Mesh parameterization: Difference between revisions

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Given two surfaces[[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 getsis mapped toonto.

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.

== Applications ==

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* [[Surface fitting]]

== Techniques ==

* Barycentric Mappings

* Differential Geometry Primer

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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]: ABF, ABF++, DPBF,[[Least LSCM,squares HLSCM,conformal Barycentricmap|LSCM]], mean-valueSpectral coordinates,[[Least L2 stretch, spectralsquares conformal, Periodic Global Parameterization, Constrained texture mapping, texture atlas generationmap|LSCM]]

* [[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 Linkslinks==

* [http://www.inf.usi.ch/hormann/parameterization/index.html "Mesh Parameterization: theory and practice"]

{{Computer-graphics-stub}}

[[Category:3D computer graphics]]

{{Portal|Computer -graphics-stub}}