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Title: Disk Density Tuning of a Maximal Random Packing

Abstract

We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve a user-defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict-free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially-varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non-obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.

Authors:
 [1];  [2];  [3];  [4];  [5];  [1];  [4];  [6];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of Texas, Austin, TX (United States)
  3. Alexandria Univ., Alexandria (Egypt)
  4. Univ. of California, Davis, CA (United States)
  5. Chinese Academy of Sciences (CAS), Beijing (China). National Laboratory of Pattern Recognition (NLPR). Inst. of Automation
  6. Univ. of Texas, Austin, TX (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1525127
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Computer Graphics Forum
Additional Journal Information:
Journal Volume: 35; Journal Issue: 5; Journal ID: ISSN 0167-7055
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Ebeida, Mohamed S., Rushdi, Ahmad A., Awad, Muhammad A., Mahmoud, Ahmed H., Yan, Dong-Ming, English, Shawn A., Owens, John D., Bajaj, Chandrajit L., and Mitchell, Scott A. Disk Density Tuning of a Maximal Random Packing. United States: N. p., 2016. Web. doi:10.1111/cgf.12981.
Ebeida, Mohamed S., Rushdi, Ahmad A., Awad, Muhammad A., Mahmoud, Ahmed H., Yan, Dong-Ming, English, Shawn A., Owens, John D., Bajaj, Chandrajit L., & Mitchell, Scott A. Disk Density Tuning of a Maximal Random Packing. United States. doi:https://doi.org/10.1111/cgf.12981
Ebeida, Mohamed S., Rushdi, Ahmad A., Awad, Muhammad A., Mahmoud, Ahmed H., Yan, Dong-Ming, English, Shawn A., Owens, John D., Bajaj, Chandrajit L., and Mitchell, Scott A. Mon . "Disk Density Tuning of a Maximal Random Packing". United States. doi:https://doi.org/10.1111/cgf.12981. https://www.osti.gov/servlets/purl/1525127.
@article{osti_1525127,
title = {Disk Density Tuning of a Maximal Random Packing},
author = {Ebeida, Mohamed S. and Rushdi, Ahmad A. and Awad, Muhammad A. and Mahmoud, Ahmed H. and Yan, Dong-Ming and English, Shawn A. and Owens, John D. and Bajaj, Chandrajit L. and Mitchell, Scott A.},
abstractNote = {We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve a user-defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict-free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially-varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non-obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.},
doi = {10.1111/cgf.12981},
journal = {Computer Graphics Forum},
number = 5,
volume = 35,
place = {United States},
year = {2016},
month = {8}
}

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Cited by: 5 works
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Figures / Tables:

Figure 1 Figure 1: Tuning nonuniform meshes on curved surface elephant and homer models, successfully eliminating obtuse angles.

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