Computation of Self-Intersections of Offsets of Be´zier Surface Patches
- 1 June 1997
- journal article
- Published by ASME International in Journal of Mechanical Design
- Vol. 119 (2) , 275-283
- https://doi.org/10.1115/1.2826247
Abstract
Self-intersection of offsets of regular Be´zier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Be´zier surface patches. Examples illustrate the principal features and robustness characteristics of the method.Keywords
This publication has 16 references indexed in Scilit:
- Umbilics and lines of curvature for shape interrogationPublished by Elsevier ,1999
- Interrogation of differential geometry properties for design and manufactureThe Visual Computer, 1994
- Computation of stationary points of distance functionsEngineering with Computers, 1993
- Computation of singularities and intersections of offsets of planar curvesComputer Aided Geometric Design, 1993
- Computation of the solutions of nonlinear polynomial systemsComputer Aided Geometric Design, 1993
- Localization of rational B-spline surfacesEngineering with Computers, 1991
- Free-Form Plate Modeling Using Offset SurfacesJournal of Offshore Mechanics and Arctic Engineering, 1988
- Loop detection in surface patch intersectionsComputer Aided Geometric Design, 1988
- Offset Surface Generation and Contouring in Computer-Aided DesignJournal of Mechanical Design, 1987
- Offsetting operations in solid modellingComputer Aided Geometric Design, 1986