Classical and Discrete Differential Geometry: Theory, Applications and Algorithms
暫譯: 經典與離散微分幾何：理論、應用與演算法

Gu, David Xianfeng, He, Ruijun, Saucan, Emil

Classical and Discrete Differential Geometry: Theory, Applications and Algorithms
  • 出版商: CRC
  • 出版日期: 2023-01-31
  • 售價: $5,500
  • 貴賓價: 9.5 折 $5,225
  • 語言: 英文
  • 頁數: 608
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1032390174
  • ISBN-13: 9781032390178
  • 相關分類: Algorithms-data-structures

    • 立即出貨 (庫存=1)

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商品描述

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.

With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation.
The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.

商品描述(中文翻譯)

這本書介紹了微分幾何及其前沿研究成果，結合了經典方法和現代離散微分幾何，涵蓋了所有面向和應用，包括圖形與影像、物理學和網絡。

以曲率為中心，作者呈現了微分幾何的發展，從曲線到曲面，再到更高維的流形；以及從光滑結構到度量空間、加權流形和複合體，最後到影像、網格和網絡。書的第一部分是對歐幾里得空間中曲線和曲面的微分幾何研究，第二部分則處理以曲率為中心的高維流形，探索將其擴展到更高維物體和更一般結構的各種方法，以及如何回到低維構造。第三部分專注於代數拓撲和共形幾何中的計算算法，適用於表面參數化、形狀註冊和結構化網格生成。

本書將成為數學和計算機科學學生，以及對圖形與影像、複雜網絡、微分幾何和曲率感興趣的研究人員和工程專業人士的有用參考資料。

作者簡介

David Xianfeng Gu is a SUNY Empire Innovation Professor of Computer Science and Applied Mathematics at State University of New York at Stony Brook, USA. His research interests focus on generalizing modern geometry theories to discrete settings and apply them in engineering and medical fields and recently on geometric views of optimal transportation theory. He is one of the major founders of an interdisciplinary field, Computational Conformal Geometry.

Emil Saucan is Associate Professor of Applied Mathematics at Braude College of Engineering, Israel. His main research interest is geometry in general (including Geometric Topology), especially Discrete and Metric Differential Geometry and their applications to Imaging and Geometric Design, as well as Geometric Modeling. His recent research focuses on various notions of discrete Ricci curvature and their practical applications.

作者簡介(中文翻譯)

大衛·賢峰·顧（David Xianfeng Gu）是美國紐約州立大學石溪分校（State University of New York at Stony Brook）計算機科學與應用數學的創新教授。他的研究興趣集中在將現代幾何理論推廣到離散環境中，並將其應用於工程和醫學領域，最近則專注於最佳運輸理論的幾何觀點。他是計算共形幾何（Computational Conformal Geometry）這一跨學科領域的主要創始人之一。

艾米爾·索坎（Emil Saucan）是以色列布勞德工程學院（Braude College of Engineering）應用數學的副教授。他的主要研究興趣是幾何學（包括幾何拓撲），特別是離散和度量微分幾何及其在成像和幾何設計中的應用，以及幾何建模。他最近的研究專注於各種離散里奇曲率的概念及其實際應用。

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