Geometric modeling: Difference between revisions

Revision as of 23:01, 11 February 2018

Revision as of 19:06, 17 February 2018

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{{refimprovemore citations needed|date=August 2014}}

'''Geometric modeling''' is a branch of [[applied mathematics]] and [[computational geometry]] that studies methods and [[algorithms]] for the mathematical description of shapes.

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Geometric models are usually distinguished from [[procedural modeling|procedural]] and [[object-oriented modeling|object-oriented model]]s, which define the shape implicitly by an opaque [[algorithm]] that generates its appearance.{{cn|date=August 2014}} They are also contrasted with [[digital image]]s and [[volumetric model]]s which represent the shape as a subset of a fine regular partition of space; and with [[fractal]] models that give an infinitely recursive definition of the shape. However, these distinctions are often blurred: for instance, a [[digital image]] can be interpreted as a collection of [[color]]ed [[square (geometry)|square]]s; and geometric shapes such as [[circle]]s are defined by implicit mathematical equations. Also, a [[fractal]] model yields a parametric or implicit model when its recursive definition is truncated to a finite depth.

Notable awards of the area are the John A. Gregory Memorial Award<ref>http://geometric-modelling.org</ref> and the BezierBézier award.<ref>http://www.solidmodeling.org/bezier_award.html</ref>

==See also==

* [[Geometric modeling kernel]]

* [[Architectural geometry]]

* [[Conformal geometry | Computational conformal geometry]]

* [[Computational topology]]

* [[Computer-aided engineering]]

* [[Computer-aided manufacturing]]

* [[Computational topology]]

* [[Digital geometry]]

* [[Geometric modeling kernel]]

* [[List of interactive geometry software]]

* [[Parametric curveequation]]s

* [[Parametric surface]]s

* [[Pythagorean-hodograph curve]]s

* [[Solid modeling]]

* [[Space partitioning]]

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* {{cite book|author=Michael E. Mortenson|title=Geometric Modeling|year=2006|publisher=Industrial Press|isbn=978-0-8311-3298-9|edition=3rd}}

* {{cite book|author=Ronald Goldman|authorlink=Ron Goldman (mathematician)|title=An Integrated Introduction to Computer Graphics and Geometric Modeling|year=2009|publisher=CRC Press|isbn=978-1-4398-0334-9|edition=1st}}

* {{cite book|author=Nikolay N. Golovanov |title=Geometric Modeling: The mathematics of shapes |url=https://www.amazon.com/Geometric-Modeling-The-mathematics-shapes/dp/1497473195 |publisher=[[CreateSpace Independent Publishing Platform]] |isbn=978-1497473195 |year=2014|asin=1497473195 }}

For multi-resolution (multiple [[level of detail]]) geometric modeling :

* {{cite book|author1=Armin Iske|author2=Ewald Quak|author3=Michael S. Floater|title=Tutorials on Multiresolution in Geometric Modelling: Summer School Lecture Notes|year=2002|publisher=Springer Science & Business Media|isbn=978-3-540-43639-3}}