# Find the coordinate of a corner when you know the center, size and rotation

I know the coordinate of the center of an object (box of any size). I also know the rotation of the box and its size.

How could I calculate the position of the top left corner?

I have no math knowledge, and this problem is killing me.

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Just to make sure we're on the same page: Is this in 2D, or 3D? "box" means a square, right? What's the "size" of the box? Do you mean "side length" or area/volume? What's the "rotation" of a box? It is the angle it's diagonal makes with the $x$-axis? –  user2468 Oct 20 '12 at 0:28

## 1 Answer

In 2D

The position of $D'$ is

$$\left\{\left(x_1-x_0\right) \cos (\theta )+x_0+\left(y_0-y_1\right) \sin (\theta ),\left(x_1-x_0\right) \sin (\theta )+\left(y_1-y_0\right) \cos (\theta )+y_0\right\}$$

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