A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral processing of point-sampled geometry
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
A fast spherical harmonics transform algorithm
Mathematics of Computation
3D mesh compression using fixed spectral bases
GRIN'01 No description on Graphics interface 2001
FFTs for the 2-Sphere-Improvements and Variations
FFTs for the 2-Sphere-Improvements and Variations
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Rotation invariant spherical harmonic representation of 3D shape descriptors
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Symmetry descriptors and 3D shape matching
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Visualization of Point-Based Surfaces with Locally Reconstructed Subdivision Surfaces
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Reconstruction of solid models from oriented point sets
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
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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.