New from International Press, July 2008

Advanced Lectures in Mathematics, Vol. 3

Computational Conformal Geometry

Edited by
Xianfeng David Gu (SUNY Stony Brook)
Shing-Tung Yau (Harvard University)

This new volume presents thorough introductions to the theoretical foundations—as well as to the practical algorithms—of computational conformal geometry. These have direct applications to engineering and digital geometric processing, including surface parameterization, surface matching, brain mapping, 3-D face recognition and identification, facial expression and animation, dynamic face tracking, mesh-spline conversion, and more.

Publication Details

Hardcover. 295 pages. DVD included.
ISBN-13: 978-1-57146-171-1
ISBN-10: 1-57146-171-X
2000 MSC: 68U05
Published: July 2008
Publisher: International Press of Boston
List price: $89.00.

Full Description

Computational conformal geometry is an emerging inter-disciplinary field, with applications to algebraic topology, differential geometry and Riemann surface theories applied to geometric modeling, computer graphics, computer vision, medical imaging, visualization, scientific computation, and many other engineering fields.

This new volume presents thorough introductions to the theoretical foundations—as well as to the practical algorithms—of computational conformal geometry. These have direct applications to engineering and digital geometric processing, including surface parameterization, surface matching, brain mapping, 3-D face recognition and identification, facial expression and animation, dynamic face tracking, mesh-spline conversion, and more.

Table of Contents

• Introduction
  • Overview of Theories
  • Algorithms for Computing Conformal Mappings
  • Applications
  • Further Readings
• Part I: Theories
  • Homotopy Group
  • Homology and Cohomology
  • Exterior Differential Calculus
  • Differential Geometry of Surfaces
  • Riemann Surface
  • Harmonic Maps and Surface Ricci Flow
  • Geometric Structure
• Part II: Algorithms
  • Topological Algorithms
  • Algorithms for Harmonic Maps
  • Harmonic Forms and Holomorphic Forms
  • Discrete Ricci Flow
• Appendix A: Major Algorithms
• Appendix B: Acknowledgement
• Reference
• Index

About the Series

Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cutting-edge results.

Other volumes in the Advanced Lectures in Mathematics series

Vol. 7. Handbook of Geometric Analysis, No. 1

Vol. 6. Geometry, Analysis and Topology of Discrete Groups

Vol. 5. Fourth International Congress of Chinese Mathematicians (2007)

Vol. 4. Variational Principles for Discrete Surfaces

Vol. 2. Asymptotic Theory in Probability and Statistics with Applications

Vol. 1. Superstring Theory

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