langbein.org: Low-Discrepancy Sampling of Meshes for Rendering

Contents

J. A. Quinn, F. C. Langbein, R. R. Martin

In: Proc. Symp. Point-Based Graphics, Eurographics Assocication, pp. 19-28, 2007.
ISBN 3905673517.

[DOI: 10.2312/SPBG/SPBG07/019-028] [Preprint] [CiteSeer]

A novel point sampling framework for polygonal meshes is presented, based on sampling a mesh according to a density-controlled low-discrepancy distribution. The local sampling density can be controlled by a density functional defined by the user, e.g. to preserve local features, or to achieve desired data reduction rates. To sample the mesh, it is cut into a disc topology, and a parametrisation is generated. The parameterised mesh is sampled using a Hilbert curve in the parameter domain, which is adapted to parametric distortions and mapped onto the mesh. 1D sample points along the Hilbert curve are then generated, correcting for parametric distortion and a user-specified local density, to give a density-controlled low-discrepancy sampling of the mesh. After a pre-processing step, the sampling density can be adjusted in real-time. Experiments show that this approach can quickly resample existing meshes with low discrepancy samples. The effectiveness and speed of the approach are demonstrated by applying it to viewpoint dependent rendering, level of detail representation, and interactive remeshing.

@INPROCEEDINGS{Quinn2007,
  author =       {Jonathan A. Quinn and Frank C. Langbein and Ralph R.
                  Martin},
  title =        {Low-Discrepancy Point Sampling of Meshes for
                  Rendering},
  booktitle =    {Eurographics Symposium on Point-Based Graphics},
  year =         2007,
  editor =       {M. Botsch and R. Pajarola and B. Chen and M.
                  Zwicker},
  pages =        {19-28},
  publisher =    {Eurographics Association},
  isbn =         3905673517,
  doi =          {10.2312/SPBG/SPBG07/019-028},
  url =          {http://www.langbein.org/research/points/sampling/quinn2007/},
  abstract =     {A novel point sampling framework for polygonal
                  meshes is presented, based on sampling a mesh
                  according to a density-controlled low-discrepancy
                  distribution. The local sampling density can be
                  controlled by a density functional defined by the
                  user, e.g. to preserve local features, or to achieve
                  desired data reduction rates. To sample the mesh, it
                  is cut into a disc topology, and a parametrisation
                  is generated. The parameterised mesh is sampled
                  using a Hilbert curve in the parameter domain, which
                  is adapted to parametric distortions and mapped onto
                  the mesh. 1D sample points along the Hilbert curve
                  are then generated, correcting for parametric
                  distortion and a user-specified local density, to
                  give a density-controlled low-discrepancy sampling
                  of the mesh. After a pre-processing step, the
                  sampling density can be adjusted in real-time.
                  Experiments show that this approach can quickly
                  resample existing meshes with low discrepancy
                  samples. The effectiveness and speed of the approach
                  are demonstrated by applying it to viewpoint
                  dependent rendering, level of detail representation,
                  and interactive remeshing.},
}

Cite as Low-Discrepancy Sampling of Meshes for Rendering, http://www.langbein.org/research/points/sampling/quinn2007 by Frank C Langbein [ 6/December/2008, 19:34].

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