### Abstract

The Graham scan is a fundamental backtracking technique in computational geometry which was originally designed to compute the convex hull of a set of point in the plane [9] and has since found application in several different contexts. In this note we show how to use the Graham scan to triangulate a simple polygon. The resulting algorithm triangulates an n-vertex polygon P in O(kn) time where k -1 is the number of concave vertices in P. Although the worst case running time of the algorithm is O(n^{2}), it is easy to implement and is therefore of practical interest.

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

Pages (from-to) | 713-716 |

Number of pages | 4 |

Journal | Pattern Recognition Letters |

Volume | 11 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1990 |

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### ASJC Scopus subject areas

- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Artificial Intelligence

### Cite this

*Pattern Recognition Letters*,

*11*(11), 713-716. https://doi.org/10.1016/0167-8655(90)90089-K

**The Graham scan triangulates simple polygons.** / Kong, Xianshu; Everett, Hazel; Toussaint, Godfried.

Research output: Contribution to journal › Article

*Pattern Recognition Letters*, vol. 11, no. 11, pp. 713-716. https://doi.org/10.1016/0167-8655(90)90089-K

}

TY - JOUR

T1 - The Graham scan triangulates simple polygons

AU - Kong, Xianshu

AU - Everett, Hazel

AU - Toussaint, Godfried

PY - 1990/1/1

Y1 - 1990/1/1

N2 - The Graham scan is a fundamental backtracking technique in computational geometry which was originally designed to compute the convex hull of a set of point in the plane [9] and has since found application in several different contexts. In this note we show how to use the Graham scan to triangulate a simple polygon. The resulting algorithm triangulates an n-vertex polygon P in O(kn) time where k -1 is the number of concave vertices in P. Although the worst case running time of the algorithm is O(n2), it is easy to implement and is therefore of practical interest.

AB - The Graham scan is a fundamental backtracking technique in computational geometry which was originally designed to compute the convex hull of a set of point in the plane [9] and has since found application in several different contexts. In this note we show how to use the Graham scan to triangulate a simple polygon. The resulting algorithm triangulates an n-vertex polygon P in O(kn) time where k -1 is the number of concave vertices in P. Although the worst case running time of the algorithm is O(n2), it is easy to implement and is therefore of practical interest.

UR - http://www.scopus.com/inward/record.url?scp=0025638579&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025638579&partnerID=8YFLogxK

U2 - 10.1016/0167-8655(90)90089-K

DO - 10.1016/0167-8655(90)90089-K

M3 - Article

VL - 11

SP - 713

EP - 716

JO - Pattern Recognition Letters

JF - Pattern Recognition Letters

SN - 0167-8655

IS - 11

ER -