How is this idea applied to a polygon model in order to rotate the entire object? Can this be connected to circles with a formula for performing rotation?
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You probably work with matrices (if you don't, I'd suggest you do), so what you want to check out is rotation matrices.
Basically, by multiplying the vectors by the rotation matrix, you obtain the rotated vector, and by applying this to every point of the polygon, you get your rotated polygon.
Note that it also applies to 3D rotations, even if it's not exactly the same matrix.

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