Computational Intelligence In CAD/CAM Applications

This paper presents a fundamental, direct, and powerful approach to the surface/surface intersection problem in CAD/CAM applications. The algorithm is designed and implemented in three steps: a) Preprocessing- locate the potentially intersecting sections of the surfaces and decompose the surfaces into surface elements within specified flatness tolerance; b) Intersection- decompose the possibly intersecting pairs of surface elements into continuous surface triangulations to find the approximate intersections between the pairs of surface elements; c) Postprocessing-assemble the intersection primitives into curves of intersection, refine the accuracy of computed intersection points, and compact the intersection curves. This surface/surface intersection algorithm is applicable to the widest class, C°, of parametric surfaces, an enhancement over the existing algorithms applicable to only Ck, k≥ 1, surfaces. This implementation, based on computational intelligence, requires no human interaction for intersection curve pattern recognition

A Line/Trimmed NURBS Surface Intersection Algorithm Using Matrix Representations

International audienceWe contribute a reliable line/surface intersection method for trimmed NURBS surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to intersection points with multiple pre-images. We then apply our intersection algorithm to mesh NURBS surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other intersection approaches as well as a variety of meshing experiments

Beiträge zu globalen Fragen in der NURBS-Technik

Die vorliegende Dissertation befasst sich mit den Eigenschaften von NURBS-Kurven und -Flächen und deren Anwendung in praktischen Algorithmen zur Lösung von geometrischen Problemen wie z.B. der Berechnung von Projektions- oder Schnittpunkten. Weiterhin ist eine differentialgeometrische Aussage enthalten, die Aussagen über das freie Rollen von Kugeln auf offenen Kurven erlaubt