Computational Geometry With Independent And Dependent Uncertainties

A parametric model and algorithmic theory, named Linear Parametric Geometric Uncertainty Model (LPGUM), is presented to represent geometric entities with dependent uncertainties. It is an expressive and computationally efficient framework for studying geometric uncertainty and its related algorithms in computer geometry, with applications in mechanical CAD/CAM, robotics, computer vision, and wireless networks.

Format: Hardback
Length: 160 pages
Publication date: 12 September 2022
Publisher: World Scientific Publishing Co Pte Ltd

This extensive compendium presents a parametric model and algorithmic theory to represent geometric entities with dependent uncertainties between them. The theory, known as the Linear Parametric Geometric Uncertainty Model (LPGUM), is an expressive and computationally efficient framework that enables the systematic study of geometric uncertainty and its related algorithms in computer geometry. The self-contained monograph holds immense scientific, technical, and economic significance, as geometric uncertainty permeates various fields such as mechanical CAD/CAM, robotics, computer vision, wireless networks, and numerous others. Geometric models, conversely, typically assume exactness and fail to account for these inaccuracies. This valuable reference text serves as a valuable resource for academics, researchers, and practitioners in computer science, robotics, mechanical engineering, and related domains.

Introduction:
Geometric uncertainty arises when the dimensions, shapes, or positions of geometric entities in a digital model deviate from their actual values. This uncertainty can significantly impact the accuracy and reliability of subsequent computations and analyses. Traditional geometric models, which are typically exact, do not account for these inaccuracies, leading to potential errors and inefficiencies.

Parametric Model:
The parametric model presented in this compendium is a powerful tool for representing and analyzing geometric entities with dependent uncertainties. It allows for the definition of geometric entities using parameters, which can vary within specified ranges. By defining the uncertainties associated with these parameters, the model can capture the variability and dependencies between different geometric features.

Algorithmic Theory:
The algorithmic theory developed alongside the parametric model is crucial for studying geometric uncertainty and its related algorithms. The LPGUM framework provides a systematic approach to analyzing and manipulating geometric uncertainty, enabling the development of efficient algorithms for tasks such as uncertainty quantification, optimization, and visualization.

Applications:
The applications of geometric uncertainty modeling and algorithms are diverse and widespread. In mechanical CAD/CAM, for instance, geometric uncertainty can be used to improve the accuracy of product design and manufacturing processes. In robotics, geometric uncertainty can be utilized to enhance the navigation and manipulation capabilities of robots. In computer vision, geometric uncertainty can be employed to improve the accuracy of object detection and tracking.

Conclusion:
The Linear Parametric Geometric Uncertainty Model (LPGUM) presents a comprehensive and effective framework for representing and analyzing geometric entities with dependent uncertainties. By leveraging the parametric model and algorithmic theory developed within this framework, researchers and practitioners can gain a deeper understanding of geometric uncertainty and develop innovative solutions to address its challenges in various fields. The significance of this work lies in its potential to enhance the accuracy, efficiency, and reliability of computations and analyses in a wide range of applications.

ISBN-13: 9789811253836