Given two
surfaces with the same
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
, a
bijective mapping between them exists. On
triangular mesh surfaces, the problem of computing this mapping is called mesh
parameterization
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, ...
. The parameter domain is the surface that the mesh is mapped onto.
Parameterization was mainly used for
mapping textures to surfaces. Recently, it has become a powerful tool for many applications in mesh processing. Various techniques are developed for different types of parameter domains with different parameterization properties.
Applications
*
Texture mapping
Texture mapping is a method for mapping a texture on a computer-generated graphic. Texture here can be high frequency detail, surface texture, or color.
History
The original technique was pioneered by Edwin Catmull in 1974.
Texture mappi ...
* Normal mapping
* Detail transfer
*
Morphing
* Mesh completion
* Mesh Editing
* Mesh Databases
*
Remeshing
*
Surface fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is ...
Techniques
* Barycentric Mappings
* Differential Geometry Primer
* Non-Linear Methods
Implementations
A fast and simple stretch-minimizing mesh parameterization ABF++,
LSCM, Spectral
LSCM
Linear discrete conformal parameterizationBoundary First FlatteningScalable Locally Injective Mappings
See also
*
Parametrization
*
Texture atlas
*
UV Mapping
External links
"Mesh Parameterization: theory and practice"
3D computer graphics
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