A formalization of geometric constraint systems and their decomposition

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) h...

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Bibliographic Details
Published inFormal aspects of computing Vol. 22; no. 2; pp. 129 - 151
Main Authors Mathis, Pascal, Thierry, Simon E. B.
Format Journal Article
LanguageEnglish
Published London Springer-Verlag 01.03.2010
Association for Computing Machinery
Springer Verlag
Subjects
Computer Science
Math Applications in Computer Science
Original Article
Theory of Computation
Decomposition
Formalization
Transformation groups
Parametric CAD
Geometric constraints solving
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Summary: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.
Bibliography:ObjectType-Article-2
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ISSN:0934-5043
1433-299X
DOI:10.1007/s00165-009-0117-8