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| | 內容介紹 | |
出版社：科學出版社 ISBN：9787030367648 商品編碼：68387712285 開本：小16開 出版時間：2013-05-01 頁數：371 代碼：128
"| 商品基本信息，請以下列介紹為準 | | 商品名稱： | 計算幾何中的幾何偏微分方程方法-54 | | 作者： | Guoliang Xu，Qin Zhang[著] | | 代碼： | 128.0 | | 出版社： | 科學出版社 | | 出版日期： | 2013-05-01 | | ISBN： | 9787030367648 | | 印次： | 1 | | 版次： | 1 | | 裝幀： | 精裝 | | 開本： | 小16開 |
| 內容簡介 | 《計算幾何中的幾何偏微分方程方法（英文版）》的主要內容包括幾何偏微分方程的構造方法、各種微分幾何算子的離散化方法及其離散格式的收斂性、幾何偏微分方程數值求解的有限差分法法以及水平集方法，還包括幾何偏微分方程在曲而平滑、曲面拼接、N邊洞填補、自由曲面設計、曲面重構、曲而恢復、分子曲面構造以及三維實體幾何形變中的應用。
《計算幾何中的幾何偏微分方程方法（英文版）》內容新穎、文字簡練、可讀性強，可作為理工科院校的應用數學、計算數學、計算幾何、計算機輔助設計以及計算機圖形學等專業本科生和研究生的教材，也可作為在上述領域中從事研究工作的廣大科技工作者的參考書。 |
| 目錄 | Preface
Acronyms
Chapter 1 Elementary DifferentiaIGeometry
1.1 Parametric Representation of Surfaces
1.2 Curvatures of Surfaces
1.3 The Fundamental E
Preface
Acronyms
Chapter 1 Elementary DifferentiaIGeometry
1.1 Parametric Representation of Surfaces
1.2 Curvatures of Surfaces
1.3 The Fundamental Equations and the Fundamental Theorem of
Surfaces
1.4 Gauss-Bonnet Theorem
1.5 Differential Operators on Surfaces
1.6 Basic Properties of Differential Operators
1.7 Differential Operators Acting on Surface and Normal Vector
1.8 Some Global Properties of Surfaces
1.8.1 Green's Formulas
1.8.2 Integral Formulas of Surfaces
1.9 Differential Geometry of Implicit Surfaces
Chapter 2 Construction of Geometric Partial Differential Equations
for Parametric Surfaces
2.1 Variation of Functionals for Parametric Surfaces
2.2 The Second-order Euler-Lagrange Operator
2.3 The Fourth-order Euler-Lagrange Operator
2.4 The Sixth-order Euler-Lagrange Operator
2.5 Other Euler-Lagrange Operators
2.5.1 Additivity of Euler-Lagrange Operators
2.5.2 Euler-Lagrange Operator for Surfaces with Graph
Representation
2.6 Gradient Flow
2.6.1 L2-Gradient Flow for Parametric Surfaces
2.6.2 H-1 Gradient Flow for Parametric Surfaces
2.7 Other Geometric Flows
2.7.1 Area-Preserving or Volume-Preserving Second-order
Geometric Flows
2.7.2 Other Sixth-order Geometric Flows
2.7.3 Geometric Flow for Surfaces with Graph Representation
2.8 Notes
2.9 Related Works
2.9.1 The Choice of Energy Functionals
2.9.2 About Geometric Flows
Chapter 3 Construction of Geometric Partial Differential Equations
for Level-Set Surfaces
3.1 Variation of Functionals on Level-Set Surfaces
3.2 The Second-order Euler-Lagrange Operator
3.3 The Fourth-order Euler-Lagrange Operator
3.4 The Sixth-order Euler-Lagrange Operator
3.5 L2_Gradient Flows for Level Sets
3.6 H-1-Gradient Flow for Level Sets
3.7 Construction of Geometric Flows from Operator Conversion
3.8 Relationship Among Three Construction Methods of the
Geometric Flows
Chapter 4 Discretization of Differential Geometric Operators and
Curvatures
4.1 Discretization of the Laplace-Beltrami Operator over
Triangular Meshes
4.1.1 Discretization of the Laplace-Beltrami Operator over
Triangular Meshes
4.1.2 Convergence Test of Different Discretization Schemes
of'the LB Operator
4.1.3 Convergence of the Discrete LB Operator over Triangular
Meshes
4.1.4 Proof of the Convergence Result |
| 編輯 | Guoliang Xu和Qin
Zhang編寫的這本《計算幾何中的幾何偏微分方程方法》的主要內容包括幾何偏微分方程的構造方法、各種微分幾何算子的離散化方法及其離散格式的收斂性、幾何偏微分方程數值求解的有限差分法法以及水平集方法，還包括幾何偏微分方程在曲而平滑、曲面拼接、N邊洞填補、自由曲面設計、曲面重構、曲而恢復、分子曲面構造以及三維實體幾何形變中的應用。
本書內容新穎、文字簡練、可讀性強，可作為理工科院校的應用數學、計算數學、計算幾何、計算機輔助設計以及計算機圖形學等專業本科生和研究生的教材，也可作為在上述領域中從事研究工作的廣大科技工作者的參考書。
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| 前言 | Computational geometry is an interdisciplinary subject composed of approximation theory，differential geometry， computational mathematics， and computer graphics， etc. This subject studies the structure， representation， analysis and synthesis of geometric shapes using computers. It is the mathematical foundation of computer aided geometric design （CAGD）.
In the 1960s， computer aided design （CAD） and computer aided manufacturing （CAM） entered the shipbuilding， aviation and the automobile industries helping to shape， design and manufacture. Stimulated by the development of computer technology and wide applications of industrial design， the subject of computational geometry has been developing rapidly. Heretofore， many effective methods， such as Bezier， B-spline， non- uniform rational B-spline （NURBS）， subdivision， and partial differential equations have been established， based on the parametric， implicit and discrete presentations of surfaces and the theory of interpolation and approximation. At present， CAGD is still an attractive field with large number of the researchers engaged with classical approximation theory， differential geometry， computational mathematics and computer graphics， devoting themselves to this area，helping to promote its comprehensive development. Under such a background， an emerging field of research， geometric partial differential equation methods in computational geometry，
is generated.
It is generally known that partial differential equations （PDEs） are equations describing the relationship among independent variables， unknown functions， and their partial derivatives. However， geometric partial differential equations， which are used to control the motion of surfaces and manifolds， are partial differential equations which |
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