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, 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.[1]

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] 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[2] and the Bézier award.[3]

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Further reading[edit]

General textbooks:

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

  • Armin Iske; Ewald Quak; Michael S. Floater (2002). Tutorials on Multiresolution in Geometric Modelling: Summer School Lecture Notes. Springer Science & Business Media. ISBN 978-3-540-43639-3. 
  • Neil Dodgson; Michael S. Floater; Malcolm Sabin (2006). Advances in Multiresolution for Geometric Modelling. Springer Science & Business Media. ISBN 978-3-540-26808-6. 

Subdivision methods (such as subdivision surfaces):

  • Joseph D. Warren; Henrik Weimer (2002). Subdivision Methods for Geometric Design: A Constructive Approach. Morgan Kaufmann. ISBN 978-1-55860-446-9. 
  • Jörg Peters; Ulrich Reif (2008). Subdivision Surfaces. Springer Science & Business Media. ISBN 978-3-540-76405-2. 
  • Lars-Erik Andersson; Neil Frederick Stewart (2010). Introduction to the Mathematics of Subdivision Surfaces. SIAM. ISBN 978-0-89871-761-7. 

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