Read Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint)

Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint)

Herbert J Bernstein

4.9/5 (24404 ratings)

Description:Excerpt from Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes A robot may see into a workspace in many ways. It may have cameras which present entire projections of a scene at once. Often, however, the robot will have to rely on simple probes into the workspace. For each probe the robot moves along some line until it encounters some sort of object boundary. By recording the locations of such contacts, the robot can infer object locations. Cole and Yap [1] considered the question of determining the shape of a mn veir polygon by such tactile probes. They did not restrict the polygons to a finite set. They showed that the shape of a polygon known to contain the origin can be determined with no more than 3n probes, where n is the number of sides of the polygon. They also showed that 3n - 1 probes are necessary. Under a mild assumption, they showed that 3n probes are necessary. Schwartz and Shatir [3] considered the question of selecting one polygon from a finite set by such probing and asserted that normally, very few probes will be required. In this note we show that 2n+k probes suffice to determine the shape of a convex polygon of n sides selected from a finite set of polygons. The number of polygons in the set enters only indirectly and some infinite sets can be handled by. The same tech nique. We show that k 3 under the assumptions of Cole and Yap. For slightly stronger assumptions we show that k 2. Under the assumptions of Schwartz and Sharit we obtain 1: -1. If we add the assumption that the number of sides n is known, then 1: drops by one in each case. Necessity is shown in a case closely related to the Schwartz and Shari: assumptions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint). To get started finding Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: —

Format: PDF, EPUB & Kindle Edition

Publisher: —

Release: —

ISBN: 1333133898

Description: Excerpt from Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes A robot may see into a workspace in many ways. It may have cameras which present entire projections of a scene at once. Often, however, the robot will have to rely on simple probes into the workspace. For each probe the robot moves along some line until it encounters some sort of object boundary. By recording the locations of such contacts, the robot can infer object locations. Cole and Yap [1] considered the question of determining the shape of a mn veir polygon by such tactile probes. They did not restrict the polygons to a finite set. They showed that the shape of a polygon known to contain the origin can be determined with no more than 3n probes, where n is the number of sides of the polygon. They also showed that 3n - 1 probes are necessary. Under a mild assumption, they showed that 3n probes are necessary. Schwartz and Shatir [3] considered the question of selecting one polygon from a finite set by such probing and asserted that normally, very few probes will be required. In this note we show that 2n+k probes suffice to determine the shape of a convex polygon of n sides selected from a finite set of polygons. The number of polygons in the set enters only indirectly and some infinite sets can be handled by. The same tech nique. We show that k 3 under the assumptions of Cole and Yap. For slightly stronger assumptions we show that k 2. Under the assumptions of Schwartz and Sharit we obtain 1: -1. If we add the assumption that the number of sides n is known, then 1: drops by one in each case. Necessity is shown in a case closely related to the Schwartz and Shari: assumptions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint). To get started finding Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Special Offer | $0.00

Special Offer! | $0.00

Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint)

Determining the Shape of a Convex N-Sided Polygon by Using 2n+k Tactile Probes (Classic Reprint)

More Books

Constraints in Real-time Data Acquisition and Control

Constraints in Real-time Data Acquisition and Control

Constraints in Real-Time Data Acquisition and Control (Classic Reprint)

Constraints in Real-Time Data Acquisition and Control (Classic Reprint)

Parallel Implementation of Bisection for the Calculation of Eigenvalues of Tridiagonal Diagonal Symmetric Matrices (Classic Reprint)

Parallel Implementation of Bisection for the Calculation of Eigenvalues of Tridiagonal Diagonal Symmetric Matrices (Classic Reprint)

The Algebraic Manipulation Package SYMBOLANG; a Manual for Users

The Algebraic Manipulation Package SYMBOLANG; a Manual for Users

Servol: Preliminary Proposal for a Programming Language for Real-Time Servo Control (Classic Reprint)

Servol: Preliminary Proposal for a Programming Language for Real-Time Servo Control (Classic Reprint)

The Algebraic Manipulation Package Symbolang: A Manual for Users (Classic Reprint)

The Algebraic Manipulation Package Symbolang: A Manual for Users (Classic Reprint)

An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix (Classic Reprint)

An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix (Classic Reprint)

Some Comments on Highly Dynamic Network Routing (Classic Reprint)

Some Comments on Highly Dynamic Network Routing (Classic Reprint)

The American Heritage Dictionary of the English Language

The American Heritage Dictionary of the English Language