Conference Paper

Efficient Spherical Harmonics Representation of 3D Objects

Claude Bernard Univ., Lyon
DOI: 10.1109/PG.2007.39 Conference: Computer Graphics and Applications, 2007. PG '07. 15th Pacific Conference on
Source: IEEE Xplore


In this paper, we present a new and efficient spherical harmonics decomposition for spherical functions defining 3D triangulated objects. Such spherical functions are intrinsically associated to star-shaped objects. However, our results can be extended to any triangular object after segmentation into star-shaped surface patches and recomposition of the results in the implicit framework. There is thus no restriction about the genus number of the object. 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 voxel-based methods. We present several applications of our research, including fast spectral surface reconstruction from point clouds, local surface smoothing and interactive geometric texture transfer.

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    • "Instead of using Fourier analysis as a theoretical tool to analyze approximations of filters, Vallet and Levy computed the Fourier transform of the signal on the mesh directly [32]. Spherical harmonic analysis, which is also called Fourier analysis on the unit sphere, was employed to conduct surface filtering, surface reconstruction, and texture transfer [17] [41]. The short-time Fourier transforms are also used for signal processing of point cloud surfaces, where each surface patch is resampled on a regular grid using a fast scattered data approximation [20]. "
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    • "Since our model generates bubbles that are non-spherical, it would be valuable to explore how the realism of the bubble sounds are affected by more advanced models. There has been recent work in graphics by Mousa et al. for efficiently calculating spherical harmonics from a triangular mesh [21], [22] and there is a large body of work in the physics and engineering communities about generating sounds from spherical harmonics. We also expect the surface tension of the bubble to pull it towards a spherical shape, so higher order harmonics should become negligible relatively quickly. "
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    • "The concept then leads to a frequency representation of mesh, which has been used in a wide variety of applications (e.g. [10], [11], and [12]). The SHT is regarded as Fourier transforms of spheres [9]. "
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