Conformal Geometry: Computational Algorithms and Engineering Applications

ISBN-13: 9783030092023 / Angielski / Miękka / 2019 / 330 str.

Miao Jin; Xianfeng Gu; Ying He

Recenzje

"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 detailed chapters that give the reader tools to apply the sophisticated geometry of conformal mappings. The abundant diagrams are helpful, and the level of rigor supports the topics well. This book is a valuable addition to a mathematics or computer science library serving graduate students and professionals." (J. McCleary, Choice, Vol. 56 (5), January, 2019)

Spis treści

Introduction.- Topological Algorithms.- Harmonic Map.- Harmonic and Holomorphic Forms.- Discrete Ricci Flow.- Computer Graphics.- Computer Vision.- Geometric Modeling.- Medical Imaging.- Wireless Sensor Networks.

O autorze

Miao Jin received her PhD from the State University of New York at Stony Brook in 2008. She is the recipient of a National Science Foundation Career Award (2011-2016) for her work in computational conformal and quasi-conformal geometry, and is currently an Associate Professor at the University of Louisiana at Lafayette. Her research interests include computational geometry and topology, and especially computational conformal geometry, computational hyperbolic geometry, and computational quasi-conformal geometry - with applications to computer graphics, wireless sensor networks, geometric modelling, and computer vision.

David Xianfeng Gu received his PhD from Harvard University in 2003. He is currently an Associate Professor at the State University of New York at Stony Brook and was an Assistant Professor at the University of Florida (2003-2004). His research interests include differential geometry, algebraic topology, Riemann surface theory and especially computational conformal geometry - with applications to computer graphics, computer vision, medical imaging, and scientific computing. He is the recipient of a National Science Foundation Career Award (2004-2009), Morningside Gold Medal in Applied Mathematics (2013) for his work in computational conformal geometry.

Blurb

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 solve them in a theoretically elegant and computationally efficient way. The fields covered include computer graphics, computer vision, geometric modeling, medical imaging, and wireless sensor networks. Each chapter concludes with a summary of the material covered and suggestions for further reading, and numerous illustrations and computational algorithms complement the text.

 The book draws on courses given by the authors at the University of Louisiana at Lafayette, the State University of New York at Stony Brook, and Tsinghua University, and will be of interest to senior undergraduates, graduates and researchers in computer science, applied mathematics, and engineering.