langbein.org: Approximate Geometric Regularities

F. C. Langbein, B. I. Mills, A. D. Marshall, R. R. Martin.

Int. J. Shape Modeling, 7(2):129-162, 2001.
ISSN 02186543.

[DOI: 10.1142/S0218654301000096] [Preprint]

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.

@ARTICLE{Langbein2001c,
  author =       {Frank C. Langbein and Bruce I. Mills and A. Dave
                  Marshall and Ralph R. Martin},
  title =        {Approximate Geometric Regularities},
  journal =      {Int. J. Shape Modeling},
  year =         2001,
  volume =       7,
  pages =        {129-162},
  number =       2,
  issn =         02186543,
  doi =          {10.1142/S0218654301000096},
  url =          {http://www.langbein.org/research/solids/borg/langbein2001c/},
  abstract =     {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.},
}

Cite as Approximate Geometric Regularities, http://www.langbein.org/research/solids/borg/langbein2001c by Frank C Langbein [27/October/2008, 21:27].

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