Mesh parameterization: Difference between revisions

Revision as of 00:34, 6 November 2010

Latest revision as of 03:58, 29 October 2023

(21 intermediate revisions by 10 users not shown)

Line 1:

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.

{{csb-pageincludes|1=http://seminarios.impa.br/cgi-bin/SEMINAR_palestra.cgi?id=4277|2=1}}

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.

For any two surfaces with similar topology, there exists a bijective mapping between them. If one of these surfaces is a triangular mesh, the problem of computing such a mapping is referred to as mesh parameterization. The surface that the mesh is mapped to is typically called the parameter ___domain.

Parameterization was introduced to computer graphics for mapping textures onto surfaces. Over the last decade, it has gradually become a ubiquitous tool for many mesh-processing applications, including detail-mapping, detail-transfer, morphing, mesh-editing, mesh-completion, remeshing, compression, surface-fitting, and shape-analysis. In parallel to the increased interest in applying parameterization, various methods were developed for different kinds of parameter domains and parameterization properties.

== Applications ==

* [[Texture mapping]]

* Normal mapping

* Detail transfer

* [[Morphing]]

* Mesh completion

* Mesh Editing

* Mesh Databases

* [[Remeshing]]

* [[Surface fitting]]

== Techniques ==

* Barycentric Mappings

* Differential Geometry Primer

* Non-Linear Methods

== Implementations ==

==References==

* [http://www.riken.jp/brict/Yoshizawa/Research/Param.html A fast and simple stretch-minimizing mesh parameterization]

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

* [http://alice.loria.fr/index.php/software/3-platform/22-graphite.html Graphite]: ABF++, [[Least squares conformal map|LSCM]], Spectral [[Least squares conformal map|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==

* [[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]]

{{Computer-graphics-stub}}