Overview

Visibility problems are of interest in a wide variety of operations research and communications problems. This monograph presents an analysis of the visibility of one point in the plane from another given the existence of random objects which may obstruct the line of sight. The author aims to emphasize the practical issues involved, and describes the algorithms discussed. In addition, a DOS diskette containing executable programs which implement these algorithms is provided. The author presupposes a basic familiarity with probability, statistics and geometry, but otherwise the book is self-contained. As a result, researchers across a number of disciplines will find this account a useful introduction to the problem.

Full Product Details

Author:   Shelemyahu Zacks
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1994 ed.
Volume:   95
Dimensions:   Width: 15.50cm , Height: 1.00cm , Length: 23.50cm
Weight:   0.310kg
ISBN:  

9780387944128

ISBN 10:   0387944125
Pages:   175
Publication Date:   13 December 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Mixed media product
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

0. Introduction.- 0.1. Aims and Objectives.- 0.2. Some Military Applications.- 0.3. Synopsis.- 1. Probability Models.- 1.1. Probability Models For Obscuring Elements.- 1.2. Glossary of Distributions.- 1.2.1. Some Discrete Distributions.- 1.2.1.1. Binomial Distributions.- 1.2.1.2. Poisson Distributions.- 1.2.1.3. Multinomial Distributions.- 1.2.2. Some Continuous Distributions.- 1.2.2.1. Uniform Distributions.- 1.2.2.2. Beta Distributions.- 1.2.2.3. Gamma Distributions.- 1.2.2.4. Normal Distributions.- 1.2.2.5. Bivariate Normal Distributions.- 1.3. Random Fields.- 2. Geometrical Probability, Coverage and Visibility in Random Fields.- 2.1. Intersection of Lines By Random Segments.- 2.2. Random Lines Intersecting Circles.- 2.3. Random Disks Intersecting Lines.- 2.4. The Coverage of a Circle By Random Arcs.- 2.5. Vacancies On The Circle.- 2.6. Vacancies On The Plane.- 2.6.1. Vacancy of a Point under Bivariate Normal Dispersion.- 2.6.2. Complete Vacancy of a Triangle.- 2.7. Visitiblity of Points on a Circle In a Poisson Field.- 2.8. Distribution of Clump Size In a Poisson Field on The Line.- 3. Visibility Probabilities.- 3.1. Geometric Methods: Standard Poisson Fields.- 3.1.1. The Target(s) and Observation Point Are Within the Scattering Region.- 3.1.2. The Targets and Observation Points Are Outside a Rectangular Scattering Region.- 3.2. Analytic Methods: General Poisson Fields.- 3.2.1. The General Theoretical Framework.- 3.2.2. Standard Poisson Fields with Uniform Distribution of Radii.- 3.2.2.1. Annular Scattering Regions.- 3.2.2.2. Trapezoidal Scattering Regions.- 3.3. An Alternative Geometric-Analytic Method.- 3.3.1. Computing the Probability of B+(r) in the Bivariate Normal Case.- 3.4. The Visibility of Windows.- 4. Visibility Probabilities II.- 4.1. The Multi-Observer Multi-Target Shadowing Model and Simultaneous Visibility Probabilities.- 4.2. General Formulae of mk(n,n?) for the Standard Poisson Field.- 4.3. Determination of mk(n,n?) in Cases of Non-Standard Poisson Fields.- 4.4. Joint Visibility of Windows.- 4.5. Visibility of Points in Space.- 4.5.1. Single Target.- 4.5.2. Several Target Points on a Line.- 4.5.3. Uniform Distribution of Sphere Radius.- 4.5.4. Derivation of K(s,t).- 5. Distributions of Visibility Measures.- 5.1. The Distribution of The Number of Visible Targets.- 5.1.1. Introductory Examples With One Observation Point.- 5.1.2. General Method For Computing Probabilities of Elementary Events.- 5.1.3. Joint Distributions of Counting Variables.- 5.2. An Integrated Measure of Visibility on a Star-Shaped Curve.- 5.3. The Moments of W.- 5.4. Approximations to the Distribution of W.- 5.4.1. A Beta Approximation.- 5.4.2. Discrete Approximation.- 5.4.3. Recursive Determination of h(N)(k; ?).- 6. Distributions of The Visible and Invisible Segments.- 6.1. The Distribution of The Length of A Visible Segment.- 6.2. The Functions K+*(x,t) in the Standard-Uniform Case.- 6.3. Distribution of The Right-Hand Limit of A Shadow Cast by a Single Disk.- 6.4. Distribution of The Right Hand Limit of a Shadow Starting at a Given Point.- 6.5. Discrete Approximation.- 6.6. Distribution of the Number of Shadows.- 6.7. Survival Probability Functions.- 7. Problems and Solutions.- 7.1.1. Problems For Chapter 1.- 7.1.2. Solutions For Chapter 1.- 7.2.1. Problems For Chapter 2.- 7.2.2. Solutions For Chapter 2.- 7.3.1. Problems For Chapter 3.- 7.3.2. Solutions For Chapter 3.- 7.4.1. Problems For Chapter 4.- 7.4.2. Solutions For Chapter 4.- 7.5.1. Problems For Chapter 5.- 7.5.2. Solutions For Chapter 5.- 7.6.1. Problems For Chapter 6.- 7.6.2. Solutions For Chapter 6.- References.- Computer Programs.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions