Topologically consistent trimmed surface approximations based on triangular patches

Topologically consistent algorithms for the intersection and trimming of free-form parametric surfaces are of fundamental importance in computer-aided design, analysis, and manufacturing. Since the intersection of (for example) two bicubic tensor-product surface patches is not a rational curve, it is usually described by approximations in the parameter domain of each surface. If these approximations are employed as "trim curves", their images in R3 do not agree precisely, and the resulting trimmed surfaces may exhibit "gaps" and "overlaps" along their common edge, an artifact that often incurs failure of downstream applications. We present a direct and simple approach to the problem, wherein the intersection curve is described explicitly by the sides of a sequence of triangular B

• Type: Journal
• Year: 2004
• Where: CAGD
• Authors: Rida T. Farouki, Chang Yong Han, Joel Hass, Thomas W. Sederberg
• Keywords: CAGD 2004, Intersection Curve, Surfaces, Triangular B´ezier Patches