COMPUTATION OF SELF-INTERSECTIONS OF OFFSETS OF BEZIER SURFACE PATCHES

Self-intersection of offsets of regular Bezier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing se lf-intersection curves of offsets is formulated in terms of a system o f nonlinear polynomial equations and solved robustly by the interval p rojected polyhedron algorithm. Trivial solutions are excluded by evalu ating the normal bounding pyramids of the surface subpatches mapped fr om the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve lo ops in the parameter domain is also discussed. The method has been suc cessfully tested in tracing complex self-intersection curves of offset s of Bezier surface patches. Examples illustrate the principal feature s and robustness characteristics of the method.