Formal Aspects of Computing

, Volume 22, Issue 2, pp 129–151 | Cite as

A formalization of geometric constraint systems and their decomposition

  • Pascal Mathis
  • Simon E. B. ThierryEmail author
Original Article


For more than a decade, the trend in geometric constraint systems solving has been to use a geometric decomposition/recombination approach. These methods are generally grounded on the invariance of systems under rigid motions. In order to decompose further, other invariance groups (e.g., scalings) have recently been considered. Geometric decomposition is grounded on the possibility to replace a solved subsystem with a smaller system called boundary. This article shows the central property that justifies decomposition, without assuming specific types of constraints or invariance groups. The exact nature of the boundary system is given. This formalization brings out the elements of a general and modular implementation.


Geometric constraints solving Decomposition Transformation groups Parametric CAD Formalization 


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Copyright information

© British Computer Society 2009

Authors and Affiliations

  1. 1.Université de StrasbourgStrasbourgFrance
  2. 2.LSIIT, UMR CNRS-UdS 7005StrasbourgFrance

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