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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
- Editing
- Databases
- Remeshing
- Surface fitting
Techniques
- Barycentric Mappings
- Differential Geometry Primer
- Non-Linear Methods