Find corners of a rotated rectangle given its center point and rotation

Question

Can someone give me an algorithm that finds the position of all four corners of a rectangle if I know its center point(in global coordinate space), width and height, and its

Answer 1

The coordinates of each vertices:

 Center point = (center.x, center.y)
 Angle        = angle
 Height       = height
 Width        = width      



TOP RIGHT VERTEX:
Top_Right.x = center.x + ((width / 2) * cos(angle)) - ((height / 2) * sin(angle))
Top_Right.y = center.y + ((width / 2) * sin(angle)) + ((height / 2) * cos(angle))



TOP LEFT VERTEX:
Top_Left.x = center.x - ((width / 2) * cos(angle)) - ((height / 2) * sin(angle))
Top_Left.y = center.y - ((width / 2) * sin(angle)) + ((height / 2) * cos(angle))



BOTTOM LEFT VERTEX:
Bot_Left.x = center.x - ((width / 2) * cos(angle)) + ((height / 2) * sin(angle))
Bot_Left.y = center.y - ((width / 2) * sin(angle)) - ((height / 2) * cos(angle))



BOTTOM RIGHT VERTEX:
Bot_Right.x = center.x + ((width / 2) * cos(angle)) + ((height / 2) * sin(angle))
Bot_Right.y = center.y + ((width / 2) * sin(angle)) - ((height / 2) * cos(angle))

This algorithm is a compressed version of these 3 steps:

Step 1: Center your rectangle around the origin

Step 2: Apply the rotation matrix to each vertex

Step 3: Move the rotated rectangle to the correct position, by adding the center point to each coordinate

This is explained in more depth here https://math.stackexchange.com/questions/126967/rotating-a-rectangle-via-a-rotation-matrix