Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

  • Mohamed S. Ebeida
  • Scott A. Mitchell
  • Anjul Patney
  • Andrew A. Davidson
  • Stanley Tzeng
  • Muhammad A. Awad
  • Ahmed H. Mahmoud
  • John D. Owens
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


We review our recent progress on efficient algorithms for generating well-spaced samples of high dimensional data, and for exploring and characterizing these data, the underlying domain, and functions over the domain. To our knowledge, these techniques have not yet been applied to computational topology, but the possible connections are worth considering. In particular, computational topology problems often have difficulty in scaling efficiently, and these sampling techniques have the potential to drastically reduce the size of the data over which these computational topology algorithms must operate. We summarize the definition of these sample distributions; algorithms for generating them in low, moderate, and high dimensions; and applications in mesh generation, rendering, motion planning and simulation.


Point Cloud Delaunay Triangulation Global Illumination Background Grid Uncovered Area 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The UC Davis authors thank the National Science Foundation (grant # CCF-1017399), Sandia LDRD award #13-0144, UC Lab Fees Research Program Award #12-LR-238449, NVIDIA and Intel Graduate Fellowships, and the Intel Science and Technology Center for Visual Computing for supporting this work.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Mohamed S. Ebeida
    • 1
  • Scott A. Mitchell
    • 1
  • Anjul Patney
    • 2
  • Andrew A. Davidson
    • 2
  • Stanley Tzeng
    • 3
  • Muhammad A. Awad
    • 4
  • Ahmed H. Mahmoud
    • 4
  • John D. Owens
    • 2
  1. 1.Computing Research, Sandia National LaboratoriesAlbuquerqueUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of CaliforniaDavisUSA
  3. 3.Department of Computer ScienceUniversity of CaliforniaDavisUSA
  4. 4.Department of Naval Architecture and Marine EngineeringAlexandria UniversityAlexandriaEgypt

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