slideframe

vector  slideframe(vector t0, vector t1, vector v0)

vector  slideframe(vector x0, vector t0, vector v0, vector x1, vector t1)

Given an arbitrary vector, v0, and two normalized vectors, t0 and t1, this function applies to v0 the minimal rotation that would take t0 to t1, and returns the result. This is equivalent to v0*dihedral(t0,t1), but should be slightly faster.

The second function signature requires that x1-x0 is in the same direction as the average of t0 and t1, and is provided for compatibility, though should produce approximately the same results.

You can use this function to extend a curve normal at the starting point of a curve to the entire curve in a rotation minimizing fashion.