NDLI: Algebraic geometry and group theory in geometric constraint satisfaction

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Algebraic geometry and group theory in geometric constraint satisfaction

Content Provider	ACM Digital Library
Author	Ferreira, Placid M. Ruiz S., Oscar E.
Abstract	The determination of a set of geometric entities that satisfy a series of geometric relations (constraints) constitutes the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem. This problem appears in different forms in Assembly Planning, Constraint Driven Design, Computer Vision, etc. Its solution is related to the existence of roots to systems of polynomial equations. Previous attempts using exclusively numerical (geometry) or symbolic (topology) solutions for this problem present shortcomings regarding characterization of solution space, incapability to deal with geometric and topological inconsistencies, and very high computational expenses. In this investigation Grobner Bases are used for the characterization of the algebraic variety of the ideal generated by the set of polynomials. Properties of Grobner Bases provide a theoretical framework responding to questions about consistency, ambiguity, and dimension of the solution space. It also allows for the integration of geometric and topological reasoning. The high computational cost of Buchberger's algorithm for the Grobner Basis is compensated by the choice of a non redundant set of variables, determined by the characterization of constraints based on the subgroups of the group of Euclidean displacements SE(3). Examples have shown the advantage of using group based variables. One of those examples is discussed.
Starting Page	224
Ending Page	233
Page Count	10
File Format	PDF
ISBN	0897916387
DOI	10.1145/190347.190421
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1994-08-01
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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