A conjecture on tangent intersections of surface patches

This note conjectures that if two surface patches intersect with G1 continuity along an entire curve, the probability is one that the curve is rational. This idea has significance for surface intersection algorithms. Surface intersection algorithms are typically designed to deal with G0 intersections, in which the normal vectors of the two surfaces are parallel at only a small number (typically zero) of points along the curve of intersection. If a connected component of an intersection curve is such that the normal vectors of the two surfaces are parallel at each point along the connected component, we will call that connected component a G1 or tangent intersection component. Surface intersection curves are generally quite complicated. For example, the curve of intersection between two generic bicubic patches in general position is a space curve of degree 324 and genus 433 (see [1]). The genus number is of interest primarily because only curves of genus zero can be represented in rati...

• Type: Journal
• Year: 2004
• Where: CAGD
• Authors: Thomas W. Sederberg, Jianmin Zheng, Xiaowen Song
• Keywords: CAGD 2004, Conjecture, Curve, Surface Intersection