Geometric constraint solving is constraint satisfaction in a computational geometry setting, which has primary applications in computer aided design.[1] A problem to be solved consists of a given set of geometric elements and a description of geometric constraints between the elements, which could be non-parametric (tangency, horizontality, coaxiality, etc) or parametric (like distance, angle, radius). The goal is to find the positions of geometric elements in 2D or 3D space that satisfy the given constraints,[2] which is done by dedicated software components called geometric constraint solvers.
Geometric constraint solving became an integral part of CAD systems in the 80s, when Pro/Engineer first introduced a novel concept of feature-based parametric modeling concept.[3][4]
There are additional problems of geometric constraint solving that are related to sets of geometric elements and constraints: dynamic moving of given elements keeping all constraints satisfied,[5] detection of over- and under-constrained sets and subsets,[6][7] auto-constraining of under-constrained problems, etc.
^Roller, edited by Beat Brüderlin, Dieter (1998). Geometric Constraint Solving and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 3–23. ISBN 978-3-642-58898-3. {{cite book}}: |first1= has generic name (help)CS1 maint: multiple names: authors list (link)
^Christoph M. Hoffmann; Pamela J. Vermeer. Geometric constraint solving in R2 and R3. doi:10.1142/9789812831699_0008. S2CID 18272588.
^Robert Joan-Arinyo. Basics on Geometric Constraint Solving. CiteSeerX 10.1.1.331.9554.
^R. Anderl; R. Mendgen (1996). "Modelling with constraints: theoretical foundation and application". Computer-Aided Design. 28 (3): 155–168. doi:10.1016/0010-4485(95)00023-2.
^Marc Freixas; Robert Joan-Arinyo; Antoni Soto-Riera (2010). "A constraint-based dynamic geometry system". Computer-Aided Design. 42 (2): 151–161. doi:10.1016/j.cad.2009.02.016.
^Rossignac, Jaroslaw; SIGGRAPH, Joshua Turner, editors; sponsored by ACM (1991). Proceedings : Symposium on Solid Modeling Foundations and CAD/CAM Applications, Radisson Plaza Hotel, Austin, Texas, June 5-7, 1991. New York: Association for Computing Machinery. ISBN 978-0-89791-427-7. {{cite book}}: |first2= has generic name (help)CS1 maint: multiple names: authors list (link)
^Simon E.B.Thierry; Pascal Schreck; Dominique Michelucci; Christoph Fünfzig; Jean-David Génevaux (2011). "Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems" (PDF). Computer-Aided Design. 43 (10): 1234–1249. doi:10.1016/j.cad.2011.06.018.
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