Appendix B. 2D Complex Frames
The basic 2D rotation matrix changing the axes by an angle θ and its interpolation in terms of a local frame on a curve, with tangent vector T and normal vector N, may be defined as
Equation B.1.
A double-valued quaternion-like parameterization of the 2D frame may be written in the form
Equation B.2.
We can easily verify that if (a, b) is a point on S1 embedded in (i.e., a2 + b2 = 1) this is an orthonormal parameterization ...
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