each axis. It then calculates the extrema angles, first for the x axis extremes, then the y axis extremes.
If the extrema angle is between the start and end angle, the x,y position of that angle is calculated and the point tested against the min and max extent.
There is a lot of room to optimize as many of the points need only the x, or y parts, and the inner while loop in function extrema can exit early if min and max are change for the axis it is working on.
Example
The example ensures I have not made any mistakes, and uses the second solution, animating an ellipse by moving the start and end angles, rotation, and y axis radius. Drawing the bounding box and the ellipse it bounds.
Update April 2022
Example shows use of both full ellipse boundEllipseAll and ellipse segment boundEllipse.
Note that boundEllipse is only for ellipse segment where endAngle n and startAngle m fit the rule {m <= n <= m + 2Pi}
Fixed bug in boundEllipse that did not show full ellipse when endAngle == startAngle + 2 * Math.PI
const ctx = canvas.getContext("2d");
const W = 200, H= 180;
const TAU = Math.PI * 2;
const ellipse = {
x: W / 2,
y: H / 2,
rx: W / 3,
ry: W / 3,
rotate: 0,
startAng: 0,
endAng: Math.PI * 2,
dir: false,
};
function boundEllipseAll({x, y, rx, ry, rotate}) {
const xAx = Math.cos(rotate);
const xAy = Math.sin(rotate);
const w = ((rx * xAx) ** 2 + (ry * xAy) ** 2) ** 0.5;
const h = ((rx * xAy) ** 2 + (ry * xAx) ** 2) ** 0.5;
return {x: -w + x, y: -h + y, w: w * 2, h: h * 2};
}
function boundEllipse({x, y, rx, ry, rotate, startAng, endAng}) {
const normalizeAng = ang => (ang % TAU + TAU) % TAU;
const getPoint = ang => {
const cA = Math.cos(ang);
const sA = Math.sin(ang);
return [cA * rx * xAx - sA * ry * xAy, cA * rx * xAy + sA * ry * xAx];
}
const extrema = a => { // from angle
var i = 0;
while(i < 4) {
const ang = normalizeAng(a + Math.PI * (i / 2));
if ((ang > startAng && ang < endAng) || (ang + TAU > startAng && ang + TAU < endAng)) {
const [xx, yy] = getPoint(ang);
minX = Math.min(minX, xx);
maxX = Math.max(maxX, xx);
minY = Math.min(minY, yy);
maxY = Math.max(maxY, yy);
}
i ++;
}
}
// UPDATE bug fix (1) for full ellipse
const checkFull = startAng !== endAng; // Update fix (1)
startAng = normalizeAng(startAng);
endAng = normalizeAng(endAng);
(checkFull && startAng === endAng) && (endAng += TAU); // Update fix (1)
const xAx = Math.cos(rotate);
const xAy = Math.sin(rotate);
endAng += endAng < startAng ? TAU : 0;
const [sx, sy] = getPoint(startAng);
const [ex, ey] = getPoint(endAng);
var minX = Math.min(sx, ex);
var maxX = Math.max(sx, ex);
var minY = Math.min(sy, ey);
var maxY = Math.max(sy, ey);
extrema(-Math.atan((ry * xAy) / (rx * xAx))); // Add x Axis extremas
extrema(-Math.atan((rx * xAy) / (ry * xAx))); // Add y Axis extremas
return {x: minX + x, y: minY + y, w: maxX - minX, h: maxY - minY};
}
function drawExtent({x,y,w,h}) {
ctx.moveTo(x,y);
ctx.rect(x, y, w, h);
}
function drawEllipse({x, y, rx, ry, rotate, startAng, endAng, dir}) {
ctx.ellipse(x, y, rx, ry, rotate, startAng, endAng, dir);
}
function drawFullEllipse({x, y, rx, ry, rotate, dir}) {
ctx.ellipse(x, y, rx, ry, rotate, 0, TAU, dir);
}
mainLoop(0);
function mainLoop(time) {
ctx.clearRect(0, 0, W, H);
// Animate ellipse
ellipse.startAng = time / 1000;
ellipse.endAng = time / 2000;
ellipse.rotate = Math.cos(time / 14000) * Math.PI * 2;
ellipse.ry = Math.cos(time / 6000) * (W / 4 - 10) + (W / 4);
// Draw full ellipse and bounding box.
ctx.strokeStyle = "#F008";
ctx.beginPath();
drawFullEllipse(ellipse);
drawExtent(boundEllipseAll(ellipse));
ctx.stroke();
// Draw ellipse segment and bounding box.
ctx.strokeStyle = "#0008";
ctx.beginPath();
drawEllipse(ellipse);
drawExtent(boundEllipse(ellipse));
ctx.stroke();
requestAnimationFrame(mainLoop)
}
canvas { border: 1px solid black }
<canvas id="canvas" width="200" height="180"></canvas>

