Robotics Research Technical Report: Ray Shooting, Implicit Point Location

Leonidas Guibas, Mark Overmars

ISBN 10: 1332184693 / ISBN 13: 9781332184699

Verlag: Forgotten Books, 2022

Beschreibung

Print on Demand. This book explores the development of advanced techniques for various types of queries on arrangements of segments and related structures. Ray shooting, implicit point location, and related problems form the core of this research. The author presents efficient techniques for answering various queries on planar arrangements of segments and certain related structures. These techniques extend and modify recent efficient techniques for half-plane range searching to obtain algorithms for answering efficiently several types of queries on arrangements of segments and certain related structures. A typical example is the implicit point location problem â " given such an arrangement A, preprocess it so that, given any query point x, we can calculate quickly certain properties of the face of A containing x. The results of this book have been conceived and developed in the summer of 1987, but for various reasons were left unpublished for almost two years. Meanwhile, there has been significant progress on the problems studied here. In particular, a recent work by Agarwal presents techniques that achieve query time roughly O(sqrt(n)) and involve deterministic, rather than randomized, preprocessing. Agarwal's results are based on a decomposition technique that is different from the one used in this book. Still, many of Agarwal's arguments are taken from this book. As a public service, to make our results somewhat more accessible, the author has decided to elevate this book from the status of unpublished manuscript to that of a technical report. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Bestandsnummer des Verkäufers 9781332184699_0

Bibliografische Details

• Titel: Robotics Research Technical Report: Ray Shooting, Implicit Point Location
• Verlag: Forgotten Books
• Erscheinungsjahr: 2022
• Sprache: Englisch
• ISBN-10: 1332184693
• ISBN-13: 9781332184699
• Einband: Paperback
• Zustand: New
• Buchtyp: print-on-demand item
• Verkäuferkataloge:
  • Geometry

Über diesen Titel

Inhaltsangabe

Excerpt from Robotics Research Technical Report: Ray Shooting, Implicit Point Location, and Related Queries in Arrangements of Segments

Typically, the queries we are interested in are trivially answered in 0(log n) time, if we are willing to calculate and store A explicitly. Since the combinatorial complexity of A can be quadratic in n in the worst case, this might be too expensive, and we therefore seek alterna tive methods of more efficient but implicit representation of A, which still facilitates reason ably efficient query handling, although not as efficient as the (optimal) 0(log n) time that can be achieved with explicit representation.

As a typical example, consider the following implicit point location problem. Given such an arrangement A, preprocess it so that, given any query point 1, we can calculate quickly certain properties of the face of A containing x. For example, suppose A is formed as the overlay of n (possibly intersecting) triangles, and the property in question is how many triangles contain the query point x, or more generally, if each triangle is associated a certain weight, what is the sum of the weights of the triangles covering x, etc. Clearly, by calculating the arrangement A induced by these triangles, and by further preprocessing it for efficient point location, it is easy to answer such a query in (optimal) 0(log n) time. Can we obtain faster preprocessing and more compact representation of A that will still enable us to answer these queries reasonably efficiently?

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.