Computational Geometry with Independent and Dependent Uncertainties

This comprehensive compendium describes a parametric model and algorithmic theory to represent geometric entities with dependent uncertainties between them. The theory, named Linear Parametric Geometric Uncertainty Model (LPGUM), is an expressive and computationally efficient framework that allows to systematically study geometric uncertainty and its related algorithms in computer geometry.The self-contained monograph is of great scientific, technical, and economic importance as geometric uncertainty is ubiquitous in mechanical CAD/CAM, robotics, computer vision, wireless networks and many other fields. Geometric models, in contrast, are usually exact and do not account for these inaccuracies.This useful reference text benefits academics, researchers, and practitioners in computer science, robotics, mechanical engineering and related fields.

這本全面的彙編描述了一個參數模型和算法理論，用於表示幾何實體之間的相依不確定性。該理論被稱為線性參數幾何不確定性模型（LPGUM），它是一個表達豐富且計算效率高的框架，可以系統地研究計算機幾何中的幾何不確定性及其相關算法。這本獨立的專著在科學、技術和經濟上具有重要意義，因為幾何不確定性在機械CAD/CAM、機器人學、計算機視覺、無線網絡和許多其他領域中無處不在。相比之下，幾何模型通常是精確的，並且不考慮這些不準確性。這本有用的參考書對計算機科學、機器人學、機械工程和相關領域的學者、研究人員和從業人員都有益處。