Curvature continuity between adjacent rational Bézier patches (Q1195759)

The paper discusses the curvature continuity between two adjacent rational Bézier patches. Therefore the connecting functions, which are in polynomial or rational polynomial form, are investigated in more detail. In particular, the cases of rectangular and triangular patches are compared and the corresponding costraints conditions are obtained. Main results are necessary and sufficient conditions for curvature continuity, expressed by the control points and the connecting functions. Furthermore, simple sufficient conditions are derived. The proofs show how the free shape parameters in the constraint equations can be chosen. Two simple constructions of a smooth connection of adjacent patches complete this interesting paper.