Given two
surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
s with the same
topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
, 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 (mathematics), surface, or, more generally, a ma ...
. 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 term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut ap ...
* Normal mapping
* Detail transfer
*
Morphing
Morphing is a special effect in motion pictures and animations that changes (or morphs) one image or shape into another through a seamless transition. Traditionally such a depiction would be achieved through dissolving techniques on film. Si ...
* Mesh completion
* Mesh Editing
* Mesh Databases
*
Remeshing
*
Surface fitting
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
In computer graphics, a texture atlas (also called a spritesheet or an image sprite in 2D game development) is an image containing multiple smaller images, usually packed together to reduce overall dimensions. An atlas can consist of uniformly-siz ...
*
UV Mapping
UV mapping is the 3D modeling process of projecting a 3D model's surface to a 2D image for texture mapping. The letters "U" and "V" denote the axes of the 2D texture because "X", "Y", and "Z" are already used to denote the axes of the 3D object i ...
External links
"Mesh Parameterization: theory and practice"
3D computer graphics
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