# Aperture-Angle Optimization Problems in Three Dimensions

Elsa Omaña-Pulido, Godfried Toussaint

Research output: Contribution to journalArticle

### 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 θmax(ν) and θmin(ν), the maximum and minimum values of θ(ν) as ν varies over all points in P. We obtain two characterizations of θmax(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) 301-329 29 Journal of Mathematical Modelling and Algorithms 1 4 https://doi.org/10.1023/A:1021666512528 Published - Dec 1 2002

### Fingerprint

Three-dimension
Optimization Problem
Angle
Interior angle
Convex polyhedron
Models of Computation
End point
Line segment
Upper and Lower Bounds
Triangle
Vary
Computing

### Keywords

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

### ASJC Scopus subject areas

• Modeling and Simulation
• Applied Mathematics

### Cite this

Aperture-Angle Optimization Problems in Three Dimensions. / Omaña-Pulido, Elsa; Toussaint, Godfried.

In: Journal of Mathematical Modelling and Algorithms, Vol. 1, No. 4, 01.12.2002, p. 301-329.

Research output: Contribution to journalArticle

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