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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. 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: This book is out of print and freely available from the author.
For multi-resolution (multiple level of detail) geometric modeling :
Subdivision methods (such as subdivision surfaces):
External links Geometry and Algorithms for CAD (Lecture Note, TU Darmstadt)