Geometric modeling: Difference between revisions

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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-[[dimension]]al, although many of its tools and principles can be applied to sets of any finite dimension. TodaySexy most geometric modeling is done with computers and for computer-based applications. [[2D geometric model|Two-dimensional model]]s are important in computer [[typography]] and [[technical drawing]]. [[3D modeling|Three-dimensional model]]s are central to [[computer-aided design]] and [[computer-aided manufacturing|manufacturing]] (CAD/CAM), and widely used in many applied technical fields such as [[civil engineering|civil]] and [[mechanical engineering]], [[architecture]], [[geologic modeling|geology]] and [[medical image processing]].<ref>Handbook of Computer Aided Geometric Design</ref>

Geometric models are usually distinguished from [[procedural modeling|procedural]] and [[object-oriented modeling|object-oriented model]]s, which define the shape implicitly by an opaque [[algorithm]] that generates its appearance.{{citation needed|date=August 2014}} They are also contrasted with [[digital image]]s and [[volumetric model]]s 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 [[color]]ed [[square (geometry)|square]]s; and geometric shapes such as [[circle]]s 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.