How to find the vertex coordinates of a rotated rectangle in 2D space?

Question

Geometry

There is a rectangle known for its length and width, and the angle of rotation. Axis of rotation in the center. This rectangle.
How do I find the coordinates of the vertices of this rectangle. I found an article
on Wikipedia . It describes the rotation formula in two-dimensional space, I did not understand how to use it. you need something like: var a_x = ... var a_y = ... var b_x = ... var b_y = ... var c_x = ... var c_y = ... var d_x = ... var d_y = ... Maybe in as there is some function that returns the coordinates? If not, how do you find them?

Answer 1

For example - let's rotate the rectangle by 90 degrees, its width will be 6, height 4.
Since it is known that the pivot point is in the center - we can easily find the coordinates by dividing the width and height in half
A (x, y) - Ax \u003d 0 (coordinate) - ( 6 / 2), Ay \u003d 0 + (4 / 2) A (-3, 2)
B (x, y) - Bx \u003d 0 (coordinate) + (6 / 2), Wu \u003d 0 + (4 / 2) B(3, 2)
C(x, y) - Cx = 0(coordinate) + (6 / 2), Cy = 0 - (4 / 2) C(3, -2)
D(x, y) - Dx = 0(coordinate) - (6 / 2), Dy = 0 - (4 / 2) D(-3, -2)
Find point A after rotation
according to your formula
Ax = -3 * cos90 - 2 * sin90 = -3 * 0 - 2 * 1 = -2
Ay = -3 * sin90 + 2 *cos90 = -3 * 1 + 2 * 0 = -3
A(x, y) = (-2, -3);
We do the same actions with all points, and round the numbers if possible.