Ebook: Stochastic Visibility in Random Fields

The present monograph is a comprehensive summary of the research on visibility in random fields, which I have conducted with the late Professor Micha Yadin for over ten years. This research, which resulted in several published papers and technical reports (see bibliography), was motivated by some military problems, which were brought to our attention by Mr. Pete Shugart of the US Army TRADOC Systems Analysis Activity, presently called US Army TRADOC Analysis Command. The Director ofTRASANA at the time, the late Dr. Wilbur Payne, identified the problems and encouraged the support and funding of this research by the US Army. Research contracts were first administered through the Office of Naval Research, and subsequently by the Army Research Office. We are most grateful to all involved for this support and encouragement. In 1986 I administered a three-day workshop on problem solving in the area of sto­ chastic visibility. This workshop was held at the White Sands Missile Range facility. A set of notes with some software were written for this workshop. This workshop led to the incorporation of some of the methods discussed in the present book into the Army simulation package CASTFOREM. Several people encouraged me to extend those notes and write the present monograph on the level of those notes, so that the material will be more widely available for applications.

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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 here. In addition, a (DOS) disk 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 valuable introduction to this problem.

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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 here. In addition, a (DOS) disk 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 valuable introduction to this problem.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
Probability Models....Pages 6-16
Geometrical Probability, Coverage and Visibility In Random Fields....Pages 17-35
Visibility Probabilities....Pages 36-61
Visibility Probabilities II....Pages 62-81
Distributions of Visibility Measures....Pages 82-104
Distributions of Visible and Invisible Segments....Pages 105-119
Problems and Solutions....Pages 120-165
Back Matter....Pages 166-175

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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 here. In addition, a (DOS) disk 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 valuable introduction to this problem.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
Probability Models....Pages 6-16
Geometrical Probability, Coverage and Visibility In Random Fields....Pages 17-35
Visibility Probabilities....Pages 36-61
Visibility Probabilities II....Pages 62-81
Distributions of Visibility Measures....Pages 82-104
Distributions of Visible and Invisible Segments....Pages 105-119
Problems and Solutions....Pages 120-165
Back Matter....Pages 166-175
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