Volumetric Methods for Surface Reconstruction and Manipulation
The RBF method (introduced in the previous chapter) involves solving a dense linear system. For huge numbers of points, this becomes too computationally demanding. Like the RBF method, volumetric methods for reconstruction produce an implicit representation of the reconstructed surface, but instead of solving a linear system, these methods proceed by solving a partial differential equation discretized on a 3D grid. Volumetric reconstruction algorithms become rather simple: essentially it boils down to repeatedly smoothing data on a 3D grid while keeping the values at some grid points constant. Having discussed the basic approach, we also explain how normals for point data can be estimated, since point normal estimates are generally required for volumetric reconstruction.
This chapter also covers the Level Set Method which, again, is based on the implicit representation of 3D surface using discrete 3D grids. However the LSM allows us to deform a surface. Distance fields are typically used as the input to the LSM and they have numerous other uses, so this chapter also covers the construction of 3D distance fields from triangle meshes.
KeywordsCurvature Flow Delaunay Triangulation Implicit Representation Input Point Volumetric Method
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