Approximate development of trimmed patches for surface tessellation

This paper presents a method to construct an auxiliary planar domain of triangulation for tessellating trimmed parametric surface patches. By minimizing a mapping error function, an approximate locally isometric mapping between a given trimmed parametric surface patch and its triangulation domain is constructed. In this way the shape of triangular elements on the triangulation domain is approximately preserved when mapped into three-dimensional space. We also provide an efficient method to achieve a good initial guess for the minimization of mapping error function. Furthermore, our proposed method guarantees a homeomorphism between a triangulation domain and parametric space/given surface patch by robustly removing the possibility of self-intersection on the developed surface net. Furthermore, practical application of the proposed algorithm can include the formation of ship hulls, ducts, shoes, clothing and automobile parts as well as the surface meshing procedure.