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Conformal geometry : computational algorithms and engineering applications

Author: Miao Jin; Xianfeng Gu; Ying He; Yalin Wang
Publisher: Cham : Springer, [2018]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental problems in specific fields of application, and detail how computational conformal geometric methods can be used to  Read more...
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Genre/Form: Electronic book
Electronic books
Additional Physical Format: Print version:
Jin, Miao.
Conformal geometry.
Cham : Springer, [2018]
(OCoLC)1019661400
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Miao Jin; Xianfeng Gu; Ying He; Yalin Wang
ISBN: 9783319753324 3319753320
OCLC Number: 1031214459
Description: 1 online resource (xiii, 314 pages) : illustrations
Contents: Intro; Preface; Contents; 1 Introduction; 1.1 Riemann Mapping Theorem; 1.2 Holomorphic Differential; 1.3 Uniformization Theorem; 1.4 Shape Space; 1.5 Geometric Structures; Part I Computational Algorithms; 2 Topological Algorithms; 2.1 Halfedge Data Structure; 2.2 Cut Graph and Fundamental Domain; 2.3 Homotopy and Homology Group Basis; 2.4 Canonical Homotopy Group Generators; 3 Harmonic Map; 3.1 Discrete Harmonic Energy; 3.2 Topological Disk Surfaces; 3.3 Topological Sphere Surfaces; 3.4 Riemann Mapping; 4 Harmonic and Holomorphic Forms; 4.1 Characteristic Forms; 4.2 Cohomology Basis. 4.3 Harmonic 1-Form4.4 Hodge Star Operator; 4.5 Holomorphic 1-Form; 5 Discrete Ricci Flow; 5.1 Discrete Background; 5.2 Discrete Surface Ricci Flow; 5.3 Isometric Planar Embedding; 5.4 Hyperbolic Ricci Flow; 5.5 Isometric Hyperbolic Embedding; Part II Engineering Applications; 6 Computer Graphics; 6.1 Introduction; 6.2 Global Surface Parametrization; 6.2.1 Optimal Global Conformal Parametrization Using Discrete One-Form; 6.2.2 Global Conformal Parameterization Using Discrete Euclidean Ricci Flow; 6.3 Uniform Remeshing; 6.3.1 Voronoi Diagram in Different Spaces. 6.3.2 Centroid Voronoi Tessellation in Different Spaces6.3.3 CVT Energy in Different Spaces; 6.3.4 Computing Centroidal Voronoi Tessellations; 6.3.5 Uniform Remeshing and Partition; 6.4 Metric-Driven RoSy Fields Design; 6.4.1 Theory of Compatibility; 6.4.2 Computing N-RoSy Fields; 6.4.3 Remeshing; 6.4.4 Celtic Knot on Surfaces; 6.4.5 Pen-and-Ink Sketching of Surfaces; 6.5 Computing Shortest Homotopic Cycles on Polyhedral Surfaces; 6.5.1 Geodesic Uniqueness; 6.5.2 Fuchsian Group Method; 6.5.3 Birkhoff Curve Shortening Method; 6.5.4 Extremal Quasiconformal Mapping; 6.5.5 Homotopy Detection. 6.6 Summary and Further Reading7 Computer Vision; 7.1 Introduction; 7.2 Teichmuller Shape Space; 7.2.1 Luo Coordinates; 7.2.2 Fenchel-Nielsen Coordinates; 7.2.3 Robustness of Teichmuller Space Coordinates; 7.2.4 Surface Indexing and Classification; 7.3 3D Facial Shape Index; 7.3.1 Generalized Discrete Ricci Flow; 7.3.2 Doubly Connected Domain; 7.3.3 Multiply Connected Domain; 7.4 Shape Signature; 7.4.1 Beltrami Equation; 7.4.2 Conformal Module; 7.4.3 Holomorphic Differentials; 7.4.4 Conformal Welding; 7.4.5 Computing Shape Signatures of Planar Domains; 7.4.6 Shape Clustering. 7.5 Summary and Further Reading8 Geometric Modeling; 8.1 Introduction; 8.2 Triangular B-Splines; 8.2.1 Definition; 8.2.2 Properties; 8.2.3 Surface Reconstruction; 8.3 Theoretical Foundation of Manifold Splines; 8.3.1 Definitions and Concepts; 8.3.2 Equivalence to Affine Atlas; 8.3.3 Existence; 8.4 Constructing Affine Atlas; 8.4.1 Computing Affine Structure Using Holomorphic 1-form; 8.4.2 Computing Affine Structure Using Discrete Ricci Flow; 8.4.3 Computing Affine Structure Using Polycube Maps; 8.5 Extending Planar Splines to Manifold Domains; 8.5.1 Manifold Triangular B-spline.
Responsibility: Miao Jin, Xianfeng Gu, Ying He, Yalin Wang.

Abstract:

This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields.  Read more...

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"Such algorithms make conformal maps into a computational tool for subjects such as computer graphics, computer vision ... and wireless sensor networks. The authors develop each of these topics in Read more...

 
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