On the Use of Conformal Geometric Algebra in Geometric Constraint Solving

  • Philippe Serré
  • Nabil Anwer
  • JianXin Yang


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.


Geometric Constraint Geometric Object Rigid Body Motion Rigid Motion Geometric Algebra 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.LISMMAInstitut Supérieur de Mécanique de ParisParisFrance
  2. 2.LURPAÉcole Normale Supérieure de CachanCachanFrance
  3. 3.Robotics and Machine Dynamics LaboratoryBeijing University of TechnologyBeijingP.R. China

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