# How to calculate a bounding box for a rectangle rotated around its center?

I am looking to calculate the bounding box of a rectangle rotated around its center. I have read this question and while MarkusQ’s answer works in general, it is not efficient enough for my needs. I am trying to get Troubadour’s answer working, but it seems to only work when the origin of rotation is around a corner, not the center.

Is it possible to adapt his solution to work with rectangles that have their origin of rotation around their center?

I’ve developed a full recreation of the problem below:

```let canvas = document.querySelector("canvas");
let ctx = canvas.getContext("2d");

function drawRectangle(rX, rY, rW, rH) {
ctx.beginPath();
ctx.rect(rX, rY, rW, rH);
ctx.stroke();
}

function degreesToRadians(degrees) { return degrees * (Math.PI / 180); }

ctx.translate(centerX, centerY);
ctx.translate(-centerX, -centerY);
}

function drawRotatedRectangle(rX, rY, rW, rH, rAngle) {
let rXCenter = rX + rW / 2;
let rYCenter = rY + rH / 2;

rotateCanvas(rAngle, rXCenter, rYCenter);
drawRectangle(rX, rY, rW, rH);
rotateCanvas(-rAngle, rXCenter, rYCenter);
}

function computeAABBCenter(x, y, w, h, theta) {
const ux = Math.cos(theta) * 0.5; // half unit vector along w
const uy = Math.sin(theta) * 0.5;
const wx = w * ux;
const wy = w * uy; // vector along w
const hx = h * -uy;
const hy = h * ux; // vector along h

// all point from top left CW
const x1 = x - wx - hx;
const y1 = y - wy - hy;
const x2 = x + wx - hx;
const y2 = y + wy - hy;
const x3 = x + wx + hx;
const y3 = y + wy + hy;
const x4 = x - wx + hx;
const y4 = y - wy + hy;

return {
x1: Math.min(x1, x2, x3, x4),
y1: Math.min(y1, y2, y3, y4),
x2: Math.max(x1, x2, x3, x4),
y2: Math.max(y1, y2, y3, y4),
};
}

let rX = 100;
let rY = 100;
let rW = 100;
let rH = 50;
let rA = 0.707;

drawRotatedRectangle(rX, rY, rW, rH, rA);

let bb = computeAABBCenter(rX, rY, rW, rH, rA);

drawRectangle(bb.x1, bb.y1, bb.x2 - bb.x1, bb.y2 - bb.y1);```
`body { margin: 0; overflow: hidden; }`
`<canvas width="800" height="800"></canvas>`

As you can see, the bounding box rectangle is not correct. Here’s what it currently looks like, and what it should look like: ```H = w * Abs(Sin(Fi)) + h * Abs(Cos(Fi))
Having `rXCenter, rYCenter`, you can find get bounds coordinates
```x0  = rXCenter - W/2