How to transalate hexagon in canvas html using typescript

i drew a hexagon on canvas in html and i want to tranaslate the hexagon in canvas when i use a translate method it doesn't translate the hexagon but when i translate it does translate when i use the rectangle .
var canvas:HTMLCanvasElement = document.getElementById("myCanvas");
var context:CanvasRenderingContext2D = canvas.getContext("2d");
var x = 300;
var y = 100;
context.beginPath();
context.moveTo(x, y);
x = x + 120;
y = y + 100;
context.lineTo(x, y);
y = y + 120;
context.lineTo(x, y);
x = x - 125;
y = y + 100;
context.lineTo(x, y);
x = x - 125;
y = y - 100;
context.lineTo(x, y);
y = y - 120;
context.lineTo(x, y);
x = x + 130;
y = y - 100;
context.lineTo(x, y);
context.strokeStyle = "red";
context.lineWidth = 4;
context.fillStyle = "blue";
context.fill();
context.translate(400,400);
context.fillStyle = "blue";
context.fill();
context.save();
context.fillRect(10, 10, 100, 50);
context.translate(70, 70);
context.fillRect(10, 10, 100, 50);
Edit 1:
according to the #helder gave the answer I've made the changes but translate is not working
function hexagon(x:number, y:number, r:number, color:string) {
context.beginPath();
var angle = 0
for (var j = 0; j < 6; j++) {
var a = angle * Math.PI / 180
var xd = r * Math.sin(a)
var yd = r * Math.cos(a)
context.lineTo(x + xd, y + yd);
angle += 360 / 6
}
context.fillStyle = color;
context.fill();
context.translate(70,70);
context.fill();
}
hexagon(100, 100, 50, "red")

I would try to create a function that draws the hexagon that way you don't have to use translate.
See below
c = document.getElementById("canvas");
context = c.getContext("2d");
function hexagon(x, y, r, color) {
context.beginPath();
var angle = 0
for (var j = 0; j < 6; j++) {
var a = angle * Math.PI / 180
var xd = r * Math.sin(a)
var yd = r * Math.cos(a)
context.lineTo(x + xd, y + yd);
angle += 360 / 6
}
context.fillStyle = color;
context.fill();
}
hexagon(50, 50, 30, "red")
hexagon(40, 40, 10, "blue")
hexagon(60, 60, 10, "lime")
<canvas id=canvas >
Here is a break down of function hexagon(x, y, r, color)
it takes the center of the hexagon (x,y) a radius (r) and color
we loop over the six vertices and draw lines
the calculations are just a bit of trigonometry nothing fancy
With that we can draw hexagons at any location we want.
and that same function you can easily refactor to draw an octagon or other polygons.
Here is an animated version of those hexagons
c = document.getElementById("canvas");
context = c.getContext("2d");
delta = 0
function hexagon(x, y, r, color) {
context.beginPath();
var angle = 0
for (var j = 0; j < 6; j++) {
var a = angle * Math.PI / 180
var xd = r * Math.sin(a)
var yd = r * Math.cos(a)
context.lineTo(x + xd, y + yd);
angle += 360 / 6
}
context.fillStyle = color;
context.fill();
}
function draw() {
context.clearRect(0, 0, c.width, c.height)
var xd = 10 * Math.sin(delta)
var yd = 10 * Math.cos(delta)
hexagon(50 - xd, 50 - yd, 30, "red")
hexagon(40 + xd, 40 + yd, 10, "blue")
delta += 0.2
}
setInterval(draw, 100);
<canvas id=canvas>
As you can see there is no need to use translate

given 2 center coordinates, how to find all Rectangle axes?

for a game I'm building, I need to draw a rectangle on two sides of a line made from two coordinates.
I have an image illustrating this "hard to ask" question.
given coordinates (-4,3) and (3, -4)
given that the width of the rectangle will be 4 (for example)
I need to find all (x1, y1), (x2, y2), (x3, y3), (x4, y4)
** I need to write this in Javascript eventually.
your help is much appreciated.

