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Solving spatial basic geometric constraint configurations with locus intersection
Authors:Xiao-Shan Gao [Author Vitae]  Christoph M. Hoffmann [Author Vitae]  Wei-Qiang Yang [Author Vitae]
Affiliation:a Institute of Systems Science, AMSS, Academia Sinica, Beijing 100080, People's Republic of China
b Department of Computer Science, Purdue University, West Lafayette, IN 47907-1398, USA
Abstract:A basic idea of geometric constraint solving (GCS) is to decompose the constraint problem into smaller ones according to some basic configurations. In this paper, we find all spatial basic configurations involving points, lines, and planes containing up to six geometric primitives in an automated way. Many of these basic configurations still resist effective analytical solutions. We propose the locus intersection method (LIM) for GCS, a hybrid method based on geometric computation and numerical search that can be used to find all the solutions for a geometric constraint problem. We show that the LIM can be used to solve all the above basic configurations.
Keywords:Geometric constraint solving   Parametric CAD   Spatial basic configuration   Locus intersection
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