Robust Interference Calculation Based on Topological Constrants

There still remain serious problems in the current solid modeling systems concerning robustness of interference calculation. When we execute interference calculation, the results of geometrical calculation and topological information are inconsistent because of numerical errors by the floating-pint arithmetic. We consider geometrical elements are incident each other when their intersection is ambiguous because of numerical errors. Previously, we have proposed a method which determines the connection of the intersection graph based on the topological connectivity of intersection points represented symbolically with face names. The incident information is deduced as topological constraints from minimal geometrical judgements, and it is modified to hold consistent relations and utilized to generate a topological structure of an output solid. The local structure at the intersection is determined symbolically using the constraints and convex/concave properties around the cluster: a set of coincident intersection points. Further, high-precision arithmetic is used partially not to cause larger errors than the tolerance detecting cancellation errors. Using these algorithms, we always obtain consistent results efficiently.

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