Geometric modeling

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'''Geometric modeling''' is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three-dimensional (''solid figures''), although many of its tools and principles can be applied to sets of any finite dimension. Today most geometric modeling is done with computers and for computer-based applications. Two-dimensional models are important in computer typography and technical drawing. Three-dimensional models are central to computer-aided design and manufacturing (CAD/CAM), and widely used in many applied technical fields such as civil and mechanical engineering, architecture, geology and medical image processing.<ref>Handbook of Computer Aided Geometric Design</ref>

Geometric models are usually distinguished from procedural and object-oriented models, which define the shape implicitly by an opaque algorithm that generates its appearance.{{citation needed|date=August 2014}} They are also contrasted with digital images and volumetric models 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 colored squares; and geometric shapes such as circles 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>{{Cite web |url=http://geometric-modelling.org |access-date=2025-07-08 |website=geometric-modelling.org | title=John A. Gregory Memorial Award}}</ref> and the Bézier award.<ref>{{Cite web |url=http://www.solidmodeling.org/bezier_award.html |title=Archived copy |access-date=2014-06-20 |archive-date=2014-07-15 |archive-url=https://web.archive.org/web/20140715121544/http://www.solidmodeling.org/bezier_award.html |url-status=dead }}</ref>

==References== {{Reflist}}

==Further reading== General textbooks: * {{cite book|url=http://www.cis.upenn.edu/~jean/gbooks/geom1.html|title=Curves and Surfaces in Geometric Modeling: Theory and Algorithms|author=Jean Gallier|authorlink= Jean Gallier |publisher=Morgan Kaufmann|year=1999}} This book is out of print and freely available from the author. * {{cite book|author=Gerald E. Farin|title=Curves and Surfaces for CAGD: A Practical Guide|year=2002|publisher=Morgan Kaufmann|isbn=978-1-55860-737-8|edition=5th|url=http://www.farinhansford.com/books/cagd/}} * {{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 |publisher=CreateSpace Independent Publishing Platform |isbn=978-1497473195 |year=2014}} 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}} * {{cite book|author1=Neil Dodgson|author2=Michael S. Floater|author3=Malcolm Sabin|title=Advances in Multiresolution for Geometric Modelling|year=2006|publisher=Springer Science & Business Media|isbn=978-3-540-26808-6}} Subdivision methods (such as subdivision surfaces): * {{cite book|author1=Joseph D. Warren|author2=Henrik Weimer|title=Subdivision Methods for Geometric Design: A Constructive Approach|year=2002|publisher=Morgan Kaufmann|isbn=978-1-55860-446-9}} * {{cite book|author1=Jörg Peters|author2=Ulrich Reif|title=Subdivision Surfaces|year=2008|publisher=Springer Science & Business Media|isbn=978-3-540-76405-2}} * {{cite book|author1=Lars-Erik Andersson|author2=Neil Frederick Stewart|title=Introduction to the Mathematics of Subdivision Surfaces|year=2010|publisher=SIAM|isbn=978-0-89871-761-7}}

==External links== * [http://www.mathematik.tu-darmstadt.de/~ehartmann/cdgen0104.pdf Geometry and Algorithms for CAD ] (Lecture Note, TU Darmstadt)

Category:Geometric algorithms Category:Computer-aided design Category:Applied geometry