The invariant functions and invariant-image conditions of the rational Bezier triangles
A functional equation for invariant-image is presented and solved to identify the largest group of image-preserving weight transformations for the rational B,zier triangles. A fundamental theorem on the invariants of Lie group actions is used to demonstrate that 1/2(n + 1)(n + 2) - 3 real-valued, functionally-independent invariants exist for the degree triangles. Explicit forms of the real-valued invariants are derived; and a further, discrete-valued, invariant is identified and shown to complete the set required for invariant image.
invariant functions rational parametrisation geometric modeling transformation groups