I get your point.

(Though I can't use the same matrix for two consecutive transformations as the point at the maxima will generally not be at the middle.)

Still calling sin/cos twice is negligible w.r.t say.... 40-50 calls...and it was a bit of premature optimization to think otherwise.

I don't understand interpolation yet and it seems interesting, so I'd try to get its theory first, provided that it doesn't need more maths than I know or can learn in a day or two .