## Abstract

Let [a,b] be a line segment with end points a, b and ν a point at which a viewer is located, all in R ^{3}. The aperture angle of [a,b] from point ν, denoted by θ(ν), is the interior angle at ν of the triangle Δ(a,b,ν). Given a convex polyhedron P not intersecting a given segment [a,b] we consider the problem of computing θ_{max}(ν) and θ_{min}(ν), the maximum and minimum values of θ(ν) as ν varies over all points in P. We obtain two characterizations of θ_{max}(ν). Along the way we solve several interesting special cases of the above problems and establish linear upper and lower bounds on their complexity under several models of computation.

Original language | English (US) |
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Pages (from-to) | 301-329 |

Number of pages | 29 |

Journal | Journal of Mathematical Modelling and Algorithms |

Volume | 1 |

Issue number | 4 |

DOIs | |

State | Published - 2002 |

## Keywords

- algorithms
- aperture-angle
- computational-complexity
- convexity
- discrete-optimization
- geometry

## ASJC Scopus subject areas

- Modeling and Simulation
- Applied Mathematics