### Abstract

It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices inside the polygon are allowed? We give a positive answer and construct a pair of such triangulations with O(n^{2}) new triangulation vertices. Moreover, we show that there exists a 'universal' way of triangulating an n-sided polygon with O(n^{2}) extra triangulation vertices. Finally, we also show that creating compatible triangulations requires a quadratic number of extra vertices in the worst case.

Original language | English (US) |
---|---|

Pages (from-to) | 27-35 |

Number of pages | 9 |

Journal | Computational Geometry: Theory and Applications |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - 1993 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*3*(1), 27-35. https://doi.org/10.1016/0925-7721(93)90028-5

**On compatible triangulations of simple polygons.** / Aronov, Boris; Seidel, Raimund; Souvaine, Diane.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 3, no. 1, pp. 27-35. https://doi.org/10.1016/0925-7721(93)90028-5

}

TY - JOUR

T1 - On compatible triangulations of simple polygons

AU - Aronov, Boris

AU - Seidel, Raimund

AU - Souvaine, Diane

PY - 1993

Y1 - 1993

N2 - It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices inside the polygon are allowed? We give a positive answer and construct a pair of such triangulations with O(n2) new triangulation vertices. Moreover, we show that there exists a 'universal' way of triangulating an n-sided polygon with O(n2) extra triangulation vertices. Finally, we also show that creating compatible triangulations requires a quadratic number of extra vertices in the worst case.

AB - It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices inside the polygon are allowed? We give a positive answer and construct a pair of such triangulations with O(n2) new triangulation vertices. Moreover, we show that there exists a 'universal' way of triangulating an n-sided polygon with O(n2) extra triangulation vertices. Finally, we also show that creating compatible triangulations requires a quadratic number of extra vertices in the worst case.

UR - http://www.scopus.com/inward/record.url?scp=0002312196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002312196&partnerID=8YFLogxK

U2 - 10.1016/0925-7721(93)90028-5

DO - 10.1016/0925-7721(93)90028-5

M3 - Article

VL - 3

SP - 27

EP - 35

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 1

ER -