Harmonic Manifold Simulation (HMS).

in: Proc. 29th Gocad Meeting, Nancy

Abstract

This paper uses a Manifold Harmonics Basis (MHB) decomposition technique to simulate random geometry. Manifold Harmonics Transform is a Fourier-like method to decompose a surface S into a series of surface components Sk using the m-first eigenfunctions of the Laplace-Beltrami operator [Vallet and Lévy(2008)]. Two techniques are investigated to perform harmonic manifold simulation: (i) the first one is based on the Fourier-like inverse transform which reconstructs a manifold from its representation in the frequency domain; (ii) the second one use the spectral displacement representation in the frequency space to simulate random surface by gradual deformation. This last method is more flexible to impose various conditioning constraints such as the surface passing through control points, or moving along a direction, or along a surface.

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    BibTeX Reference

    @inproceedings{Royer2GM2009,
     abstract = { This paper uses a Manifold Harmonics Basis (MHB) decomposition technique to simulate random geometry. Manifold Harmonics Transform is a Fourier-like method to decompose a surface S into a series of surface components Sk using the m-first eigenfunctions of the Laplace-Beltrami operator [Vallet and Lévy(2008)]. Two techniques are investigated to perform harmonic manifold simulation: (i) the first one is based on  the Fourier-like inverse transform which reconstructs a manifold from its representation in the frequency domain; (ii) the second one use the spectral displacement representation in the frequency space to simulate random surface by gradual deformation. This last method is more flexible to impose various conditioning constraints such as the surface passing through control points, or moving along a direction, or along a surface. },
     author = { Royer, Jean-Jacques },
     booktitle = { Proc. 29th Gocad Meeting, Nancy },
     title = { Harmonic Manifold Simulation (HMS). },
     year = { 2009 }
    }