From Degenerate Patches to Triangular and Trimmed Patches

CAD systems are usually based on a tensor product representation of free form surfaces. In this case, trimmed patches are used for modeling non rectangular zones. Trimmed patches provide a reasonable solution for the representation of general topologies, provided that the gap between equivalent trimming curves in the euclidean space is small enough. Several commercial CAD systems, however, represent certain non rectangular surface regions through degenerate rectangular patches. Degenerate patches produce rendering artifacts and can lead to malfunctions in the subsequent geometric operations. In the present paper, two algorithms for converting degenerate tensor-product patches into triangular and trimmed rectangular patches are presented. The algorithms are based on speciic degree reduction algorithms for B ezier curves. In both algorithms, the nal surface approximates the initial one in a quadratic sense while inheriting its boundary curves. In the second one, " ? G 1 continuity is achieved. Approximation errors are analyzed and some examples are presented and discussed. Approximation errors can be arbitrarily decreased through the degree elevation of the degenerate patches.