TRIANGULATION OF TRIMMED SURFACES IN PARAMETRIC SPACE

The paper presents a new approach for triangulating trimmed surfaces. The basic idea is to perform the triangulation completely in parametric space. The trimmed regions of the surfaces are first mapped into parametric space and approximated by 2D polygonal regions, which are then pretriangulated hy a restricted Delaunay triangulation algorithm. The generated triangles are subdivided further until each edge of the triangles is smaller than the allowed length that results from the surface definition and the specified tolerance. All the triangles are finally mapped back into Euclidean space so that the coordinate triples for the triangle vertices can be calculated. This approach makes the triangulation more reliable and faster, and it is also easy to avoid cracks between patches and surfaces. Thus, the algorithm is particularly suitable for the generation of a valid triangulation model for many engineering applications,for example stereolithography.