Mesh Generation from Boundary Models with Parametric Face Representation

The triangulation of boundary representation geomet-ries (BRep geometries) is neccessary for display generation , stereo-lithography applications and also nite element mesh (FE mesh) generation. The accuracy of the tesselation is of great signiic-ance not only for stereo-lithography and rendering algorithms but also for FE mesh generation, since even minor simpliications of the geometry of the solid can lead to large errors in the FE computation. We therefore turn our attention to a new incremental algorithm for the accurate triangulation of meshes of trimmed parametric surfaces. Instead of triangulating each face seperately, the faces of the solid are glued and triangu-lated together according to the neighbourhood information of the BRep. By this procedure, glueing together faces with diierent triangulations is avoided. Another advantage of the algorithm is that the error between the linear approximation of the boundary and the boundary itself is controlled step by step until it lies within a predeened tolerance : Because the algorithm is fully incremental, later improvements of this tolerance can be easily added. The techniques we used to produce a robust implementation of this algorithm under nite precision arithmetic are reported.