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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.Handbook of Computer Aided Geometric Design

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 Awardhttp://geometric-modelling.org and the Bézier award.{{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 }}

See also

References

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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)

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Category:Geometric algorithms

Category:Computer-aided design

Category:Applied geometry

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