Use of Topological Constraints in Construction and Processing of Robust Solid Models

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This paper introduces topological constraints to robustly and comprehensively process interference calculation in solid modeling and feature modeling, and describes a method of symbolic notation of their expressions and algorithms to handle them. The interference calculation should be processed consistently against the contradictions in numerical values and should output the result model in the same form of representation as that in the input. To satisfy this, the topological constraints are relied on in the processing rather than numerical values, and represented symbolically and explicitly in the solid model, which is based on the Face-based representation using a table of sequences of face names around each face of the solid. The topological constraints represent degeneracy and connectedness among faces, edges and vertices, and are used against errors derived from the ambiguities caused in the numerical calculation as well as in the input data, while the errors are deliberately kept within a given tolerance. The constraints are also specified by a designer for representing his intention. When the intersection is regarded as degenerate at a point such as vertex-vertex coincidence, its topological constraint is represented by a cluster of multiple basic intersection points between edges and faces, and the name of the cluster is expressed with face names around the degenerate point. In the calculation for the set operation, the symbols of cluster names and non-cluster intersection points are used to make intersection line loops, to divide the faces of both solids along the intersection lines and to reconnect the divided ones to make the result solid. Examples are shown to demonstrate that the algorithms generate output solids even when they are subtly intersected.