Lummox JR wrote:
The final equation for the x and y of each corner has six terms, combining t, sin(n+mt), cos(n+mt), t*sin(n+mt), t*cos(n+mt), and a constant.
Why are the arguments of since and cosine linear? I'm not seeing why you'd have that just for applying a rotation.
Interpolation of transforms is done by this formula, when there is an angle difference (other than exactly 180°):
M = S * R * T
The S matrix represents scale and shear, and T is translation; both of those are done linearly. R is strictly a rotation matrix, and the angle is interpolated linearly. Therefore R is always in the form of matrix(cos(a+b*t), sin(a+b*t), 0, -sin(a+b*t), cos(a+b*t), 0).
So basically with the S matrix every element (except the translation parts, which aren't used) is in the form of a+b*t, and in R it's either sin(a+b*t) or cos(a+b*t). That gives you four types of terms (sine and cosine with and without being multiplied by t), and then the translation adds a t term and a constant.
Why are the arguments of since and cosine linear? I'm not seeing why you'd have that just for applying a rotation.