## 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:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of Texas, Austin, TX (United States)
- Alexandria Univ., Alexandria (Egypt)
- Univ. of California, Davis, CA (United States)
- Chinese Academy of Sciences (CAS), Beijing (China). National Laboratory of Pattern Recognition (NLPR). Inst. of Automation
- 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: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: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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