Practical Geometry Algorithms
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Practical Geometry Algorithms
This book presents practical geometry algorithms with computationally fast C++ code implementations. It covers algorithms for fundamental geometric objects, such as points, lines, rays, segments, triangles, polygons, and planes. These algorithms determine the basic 2D and 3D properties, such as area, distance, inclusion, and intersections. There are also algorithms to compute bounding containers for these objects, including a fast bounding ball, various convex hull algorithms, as well as polygon extreme points and tangents. And there is a fast algorithm for polyline simplification using decimation that works in any dimension. These algorithms have been used in practice for several decades. They are robust, easy to understand, code, and maintain. And they execute very rapidly in practice, not just in theory. For example, the winding number point in polygon inclusion test, first developed by the author in 2000, is the fastest inclusion algorithm known, and works correctly even for non-simple polygons. Also, there is a fast implementation of the Melkman algorithm for the convex hull of a simple polyline. And much more. If your programming involves geometry, this book will be an invaluable reference. Further, along with the book, there is a free download of all the C++ code from the book, plus some additional supporting code.
Principles of Computational Geometry
"Principles of Computational Geometry" delves into the intersection of mathematics, algorithms, and computer science to solve geometric problems using computational methods. We cover a wide range of topics, from fundamental geometric concepts to advanced algorithmic techniques. Our book explores geometric data structures and algorithms designed to efficiently tackle issues like geometric modeling, spatial analysis, and geometric optimization. We introduce readers to key concepts like convex hulls, Voronoi diagrams, and Delaunay triangulations, which serve as building blocks for solving complex geometric problems. Additionally, we discuss techniques for geometric transformation, intersection detection, and geometric search, providing the tools needed to analyze and manipulate geometric data effectively. Throughout the text, we highlight practical applications of computational geometry, ranging from computer graphics and image processing to robotics and geographic information systems. We also explore the theoretical underpinnings of computational geometry, offering insights into the mathematical foundations of algorithms and their computational complexity. Overall, "Principles of Computational Geometry" serves as a comprehensive guide for students, researchers, and practitioners interested in leveraging computational methods to solve geometric problems efficiently and effectively. With its blend of theory and practical applications, our book offers a valuable resource for anyone exploring the rich and diverse field of computational geometry.
Practical Geometry in the High Middle Ages
Author: Stephen K. Victor
language: en
Publisher: American Philosophical Society Press
Release Date: 1979
Contents: (I) The Place of Practical Geometry in the Middle Ages: The Nature of Practical Geometry; Practical Geometry in Education; Theory and Practice in Geometry; and Practical Geometry and Practical Concerns; (II) The Contents of "Artis cuiuslibet consummatio" and the "Pratike de geometrie"; (III) Procedures in the Editions, Translations, and Commentary: Editing "Artis cuiuslibet consummatio"; Editing the "Pratike de geometrie"; Translating the Texts; and About the commentary; and (IV) English translation of "Arts cuiuslibet consummatio" and of the "Pratike de geometrie." Selected Bibliography, Index of Latin Technical Terms, Index of Old French Technical Terms, and Index of Astronomical Parameters. Illus.