Discrete differential geometry
Encyclopedia
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are polygons
, meshes
, and simplicial complexes. It is used in the study of computer graphics
and topological combinatorics
.
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
, meshes
Mesh
Mesh consists of semi-permeable barrier made of connected strands of metal, fiber, or other flexible/ductile material. Mesh is similar to web or net in that it has many attached or woven strands.-Types of mesh:...
, and simplicial complexes. It is used in the study of computer graphics
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
and topological combinatorics
Topological combinatorics
The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this gradually turned into the field of algebraic topology....
.
See also
- Discrete exterior calculusDiscrete exterior calculusIn mathematics, the discrete exterior calculus is the extension of the exterior calculus to discrete spaces including graphs and finite element meshes. DEC methods have proved to be very powerful in improving and analyzing finite element methods: for instance, DEC-based methods allow the use of...
- Discrete Morse theory
- Topological combinatoricsTopological combinatoricsThe discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this gradually turned into the field of algebraic topology....
- Shape analysisShape analysisThis article describes shape analysis to analyze and process geometric shapes.The shape analysis described here is related to the statistical analysis of geometric shapes, to shape matching and shape recognition...
- Abstract differential geometryAbstract differential geometryThe adjective abstract has often been applied to differential geometry before, but the abstract differential geometry of this article is a form of differential geometry without the calculus notion of smoothness, developed by Anastasios Mallios and others from 1998 onwards.Instead of calculus, an...
- Analysis on fractalsAnalysis on fractalsAnalysis on fractals or calculus on fractals is a generalization of calculus on smooth manifolds to calculus on fractals.The theory describes dynamical phenomena which occur on objects modelled by fractals....