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crane k discrete differential geometry applied introduction 2025

Type:: E-books
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Uploaded On:: July 12, 2025, 9:15 a.m.
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Textbook in PDF format These notes focus on three-dimensional geometry processing, while simultaneously providing a first course in traditional differential geometry. Our main goal is to show how fundamental geometric concepts (like curvature) can be understood from complementary computational and mathematical points of view. This dual perspective enriches understanding on both sides, and leads to the development of practical algorithms for working with real-world geometric data. Along the way we will revisit important ideas from calculus and linear algebra, putting a strong emphasis on intuitive, visual understanding that complements the more traditional formal, algebraic treatment. The course provides essential mathematical background as well as a large array of real-world examples and applications. It also provides a short survey of recent developments in digital geometry processing and discrete differential geometry. Topics include: curves and surfaces, curvature, connections and parallel transport, exterior algebra, exterior calculus, Stokes’ theorem, simplicial homology, de Rham cohomology, Helmholtz-Hodge decomposition, conformal mapping, finite element methods, and numerical linear algebra. Applications include: approximation of curvature, curve and surface smoothing, surface parameterization, vector field design, and computation of geodesic distance. One goal of these notes is to provide an introduction to working with real-world geometric data, expressed in the language of discrete exterior calculus (DEC). DEC is a simple, flexible, and efficient framework which provides a unified platform for geometry processing. The notes provide essential mathematical background as well as a large array of real-world examples, with an emphasis on applications and implementation. The material should be accessible to anyone with some exposure to basic linear algebra and vector calculus, though most of the key concepts are reviewed as needed. Coding exercises depend on a basic knowledge of either JavaScript or C++, though knowledge of any programming language is likely sufficient: we do not make heavy use of paradigms like inheritance, templates, etc. The notes also provide guided written exercises that can be used to deepen understanding of the material

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Crane K. Discrete Differential Geometry. An Applied Introduction 2025.pdf 3.6 MB

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crane k discrete differential geometry applied introduction 2025

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