I've tried to solve this using javascript & canvas. The problem is that the coordinates in canvas are upside down, I suppose you already know this. Also since your rect would be extremely small, I've multiplied your numbers by 10.
const canvas = document.querySelector("canvas");
const ctx = canvas.getContext("2d");
let cw = canvas.width = 300,
cx = cw / 2;
let ch = canvas.height = 300,
cy = ch / 2;
const rad = Math.PI / 180;
ctx.translate(cx,cy)
//axis
ctx.strokeStyle = "#d9d9d9";
ctx.beginPath();
ctx.moveTo(-cx,0);
ctx.lineTo(cx,0);
ctx.moveTo(0,-cy);
ctx.lineTo(0,cy);
ctx.stroke();
// your data
let p1={x:-40,y:30};
let p2={x:30,y:-40};
// the angle of the initial line
let angle = Math.atan2(p2.y-p1.y, p2.x-p1.x);
// the center of the line
let c =
{ x: p1.x + (p2.x - p1.x)/2,
y: p1.y + (p2.y - p1.y)/2
}
let w = dist(p1, p2);//the width of the rect
let h = 60;//the height of the rect
// draw the initial line
line(p1,p2);
// draw the center as a red point
marker(c);
// calculate the opoints of the rect
function rectPoints(w,h){
let p1 = {
x : c.x -w/2,
y : c.y -h/2
}
let p2 = {
x : c.x + w/2,
y : c.y -h/2
}
let p3 = {
x : c.x + w/2,
y : c.y +h/2
}
let p4 = {
x : c.x -w/2,
y : c.y +h/2
}
// this rotate all the points relative to the center c
return [
rotate(p1,c, angle),
rotate(p2,c, angle),
rotate(p3,c, angle),
rotate(p4,c, angle)
]
}
// draw the rect
ctx.strokeStyle = "blue";
drawRect(rectPoints(w,h));
// some helpful functions
function line(p1,p2){
ctx.beginPath();
ctx.moveTo(p1.x,p1.y);
ctx.lineTo(p2.x,p2.y);
ctx.stroke();
}
function dist(p1, p2) {
let dx = p2.x - p1.x;
let dy = p2.y - p1.y;
return Math.sqrt(dx * dx + dy * dy);
}
function marker(p,color){
ctx.beginPath();
ctx.fillStyle = color || "red";
ctx.arc(p.x,p.y,4,0,2*Math.PI);
ctx.fill();
}
function rotate(p,c, angle){
let cos = Math.cos(angle);
let sin = Math.sin(angle);
return {
x: c.x + (p.x - c.x) * cos - (p.y - c.y) * sin,
y: c.y + (p.x - c.x) * sin + (p.y - c.y) * cos
}
}
function drawRect(points){
ctx.beginPath();
ctx.moveTo(points[0].x,points[0].y);
ctx.lineTo(points[1].x,points[1].y);
ctx.lineTo(points[2].x,points[2].y);
ctx.lineTo(points[3].x,points[3].y);
ctx.lineTo(points[0].x,points[0].y);
ctx.closePath();
ctx.stroke();
}
canvas{border:1px solid #d9d9d9}
<canvas></canvas>

Points A, B form vector
M.X = B.X - A.X
M.Y = B.Y - A.Y
Perpendicular vector
P.X = -M.Y
P.Y = M.X
Length of P:
Len = Math.sqrt(P.X*P.X + P.Y*P.Y)
Normalized (unit) perpendicular:
uP.X = P.X / Len
uP.Y = P.Y / Len
Points
X1 = A.X + uP.X * HalfWidth
Y1 = A.Y + uP.Y * HalfWidth
(X4, Y4) = (A.X - uP.X * HalfWidth, A.Y - uP.Y * HalfWidth)
and similar for points 2 and 3 around B

