Foundations Of Geometric Algebra Computing

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Xinyuan Wu, Xiong You, Bin Wang

Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations.The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.

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Xiang Sean Zhou, Yong Rui, Thomas S. Huang

Exploration of Visual Data presents latest research efforts in the area of content-based exploration of image and video data. The main objective is to bridge the semantic gap between high-level concepts in the human mind and low-level features extractable by the machines. The two key issues emphasized are "content-awareness" and "user-in-the-loop". The authors provide a comprehensive review on algorithms for visual feature extraction based on color, texture, shape, and structure, and techniques for incorporating such information to aid browsing, exploration, search, and streaming of image and video data. They also discuss issues related to the mixed use of textual and low-level visual features to facilitate more effective access of multimedia data. Exploration of Visual Data provides state-of-the-art materials on the topics of content-based description of visual data, content-based low-bitrate video streaming, and latest asymmetric and nonlinear relevance feedback algorithms, which to date are unpublished.

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Alexandre Ern, Jean-Luc Guermond

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

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Nadia Magnenat-Thalmann, Daniel Thalmann

With the increasing success of Networked Virtual Environments, Games and Web 3D, there is a need for new techniques to permit the creation and animation of Virtual Humans. Users may be represented by realistic avatars that they can control, but also autonomous Virtual Humans agents can now inhabit these Virtual Worlds. Virtual Humans with their soft tissues, skin, muscles, organs and clothes are completely deformable. There are many methods to enable the representation and deformation of these structures. These methods may be geometric or physics-based. Presenting a selection of the latest research work addressing various aspects related to deformable avatars, this book covers complementary topics such as body modelling and animation, face modelling and animation, physics-based and free-form deformations, motion capture, avatars technologies and agents. This volume is comprised of the combined proceedings of the DEFORM'2000 and AVATARS'2000 workshops, which were sponsored by the International Federation for Information Processing (IFIP) and organized by IFIP Working Group 5.10. The workshops were held in Geneva and Lausanne, Switzerland in November/December 2000.