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Given two [[surface (topology)|surface]]s with the same [[topology]], a [[bijective mapping]] between them exists. On [[Polygon mesh|triangular mesh]] surfaces, the problem of computing this mapping is called mesh [[Parametrization (atmospheric modeling)|parameterization]]. The parameter ___domain is the surface that the mesh is mapped onto.
Parameterization was mainly used for [[Texture mapping|mapping textures]] to surfaces. Recently, it has become a powerful tool for many applications in mesh processing.{{Citation needed|date=July 2011}} Various techniques are developed for different types of parameter domains with different parameterization properties.
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== Implementations ==
* [http://www.riken.jp/brict/Yoshizawa/Research/Param.html A fast and simple stretch-minimizing mesh parameterization]
* [http://alice.loria.fr/index.php/software/3-platform/22-graphite.html Graphite]:
* [https://web.archive.org/web/20100624001221/http://www.cs.caltech.edu/~keenan/project_dgp.html Linear discrete conformal parameterization]
* [http://www.dgp.toronto.edu/~rms/software/expmapdemo.html Discrete Exponential Map]
* [https://geometrycollective.github.io/boundary-first-flattening Boundary First Flattening]
* [https://github.com/MichaelRabinovich/Scalable-Locally-Injective-Mappings Scalable Locally Injective Mappings]
==See also==
{{Portal|Computer graphics}}▼
* [[Parametrization (geometry)|Parametrization]]
* [[Texture atlas]]
* [[UV Mapping]]
==External links==
* [http://www.inf.usi.ch/hormann/parameterization/index.html "Mesh Parameterization: theory and practice"]
[[Category:3D computer graphics]]
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