HTML5 Canvas thick lineWidth ellipse has strange blank

I'm making a drawing app with html5 canvas.
User can draw ellipses and select both line color and fill color.
(including transparent colors)
When selected color is not transparent, it works fine.
But when transparent color is selected and border line width is thick, there are problems.(Q1 and Q2)
This is the image
http://tinypic.com/view.php?pic=28ry4z&s=9#.VoRs7U8jHSg
I'm using drawEllipse() method from below.
the relation of the bezier Curve and ellipse?
Does anyone solve this problems?
Any help will be greatly appreciated.
[Q1]
When the lineWidth is larger than the ellipse's width, there is a strange blank in the ellipse, and lineWidth is strangely thin.
Internet Explorer works fine, but both Firefox and Safari web browsers have this problem.
How can I change the blank area to be blue?
[Q2]
I'm using transparent colors and I want to draw the ellipse with 2 colors.
(stroke is blue and fill is red)
But the stroke color and the fill color are mixed and there is magenta area in the ellipse.
How can I draw the ellipse with 2 colors?
(I want to change the magenta area to blue)
One time fill is preferred when possible.
Here is my code
// this method is from
// https://stackoverflow.com/questions/14169234/the-relation-of-the-bezier-curve-and-ellipse
function _drawEllipse(ctx, x, y, w, h) {
var width_over_2 = w / 2;
var width_two_thirds = w * 2 / 3;
var height_over_2 = h / 2;
ctx.beginPath();
ctx.moveTo(x, y - height_over_2);
ctx.bezierCurveTo(x + width_two_thirds, y - height_over_2, x + width_two_thirds, y + height_over_2, x, y + height_over_2);
ctx.bezierCurveTo(x - width_two_thirds, y + height_over_2, x - width_two_thirds, y - height_over_2, x, y - height_over_2);
ctx.closePath();
ctx.stroke();
}
function ellipse_test() {
var canvas = document.getElementById('sample1');
var ctx = canvas.getContext('2d');
var x = 100;
var y = 100;
var w = 40;
var h = 100;
ctx.lineWidth = 30;
ctx.fillStyle = "rgba(255,0,0,0.5)";
ctx.strokeStyle = "rgba(0,0,255,0.5)";
ctx.globalCompositeOperation = "source-over";
for (var r = 0; r < 50; r++) {
_drawEllipse(ctx, x, y, r, r * 2);
ctx.fill();
x += 60;
if (x > 1000) {
x = 100;
y += 200;
}
}
}
ellipse_test();
<canvas id="sample1" style="border:1px solid blue; background:black;" width="1200" height="800"></canvas>
this is the image on firefox

