### Abstract

In 1994 Grunbaum [2] showed, given a point set S in R3, that it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. [1] extended this work in 2008 by showing that a polyhedronization always exists that is decomposable into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present an algorithm for constructing a serpentine polyhedronization that has vertices with bounded degree of 7, answering an open question by Agarwal et al. [1].

Original language | English (US) |
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Pages | 99-102 |

Number of pages | 4 |

State | Published - Dec 1 2010 |

Event | 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010 - Winnipeg, MB, Canada Duration: Aug 9 2010 → Aug 11 2010 |

### Other

Other | 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010 |
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Country | Canada |

City | Winnipeg, MB |

Period | 8/9/10 → 8/11/10 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology

### Cite this

*Bounded-degree polyhedronization of point sets*. 99-102. Paper presented at 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg, MB, Canada.

**Bounded-degree polyhedronization of point sets.** / Barequet, Gill; Benbernou, Nadia; Charlton, David; Demaine, Erik D.; Demaine, Martin L.; Ishaque, Mashhood; Lubiw, Anna; Schulz, André; Souvaine, Diane L.; Toussaint, Godfried; Winslow, Andrew.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Bounded-degree polyhedronization of point sets

AU - Barequet, Gill

AU - Benbernou, Nadia

AU - Charlton, David

AU - Demaine, Erik D.

AU - Demaine, Martin L.

AU - Ishaque, Mashhood

AU - Lubiw, Anna

AU - Schulz, André

AU - Souvaine, Diane L.

AU - Toussaint, Godfried

AU - Winslow, Andrew

PY - 2010/12/1

Y1 - 2010/12/1

N2 - In 1994 Grunbaum [2] showed, given a point set S in R3, that it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. [1] extended this work in 2008 by showing that a polyhedronization always exists that is decomposable into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present an algorithm for constructing a serpentine polyhedronization that has vertices with bounded degree of 7, answering an open question by Agarwal et al. [1].

AB - In 1994 Grunbaum [2] showed, given a point set S in R3, that it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. [1] extended this work in 2008 by showing that a polyhedronization always exists that is decomposable into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present an algorithm for constructing a serpentine polyhedronization that has vertices with bounded degree of 7, answering an open question by Agarwal et al. [1].

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M3 - Paper

AN - SCOPUS:84882982643

SP - 99

EP - 102

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