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On the Use of Conformal Geometric Algebra in Geometric Constraint Solving

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Guide to Geometric Algebra in Practice

Abstract

To model a geometrical part in Computer Aided Design systems, declarative modeling is a well-adapted solution to declare and specify geometric objects and constraints. In this chapter, we are interested in the representation of geometric objects and constraints using a new language of description and representation, Geometric Algebra (GA). GA is used here in association with the conformal model of Euclidean geometry (CGA) which requires two extra dimensions comparing to the usual vector space model. Topologically and Technologically Related Surfaces (TTRS) Theory is introduced here as a unified framework for geometric objects representation and geometric constraints solving. Based on TTRS, this chapter shows the capability of the CGA to represent geometric objects and geometric constraints through symbolic geometric constraints solving and algebraic classification.

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Notes

  1. 1.

    http://www.me.umn.edu/labs/lincages/new.html.

  2. 2.

    http://www.umbc.edu/engineering/me/vrml/research/software/synthetica/index.html.

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Author information

Authors and Affiliations

  1. LISMMA, Institut Supérieur de Mécanique de Paris, Paris, France

    Philippe Serré

  2. LURPA, École Normale Supérieure de Cachan, Cachan, France

    Nabil Anwer

  3. Robotics and Machine Dynamics Laboratory, Beijing University of Technology, Beijing, P.R. China

    JianXin Yang

Authors
  1. Philippe Serré
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  2. Nabil Anwer
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  3. JianXin Yang
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Corresponding author

Correspondence to Philippe Serré .

Editor information

Editors and Affiliations

  1. Informatics Institute, University of Amsterdam, Science Park 107, Amsterdam, 1098 XG, Netherlands

    Leo Dorst

  2. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom

    Joan Lasenby

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Serré, P., Anwer, N., Yang, J. (2011). On the Use of Conformal Geometric Algebra in Geometric Constraint Solving. In: Dorst, L., Lasenby, J. (eds) Guide to Geometric Algebra in Practice. Springer, London. https://doi.org/10.1007/978-0-85729-811-9_11

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  • DOI: https://doi.org/10.1007/978-0-85729-811-9_11

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-810-2

  • Online ISBN: 978-0-85729-811-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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