Computational Conformal Geometry


Series: Advanced Lectures in Mathematics

Xianfeng David Gu
SUNY at Stony Brook

Shing-Tung Yau
Harvard University

Abstract

Computational conformal geometry is an emerging inter-disciplinary field, which applies algebraic topology, differential geometry and Riemann surface theories in geometric modeling, computer graphics, computer vision, medical imaging, visualization, scientific computation and many other engineering fields. This text book is the first one to thoroughly introduce both theoretical foundations and practical algorithms of computational conformal geometry, which have the direct applications in engineering and digital geometry procesing, such as surface parameterization, surface matching, brain mapping, 3D face recognition and identification, facial expression animation, dynamic face tracking, mesh-spline coversion and so on. The book has been taught in the mathematics department at Harvard and the computer science department at SUNY at Stony Brook.

The book is for graduate students in computer science or mathematics. It is also useful for researchers, developer and digital artists in geometric modeling, computer graphics, computer vision, visualization and medial imaging.

Contents

Preface;1. Introduction;

Part I: Theories
2. Algebraic Topology I: Homotopy; 3. Algebraic Topology II: Homology and Cohomology; 4. Exterior Differential Calculus; 5. Differential Geometry of Surfaces; 6. Riemann Surface; 7. Harmonic Maps and Surface Ricci Flow; 8. Geometric Structure;

Part II: Algorithms
9. Topological Algorithms; 10. Algorithms for Harmonic Maps; 11. Harmonic Forms and Holomorphic Forms; 12. Discrete Ricci Flow;

Color Figures

All the color figures of the book can be downloaded here color figure. From the figures, you can see the major algorithms covered by the book and the major applications discuss in the book.

Sample Code and Surface Samples

Some of the sample codes and surface samples are availabel upon requests. The teaching materials are also available. Please forward your requests to the first author.