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. Geometric models are usually distinguished from procedural and object-oriented models, which define the shape implicitly by an opaque algorithm that generates its appearance. 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 and the Bézier award.
See also 2D geometric modeling Architectural geometry Computational conformal geometry Computational topology Computer-aided engineering Computer-aided manufacturing Digital geometry Geometric modeling kernel List of interactive geometry software Parametric equation Parametric surface Solid modeling Space partitioning
References
Further reading General textbooks:
Jean Gallier (1999). Curves and Surfaces in Geometric Modeling: Theory and Algorithms. Morgan Kaufmann. This book is out of print and freely available from the author. Gerald E. Farin (2002). Curves and Surfaces for CAGD: A Practical Guide (5th ed.). Morgan Kaufmann. ISBN 978-1-55860-737-8. Michael E. Mortenson (2006). Geometric Modeling (3rd ed.). Industrial Press. ISBN 978-0-8311-3298-9. Ronald Goldman (2009). An Integrated Introduction to Computer Graphics and Geometric Modeling (1st ed.). CRC Press. ISBN 978-1-4398-0334-9. Nikolay N. Golovanov (2014). Geometric Modeling: The mathematics of shapes. CreateSpace Independent Publishing Platform. ISBN 978-1497473195. 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.
External links Geometry and Algorithms for CAD (Lecture Note, TU Darmstadt)
