### Abstract

One of the most recurring themes in many computer applications such as graphics automated cartography, image processing and robotics is the notion of visibility. We are concerned with the visibility between two edges of a simple n-vertex polygon. Four natural definitions of edge-to-edge visibility are proposed. There exist O(nlog n) algorithms and complicated O(nlog log n) algorithms to solve this problem partially and indirectly. A linear running time, and thus optimal algorithm is presented to determine edge-to-edge visibility under any of the four definitions. This simple, efficient, and direct algorithm without computing the triangulation of the simple polygon also identifies the visibility region if it exists.

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

Pages (from-to) | 342-357 |

Number of pages | 16 |

Journal | The Visual Computer |

Volume | 2 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 1986 |

### Fingerprint

### Keywords

- Algorithms
- Computational geometry
- Convex hull
- Geometric complexity
- Graphics
- Hidden line problems
- Jordan sorting
- Monotone polygons
- Polygon
- Visibility
- Weak visibility

### ASJC Scopus subject areas

- Software
- Education
- Human-Computer Interaction
- Computer Vision and Pattern Recognition
- Computer Science Applications
- Computer Graphics and Computer-Aided Design

### Cite this

*The Visual Computer*,

*2*(6), 342-357. https://doi.org/10.1007/BF01952419

**Visibility between two edges of a simple polygon.** / Avis, David; Gum, Teren; Toussaint, Godfried.

Research output: Contribution to journal › Article

*The Visual Computer*, vol. 2, no. 6, pp. 342-357. https://doi.org/10.1007/BF01952419

}

TY - JOUR

T1 - Visibility between two edges of a simple polygon

AU - Avis, David

AU - Gum, Teren

AU - Toussaint, Godfried

PY - 1986/12/1

Y1 - 1986/12/1

N2 - One of the most recurring themes in many computer applications such as graphics automated cartography, image processing and robotics is the notion of visibility. We are concerned with the visibility between two edges of a simple n-vertex polygon. Four natural definitions of edge-to-edge visibility are proposed. There exist O(nlog n) algorithms and complicated O(nlog log n) algorithms to solve this problem partially and indirectly. A linear running time, and thus optimal algorithm is presented to determine edge-to-edge visibility under any of the four definitions. This simple, efficient, and direct algorithm without computing the triangulation of the simple polygon also identifies the visibility region if it exists.

AB - One of the most recurring themes in many computer applications such as graphics automated cartography, image processing and robotics is the notion of visibility. We are concerned with the visibility between two edges of a simple n-vertex polygon. Four natural definitions of edge-to-edge visibility are proposed. There exist O(nlog n) algorithms and complicated O(nlog log n) algorithms to solve this problem partially and indirectly. A linear running time, and thus optimal algorithm is presented to determine edge-to-edge visibility under any of the four definitions. This simple, efficient, and direct algorithm without computing the triangulation of the simple polygon also identifies the visibility region if it exists.

KW - Algorithms

KW - Computational geometry

KW - Convex hull

KW - Geometric complexity

KW - Graphics

KW - Hidden line problems

KW - Jordan sorting

KW - Monotone polygons

KW - Polygon

KW - Visibility

KW - Weak visibility

UR - http://www.scopus.com/inward/record.url?scp=0039081770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039081770&partnerID=8YFLogxK

U2 - 10.1007/BF01952419

DO - 10.1007/BF01952419

M3 - Article

AN - SCOPUS:0039081770

VL - 2

SP - 342

EP - 357

JO - Visual Computer

JF - Visual Computer

SN - 0178-2789

IS - 6

ER -