Toward an efficient triangle-based spherical harmonics representation of 3D objects

In classical frequency-based surface decomposition, there is always a restriction about the genus number of the object to obtain the spherical harmonics decomposition of spherical functions representing these objects. Such spherical functions are intrinsically associated to star-shaped objects. In this paper, we present a new and efficient spherical harmonics decomposition for spherical functions defining 3D triangulated objects. Our results can be extended to any triangular object of any genus number after segmentation into star-shaped surface patches and recomposition of the results in the implicit framework. We demonstrate that the evaluation of the spherical harmonics coefficients can be performed by a Monte Carlo integration over the edges, which makes the computation more accurate and faster than previous techniques, and provides a better control over the precision error in contrast to the volumetric or surfacic voxel-based methods. We present several applications of our research, including fast spectral surface reconstruction from point clouds, surface compression, progressive transmission, local surface smoothing and interactive geometric texture transfer.