A Solid Modelling System Free from Topological Inconsistency

概要

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The paper presents a new method for solid modelling, by which topological inconsistency caused by numerical errors can be avoided completely. The method is based on the recognition that, if original geometric data are represented by a finite number of bits, the relative topological configuration of two or more geometric objects can be computed precisely in some finite precision. Solids are generated by set-theoretic combinations of primitives, where the primitives are polyhedra each of whose vertices is incident to exact1y three faces. All the fundamental metric data are represented by the coefficients of the surface equations, and all the computations for deciding the topological configurations are reduced to finding a type of crossing of four planes, which enables the solid modelling system to decide the topological structure precisely by finite-precision computation. The precision necessary for deciding the topological structure is only five times the precision in which the original metric data are represented. Preliminary experiments using two-dimensional geometric data certify the validity of the method. An efficient way of representing surface equations as well as other supporting techniques is also discussed.
1990-03-15