Reliable Joining Of Surfaces For Combined Mesh-Surface Models

Abstract

Algorithms to join two mesh patches along an edge are of immediate practical interest in the context of higher-level operations on models of objects formed by such mesh patches. Such models are widely used in graphical visualization and simulation, shape interrogation, and other areas. Thus, there are now available methods to join two subdivision surfaces along a common edge curve, as well as methods to join mesh patches that approximate given trimmed-surface patches. The latter problem is studied in this paper. The auxiliary information available to the algorithm, in the context of surface joining, varies, depending upon circumstances. In particular, it may or may not be true that an explicit common edge curve, representing the boundary between the two patches to be joined, is available as part of the data. Even in the case, however, when maximal auxiliary information is available algorithms are not necessarily reliable. For example, methods that do not use normal-vector error criteria, to measure the discrepancy between the surface patch and the associated mesh patch, can produce poor results, due to large changes in the normal direction of a triangle near the mesh boundary. It is even possible to give examples where the triangles near the joined boundary are turned upside down by the joining process, so that computed meshes self-intersect. In this paper an algorithm is presented that uses a proxy for a normal-vector error criterion, and the Whitney extension theorem, to produce reliable algorithms. Examples are given, and an implementation is described.