Geometric constraint solving: Difference between revisions

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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|last1=Roller|first1=edited by Beat Brüderlin, Dieter|title=Geometric Constraint Solving and Applications|date=1998|publisher=Springer Berlin Heidelberg|___location=Berlin, Heidelberg|isbn=978-3-642-58898-3|pages=3-23|url=httphttps://www.springer.com/gp/book/9783642637810|language=en}}</ref> A 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 the positions of geometric elements in 2D or 3D space that satisfy the given constraints,<ref>{{cite book|last1=Christoph M. Hoffmann|last2=Pamela J. Vermeer|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.

Geometric constraint solving became an integral part of CAD systems in the 80s, when Pro/Engineer firstly introduced a novel concept of 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|last1=R. Anderl|last2=R. Mendgen|title=Modelling with constraints: theoretical foundation and application|url=http://www.sciencedirect.com/science/article/pii/0010448595000232}}</ref>