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Title: k-d Darts: Sampling by k-dimensional flat searches

Abstract

In this work, we introduced k-d darts as a particular type of higherdimensional sampling. We described a k-d dart framework for hyperplanes of general dimension k, and then demonstrated efficiency and accuracy over three applications using k= 1, and accuracy for one application using k = 1. In particular, darts produce accurate estimates of the volume of an object regardless of the dimension, orientation, and aspect ratio of the object. Axis-aligned darts are universally preferable to unaligned ones for sampling square domains, and we expect this to extend to hyperrectangles, such as bounding boxes. Darts also produce accurate mean estimates for function integration.

Authors:
 [1];  [2];  [1];  [1];  [2];  [2]
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  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Univ. of California, Davis, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1523893
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
ACM Transaction on Graphics
Additional Journal Information:
Journal Volume: 33; Journal Issue: 1; Journal ID: ISSN 0730-0301
Publisher:
ACM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Ebeida, Mohamed S., Patney, Anjul, Mitchell, Scott A., Dalbey, Keith R., Davidson, Andrew A., and Owens, John D. k-d Darts: Sampling by k-dimensional flat searches. United States: N. p., 2014. Web. doi:10.1145/2522528.
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Ebeida, Mohamed S., Patney, Anjul, Mitchell, Scott A., Dalbey, Keith R., Davidson, Andrew A., & Owens, John D. k-d Darts: Sampling by k-dimensional flat searches. United States. https://doi.org/10.1145/2522528
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Ebeida, Mohamed S., Patney, Anjul, Mitchell, Scott A., Dalbey, Keith R., Davidson, Andrew A., and Owens, John D. Wed . "k-d Darts: Sampling by k-dimensional flat searches". United States. https://doi.org/10.1145/2522528. https://www.osti.gov/servlets/purl/1523893.
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@article{osti_1523893,
title = {k-d Darts: Sampling by k-dimensional flat searches},
author = {Ebeida, Mohamed S. and Patney, Anjul and Mitchell, Scott A. and Dalbey, Keith R. and Davidson, Andrew A. and Owens, John D.},
abstractNote = {In this work, we introduced k-d darts as a particular type of higherdimensional sampling. We described a k-d dart framework for hyperplanes of general dimension k, and then demonstrated efficiency and accuracy over three applications using k= 1, and accuracy for one application using k = 1. In particular, darts produce accurate estimates of the volume of an object regardless of the dimension, orientation, and aspect ratio of the object. Axis-aligned darts are universally preferable to unaligned ones for sampling square domains, and we expect this to extend to hyperrectangles, such as bounding boxes. Darts also produce accurate mean estimates for function integration.},
doi = {10.1145/2522528},
journal = {ACM Transaction on Graphics},
number = 1,
volume = 33,
place = {United States},
year = {Wed Jan 01 00:00:00 EST 2014},
month = {Wed Jan 01 00:00:00 EST 2014}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1145/2522528
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Cited by: 10 works
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Figures / Tables:

Fig. 1 Fig. 1: Sampling long and thin subregions (gray) using points (left), lines (center), and planes (right). Point samples may be cheap to generate and evaluate, but they contribute nothing to the final result if they miss the region of interest. Misses (blue) are frequent for regions with a small volume.more » Samples of higher dimensions, or $k$-d darts, often intersect (red) the region of interest, especially if the region is long and thin. A $k$-d dart’s greater expense is offset by it providing more information.« less
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    Works referencing / citing this record:

    Recursive Spoke Darts: Local Hyperplane Sampling for Delaunay and Voronoi Meshing in Arbitrary Dimensions
    journal, January 2016

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      Figures / Tables found in this record:

      Fig. 1 (p. 2)figure
      Fig. 2 (p. 3)figure
      Fig. 3 (p. 3)figure
      Fig. 4 (p. 3)figure
      Algorithm 1 (p. 7)figure
      Fig. 5 (p. 7)figure
      Fig. 6 (p. 8)figure
      Fig. 10 (p. 9)figure
      Fig. 7 (p. 9)figure
      Fig. 8 (p. 9)figure
      Fig. 9 (p. 9)figure
      Fig. 11 (p. 11)figure
      Fig. 12 (p. 11)figure
      Table I (p. 11)table
      Fig. 13 (p. 12)figure
      Fig. 14 (p. 13)figure
      Fig. 15 (p. 13)figure
      Table II (p. 13)table
      Fig. 16 (p. 15)figure
      Fig. 17 (p. 16)figure
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