# Interval Assignment for Volumes with Holes

## Abstract

This paper presents a new technique for automatically detecting interval constraints for swept volumes with holes. The technique finds true volume constraints that are not necessarily imposed by the surfaces of the volume. A graphing algorithm finds independent, parallel paths of edges from source surfaces to target surfaces. The number of intervals on two paths between a given source and target surface must be equal; in general, the collection of paths determine a set of linear constraints. Linear programming techniques solve the interval assignment problem for the surface and volume constraints simultaneously.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 12667

- Report Number(s):
- SAND99-2299J

TRN: AH200120%%460

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Journal Article

- Journal Name:
- Internatioanl Journal of Numerical Methods in Engineering

- Additional Journal Information:
- Other Information: Submitted to International Journal of Numerical Methods in Engineering; PBD: 7 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; LINEAR PROGRAMMING; TARGETS; MESHING; HEXAHEDRON; SWEEPING; LINEAR PROGRAM; INTERVAL ASSIGNMENT

### Citation Formats

```
BENZLEY, STEVEN, MITCHELL, SCOTT A., and SHEPHERD, JASON F.
```*Interval Assignment for Volumes with Holes*. United States: N. p., 1999.
Web.

```
BENZLEY, STEVEN, MITCHELL, SCOTT A., & SHEPHERD, JASON F.
```*Interval Assignment for Volumes with Holes*. United States.

```
BENZLEY, STEVEN, MITCHELL, SCOTT A., and SHEPHERD, JASON F. Tue .
"Interval Assignment for Volumes with Holes". United States. https://www.osti.gov/servlets/purl/12667.
```

```
@article{osti_12667,
```

title = {Interval Assignment for Volumes with Holes},

author = {BENZLEY, STEVEN and MITCHELL, SCOTT A. and SHEPHERD, JASON F.},

abstractNote = {This paper presents a new technique for automatically detecting interval constraints for swept volumes with holes. The technique finds true volume constraints that are not necessarily imposed by the surfaces of the volume. A graphing algorithm finds independent, parallel paths of edges from source surfaces to target surfaces. The number of intervals on two paths between a given source and target surface must be equal; in general, the collection of paths determine a set of linear constraints. Linear programming techniques solve the interval assignment problem for the surface and volume constraints simultaneously.},

doi = {},

journal = {Internatioanl Journal of Numerical Methods in Engineering},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}

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