### Abstract

Given a set S such as a polygon or a set of points, a quadrangulation of S is a partition of the interior of S, if 5 is a polygon, or the interior of the convex hull of S, if 5 is a set of points, into quadrangles (quadrilaterals) obtained by inserting edges between pairs of points (diagonals between vertices of the polygon) such that the edges intersect each other only at their end points. Not all polygons or sets of points admit quadrangulations, even when the quadrangles are not required to be convex (convex quadrangulations). In this paper we briefly survey some recent results concerning the characterization of those planar sets that always admit quadrangulations (convex and non-convex) as well as some related computational problems.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings |

Publisher | Springer-Verlag |

Pages | 218-227 |

Number of pages | 10 |

ISBN (Print) | 3540602208, 9783540602200 |

DOIs | |

State | Published - Jan 1 1995 |

Event | 4th Workshop on Algorithms and Data Structures, WADS 1995 - Kingston, Canada Duration: Aug 16 1995 → Aug 18 1995 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 955 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th Workshop on Algorithms and Data Structures, WADS 1995 |
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Country | Canada |

City | Kingston |

Period | 8/16/95 → 8/18/95 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings*(pp. 218-227). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955). Springer-Verlag. https://doi.org/10.1007/3-540-60220-8_64

**Quadrangulations of planar sets.** / Toussaint, Godfried.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 955, Springer-Verlag, pp. 218-227, 4th Workshop on Algorithms and Data Structures, WADS 1995, Kingston, Canada, 8/16/95. https://doi.org/10.1007/3-540-60220-8_64

}

TY - GEN

T1 - Quadrangulations of planar sets

AU - Toussaint, Godfried

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Given a set S such as a polygon or a set of points, a quadrangulation of S is a partition of the interior of S, if 5 is a polygon, or the interior of the convex hull of S, if 5 is a set of points, into quadrangles (quadrilaterals) obtained by inserting edges between pairs of points (diagonals between vertices of the polygon) such that the edges intersect each other only at their end points. Not all polygons or sets of points admit quadrangulations, even when the quadrangles are not required to be convex (convex quadrangulations). In this paper we briefly survey some recent results concerning the characterization of those planar sets that always admit quadrangulations (convex and non-convex) as well as some related computational problems.

AB - Given a set S such as a polygon or a set of points, a quadrangulation of S is a partition of the interior of S, if 5 is a polygon, or the interior of the convex hull of S, if 5 is a set of points, into quadrangles (quadrilaterals) obtained by inserting edges between pairs of points (diagonals between vertices of the polygon) such that the edges intersect each other only at their end points. Not all polygons or sets of points admit quadrangulations, even when the quadrangles are not required to be convex (convex quadrangulations). In this paper we briefly survey some recent results concerning the characterization of those planar sets that always admit quadrangulations (convex and non-convex) as well as some related computational problems.

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U2 - 10.1007/3-540-60220-8_64

DO - 10.1007/3-540-60220-8_64

M3 - Conference contribution

SN - 3540602208

SN - 9783540602200

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 218

EP - 227

BT - Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings

PB - Springer-Verlag

ER -