Discrete differential geometry is the study of discrete counterparts of notions in
differential geometry. Instead of smooth curves and surfaces, there are
polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...
s,
meshes, and
simplicial complexes. It is used in the study of
computer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal ...
,
geometry processing
Geometry processing, or mesh processing, is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulat ...
and
topological combinatorics.
See also
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Discrete Laplace operator
In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices) ...
*
Discrete exterior calculus
*
Discrete Morse theory Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman. The theory has various practical applications in diverse fields of applied mathematics and computer science, such as configuration spaces, homology co ...
*
Topological combinatorics
*
Spectral shape analysis
*
Abstract differential geometry
The adjective ''abstract'' has often been applied to differential geometry before, but the abstract differential geometry (ADG) of this article is a form of differential geometry without the calculus notion of smoothness, developed by Anastasios ...
*
Analysis on fractals
*
Discrete calculus
References
Discrete differential geometry Forum*
*
* Alexander I. Bobenko, Yuri B. Suris (2008), "Discrete Differential Geometry", American Mathematical Society,
Differential geometry
Simplicial sets
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