This article needs additional citations for
verification. (August 2014) |
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.
[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]
{{
cite web}}
: CS1 maint: archived copy as title (
link)
General textbooks:
For multi-resolution (multiple level of detail) geometric modeling :
Subdivision methods (such as subdivision surfaces):
This article needs additional citations for
verification. (August 2014) |
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.
[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]
{{
cite web}}
: CS1 maint: archived copy as title (
link)
General textbooks:
For multi-resolution (multiple level of detail) geometric modeling :
Subdivision methods (such as subdivision surfaces):