Geodesic Computations for Fast and Accurate Surface Remeshing and Parameterization [chapter]

Gabriel Peyré, Laurent Cohen
Progress in Nonlinear Differential Equations and Their Applications  
In this paper, we propose fast and accurate algorithms to remesh and flatten a genus-0 triangulated manifold. These methods naturally fits into a framework for 3D geometry modeling and processing that uses only fast geodesic computations. These techniques are gathered and extended from classical areas such as image processing or statistical perceptual learning. Using the Fast Marching algorithm, we are able to recast these powerful tools in the language of mesh processing. Thanks to some
more » ... anks to some classical geodesic-based building blocks, we are able to derive a flattening method that exhibit a conservation of local structures of the surface. On large meshes (more than 500 000 vertices), our techniques speed up computation by over one order of magnitude in comparison to classical remeshing and parameterization methods. Our methods are easy to implement and do not need multilevel solvers to handle complex models that may contain poorly shaped triangles.
doi:10.1007/3-7643-7384-9_18 fatcat:273jmw5eynflnfmi2tutjqx7zu