如何从中心找到旋转矩形的顶点？

Question

I have a rectangle that I've rotated around its center by an angle. How can I derive the verticies from the rectangle?

Answer 1

Apply the rotation matrix to the vertices.

For example, if the the origin is in the center of your rectangle and the coordinates of a vertex are given by vx and vy Then the new coordinates for this vertex are given by:

v_new.x=v.x*cos(angle)-v.y*sin(angle)
v_new.y=v.x*sin(angle)+v.y*cos(angle)

(assuming counter clockwise rotation )

Answer 2

Translate such that the rectangle's center is (0,0). View each point as not part of the rectangle, but as part of a circle, and the line segment from the rectangle's center as the center of that circle. Then you are solving a different problem: given a circle at the origin and a point on that circle (or line segment), what is the point (angle) degrees rotated around the circle. I'll leave looking up the appropriate algorithm for that one to you :)