Both problems are caused by the fact that multiple strokes/fills of semi-transparent colors over an area will cause that area to become a blend of colors (much like an artist blends multiple colors).
You can resolve both problems by converting semi-transparent colors into opaque colors:
function RGBAtoRGB(r, g, b, a, backgroundR,backgroundG,backgroundB){
var r3 = Math.round(((1 - a) * backgroundR) + (a * r))
var g3 = Math.round(((1 - a) * backgroundG) + (a * g))
var b3 = Math.round(((1 - a) * backgroundB) + (a * b))
return "rgb("+r3+","+g3+","+b3+")";
}
// convert 50%-red foreground fill + 100% black background into opaque (=="red-brownish")
ctx.fillStyle = RGBAtoRGB(255,0,0,0.50, 0,0,0,1); // "rgba(255,0,0,0.5)";
// convert 50%-blue foreground stroke + 100% black background into opaque (=="blueish")
ctx.strokeStyle = RGBAtoRGB(0,0,255,0.50, 0,0,0,1); // "rgba(0,0,255,0.5)";
Example code refactored to use opaque fills & strokes:
ellipse_test();
// this method is from
// http://stackoverflow.com/questions/14169234/the-relation-of-the-bezier-curve-and-ellipse
function _drawEllipse(ctx, x, y, w, h) {
var width_over_2 = w / 2;
var width_two_thirds = w * 2 / 3;
var height_over_2 = h / 2;
ctx.beginPath();
ctx.moveTo(x, y - height_over_2);
ctx.bezierCurveTo(x + width_two_thirds, y - height_over_2, x + width_two_thirds, y + height_over_2, x, y + height_over_2);
ctx.bezierCurveTo(x - width_two_thirds, y + height_over_2, x - width_two_thirds, y - height_over_2, x, y - height_over_2);
ctx.closePath();
}
function ellipse_test() {
var canvas = document.getElementById('sample1');
var ctx = canvas.getContext('2d');
var x = 100;
var y = 100;
var w = 40;
var h = 100;
ctx.lineWidth = 30;
ctx.fillStyle = 'black';
ctx.fillRect(0, 0, canvas.width, canvas.height);
ctx.fillStyle = RGBAtoRGB(255, 0, 0, 0.50, 0, 0, 0, 1); // "rgba(255,0,0,0.5)";
ctx.strokeStyle = RGBAtoRGB(0, 0, 255, 0.50, 0, 0, 0, 1); // "rgba(0,0,255,0.5)";
ctx.globalCompositeOperation = "source-over";
for (var r = 0; r < 50; r++) {
_drawEllipse(ctx, x, y, r, r * 2);
ctx.stroke();
ctx.fill();
x += 60;
if (x > 1000) {
x = 100;
y += 200;
}
}
}
function RGBAtoRGB(r, g, b, a, backgroundR, backgroundG, backgroundB) {
var r3 = Math.round(((1 - a) * backgroundR) + (a * r))
var g3 = Math.round(((1 - a) * backgroundG) + (a * g))
var b3 = Math.round(((1 - a) * backgroundB) + (a * b))
return "rgb(" + r3 + "," + g3 + "," + b3 + ")";
}
body {
background-color: ivory;
}
#canvas {
border: 1px solid red;
background-color=black;
}
<canvas id="sample1" width=1200 height=800></canvas>
Overlapping
...And obviously if you draw your ellipses very close together they will eventually overlap. That's what's causing your Q1-line thinning.

QML context2d lineWidth

I'm trying to make a circle of lines in a qml canvas, but when i change the lineWidth to something other than 1, it messes up the position of the strokes, so that they are extended into the center.
left:lineWidth=1 , right:lineWidth=2
screenshot
Canvas {
id:spinner
anchors.centerIn: parent
width:400
height: 400
onPaint: {
var ctx = getContext("2d");
var x,y,rotx,roty
ctx.reset();
ctx.beginPath();
for (var i=0;i<10;i++){
rotx = Math.cos(Math.PI*2*i/10)
roty = Math.sin(Math.PI*2*i/10)
x = 10*rotx + this.width/2
y = 10*roty + this.height/2
ctx.moveTo( x , y )
x = (10 + 10)* rotx + this.width/2
y = (10 + 10)* roty + this.height/2
ctx.lineTo( x , y )
ctx.closePath()
}
ctx.lineWidth = 1;
ctx.lineCap = "round";
ctx.stroke();
}
}
can someone help me?

There shouldn't be any need to use closePath() (assuming it works the same way as with html5-canvas). All this will do is to tell canvas to connect first point with last point. moveTo() will create the necessary sub-path.
Also, the calculations must be adjusted to use an inner and outer radius relative to center:
onPaint: {
var ctx = getContext("2d");
var x,y,rotx,roty, cx, cy, innerRadius, outerRadius, angle;
ctx.reset();
ctx.beginPath();
cx = this.width/2;
cy = this.height/2;
innerRadius = 10;
outerRadius = 100;
for (var i=0;i<10;i++){
angle = Math.PI*2*i/10;
x = cx + innerRadius * Math.cos(angle);
y = cy + innerRadius * Math.sin(angle);
ctx.moveTo( x , y )
x = cx + outerRadius * Math.cos(angle);
y = cy + outerRadius * Math.sin(angle);
ctx.lineTo( x , y )
}
ctx.lineWidth = 1;
ctx.lineCap = "round";
ctx.stroke();
}