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Parameterization of Surfaces
Intervenant(s) : Ana-Maria Vintescu (LTCI/Pequan) Surface parameterization, in particular mesh parameterization (where the surface is represented by a triangular mesh) has numerous geometry processing and computer graphics applications, such as texture mapping and animation transfer.
Mesh parameterization is defined as a bijective mapping between a triangular mesh and another usually simpler surface (planar domain or a sphere) with identical topology (compatible meshes). The difficulty is that only developable surfaces (cylinder, cone) can be flattened onto the plane without distortion. Therefore the problem of parameterizing a surface to the plane is defined by finding a bijective mapping between them while minimizing a certain kind of distortion, depending on the application (preservation of angles, area). Of great importance is the concept of cross-parameterization, where the goal is to achieve a mapping between two (or more) arbitrary input surfaces (meshes). Cross-parameterization has many geometry processing applications, such as morphing, fitting template meshes to scan data, etc.
Ideally the cross-parameterization algorithm should be computationally efficient, should be robust enough to handle models with different topology and/or geometry , should achieve a low distortion mapping and it should perform in an automatic fashion. The requirement for low distortion becomes even more difficult and more application- dependent in this case (limitation of detail loss, the map should be semantically meaningful). Some theoretical aspects, a state-of-the-art and a proposed method will be presented, along with visual and numerical results.
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