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Surfaces Intersection for Solid Algebra: A Classification Algorithm

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Book cover Geometric Modeling: Theory and Practice

Part of the book series: Focus on Computer Graphics ((FOCUS COMPUTER))

Abstract

Detecting intersecting surfaces and computing their intersection curves is one of the fundamental problems in solid modeling algebra. This paper introduces a new strategy to classify pairs of surfaces according to their intersection status, where exact geometric entities are replaced by fuzzy ones. Intersecting surfaces are thus replaced by fuzzy intersecting faces and a fuzzy intersection algorithm provides a 3-State classification of pairs of surfaces: certainly intersecting, certainly non-intersecting and potentially intersecting.

In the case of certainly intersecting surface couples the fuzzy intersaction algorithm provides also starting points to march along the intersection curve, which turns most of the potentially intersecting couples into certainly intersecting ones. The remaining potential intersections are then subdivided to refine their status. Statistics shows the efficiency of this global strategy.

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Authors and Affiliations

  1. 1LIGIM, Bât. 710, Université Claude Bernard Lyon I 43, Bd du 11 Novembre 1918, Villeurbanne Cedex, 69622, France

    S. Foufou, J. M. Brun & A. Bouras

Authors
  1. S. Foufou
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  2. J. M. Brun
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  3. A. Bouras
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Editor information

Editors and Affiliations

  1. Wilhelm-Schickard-Institut für auf Informatik, Auf der Morgenstelle 10, D-72076, Tübingen, Germany

    Wolfgang Strasser , Reinhard Klein  & René Rau ,  & 

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© 1997 Springer-Verlag Berlin Heidelberg

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Foufou, S., Brun, J.M., Bouras, A. (1997). Surfaces Intersection for Solid Algebra: A Classification Algorithm. In: Strasser, W., Klein, R., Rau, R. (eds) Geometric Modeling: Theory and Practice. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60607-6_9

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  • DOI: https://doi.org/10.1007/978-3-642-60607-6_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61883-6

  • Online ISBN: 978-3-642-60607-6

  • eBook Packages: Springer Book Archive

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