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Geometric constraint solving is [[constraint satisfaction]] in a computational geometry, which has a primary applications in [[computer aided design]].<ref>{{cite book|title=Geometric Constraint Solving and Applications|url=http://www.springer.com/gp/book/9783642637810}}</ref> The problem to be solved consists of a given set of geometric elements and a description of geometric [[Constraint (computer-aided design)|constraints]] between the elements, which could be non-parametric (tangency, horizontality, coaxiality, etc) or parametric (like distance, angle, radius). The goal is to find positions of the geometric elements in 2D or 3D space which satisfy the given constraints,<ref>{{cite book|title=Geometric constraint solving in R2 and R3|url=https://pdfs.semanticscholar.org/5495/673d9bda0ec575a2185ddb890f887328be58.pdf}}</ref> which is done by dedicated software components called geometric constraint solvers.
The geometric constraint solving became necessary part of CAD systems in 80s, when Pro/Engineer firstly introduced feature-based parametric modeling concept.<ref>{{cite book|last1=Robert Joan-Arinyo|title=Basics on Geometric Constraint Solving|url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.331.9554&rep=rep1&type=pdf}}</ref><ref>{{cite book|title=Modelling with constraints: theoretical foundation and application|url=http://www.sciencedirect.com/science/article/pii/0010448595000232}}</ref>
There are additional problems of geometric constraint solving that are related to sets of geometric elements and constraints: dynamic moving of given element keeping all the constraints satisfied,<ref>{{cite book|title=A constraint-based dynamic geometry system|url=http://www.sciencedirect.com/science/article/pii/S0010448509000876}}</ref> detection of over- and under-constrained sets and subsets,<ref>{{cite book|title=Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems|url=http://www.sciencedirect.com/science/article/pii/S0010448511001606}}</ref> auto-constraining of under-constrained problems, etc.
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The list of geometric constraint solvers includes at least
* [https://www.plm.automation.siemens.com/en/products/open/d-cubed/2ddcm/index.shtml DCM] (Dimensional Constraint Manager), a commercial solver from D-Cubed (subsidiary of [[Siemens PLM
* [https://www.bricsys.com/el-gr/applications/developers/components/ LGS], a commercial solver developed by LEDAS and currently owned by Bricsys, integrated in [[Cimatron#CimatronE|Cimatron E]] and [[BricsCAD]];<ref>{{cite news|title=Cimatron to Introduce New Motion Simulator Powered by LEDAS LGS 3D|url=http://www.3dcadinfo.com/news/1794/cimatron-to-introduce-new-motion-simulator-powered-by-ledas-lgs-3d/}}</ref><ref>{{cite web|title=Exclusive Q&A: What it means, now that Bricsys bought IP from Ledas|url=http://worldcadaccess.typepad.com/blog/2011/10/exclusive-qa-what-it-means-now-that-bricsys-bought-ip-from-ledas.html}}</ref>
* [http://geosolver.sourceforge.net/ GeoSolver], a GNU Public License Python package for geometric constraint solving.
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<!--- Categories --->
[[Category:Constraint programming]]
[[Category:Articles created via the Article Wizard]]
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