The invariant functions and invariant-image conditions of the rational Bézier triangles
The paper focuses on determining the invariant functions and the invariant-image conditions of rational Bézier triangles of arbitrary degree with arbitrary non-zero weights. The author shows that \(\frac{1}{2} (n+1)(n+2)-3\) real-valued invariants, and one discrete-valued invariant determine a complete set the triangles of degree \(n\). The required image-invariance conditions are expressed in a functional equation, which is solved. The explicit form of a complete set of real-valued invariants is computed and shown, when augmented by a single discrete-valued invariant, to determine a complete set. The author uses in his demonstrations the fundamental theorem on invariants of Lie groups and techniques similar to those elaborated for the biquadratic and bicubic Bézier functions.
scientific article; zbMATH DE number 6115366