How to make a pixel-by-pixel rotation of a shape (vector)?

Question

Mathematics

There is a square - like a set of pixels.
Represented as a list of points
A = [(i1,j1), (i2,j2) ....]
After rotating this square, I need to get a new list with pixels.
The problem is that if each point of the square is multiplied by the rotation matrix, then not integer values ​​are obtained, but a whole pixel .... As a result, if the whole thing is rounded, then it turns out not quite what you need.
How to get the set of pixels of a rotated square?

Answer 1

On the contrary - you go through the points of the outer square, which obviously contains the rotated square, and calculate which point of the rotated square you hit (if you hit).