Approximate Geometric Regularities

Current reverse engineering systems are able to generate simple valid boundary representation (B-rep) models from 3D range data. Such models suffer from various inaccuracies caused by noise in the input data and algorithms. Reverse engineered geometric models may be beautified by finding approximate geometric regularities in such a model, and imposing a suitable subset of them on the model by using constraints. Methods to detect suitable regularities for the beautification of B-rep models having only planar, spherical, cylindrical, conical and toroidal faces are presented in this paper. The regularities are described in terms of similarities. Different properties of faces, edges and vertices, and small groups of these elements in a B-rep model are represented as feature objects. Similar feature objects, such as directions which are parallel, form one sort of regularities. For each group of similar feature objects, special feature objects which might represent the group form further regularities, e.g. an integer value which approximates the radius of similar cylinders. Further regularities arise from symmetries of feature object sets. Experiments show that the regularities found are suitable for beautification such that subsequent steps allow the selection of a consistent regularity set.

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