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Finite Element Method Simulation of 3D Deformable Solids
This book serves as a practical guide to simulation of 3D deformable solids using the Finite Element Method (FEM). It reviews a number of topics related to the theory and implementation of FEM approaches: measures of deformation, constitutive laws of nonlinear materials, tetrahedral discretizations, and model reduction techniques for real-time simulation. Simulations of deformable solids are important in many applications in computer graphics, including film special effects, computer games, and virtual surgery. The Finite Element Method has become a popular tool in many such applications. Variants of FEM catering to both offline and real-time simulation have had a mature presence in computer...
Rethinking Quaternions
Quaternion multiplication can be used to rotate vectors in three-dimensions. Therefore, in computer graphics, quaternions have three principal applications: to increase speed and reduce storage for calculations involving rotations, to avoid distortions arising from numerical inaccuracies caused by floating point computations with rotations, and to interpolate between two rotations for key frame animation. Yet while the formal algebra of quaternions is well-known in the graphics community, the derivations of the formulas for this algebra and the geometric principles underlying this algebra are not well understood. The goals of this monograph are to provide a fresh, geometric interpretation fo...
Sound Synthesis, Propagation, and Rendering
This book gives a broad overview of research on sound simulation driven by a variety of applications. Vibrating objects produce sound, which then propagates through a medium such as air or water before finally being heard by a listener. As a crucial sensory channel, sound plays a vital role in many applications. There is a well-established research community in acoustics that has studied the problems related to sound simulation for six decades. Some of the earliest work was motivated by the design of concert halls, theaters, or lecture rooms with good acoustic characteristics. These problems also have been investigated in other applications, including noise control and sound design for urban...
An Introduction to Verification of Visualization Techniques
As we increase our reliance on computer-generated information, often using it as part of our decision-making process, we must devise tools to assess the correctness of that information. Consider, for example, software embedded on vehicles, used for simulating aircraft performance, or used in medical imaging. In those cases, software correctness is of paramount importance as there's little room for error. Software verification is one of the tools available to attain such goals. Verification is a well known and widely studied subfield of computer science and computational science and the goal is to help us increase confidence in the software implementation by verifying that the software does w...
Algorithmic Foundations of Robotics XIV
This proceedings book helps bring insights from this array of technical sub-topics together, as advanced robot algorithms draw on the combined expertise of many fields—including control theory, computational geometry and topology, geometrical and physical modeling, reasoning under uncertainty, probabilistic algorithms, game theory, and theoretical computer science. Intelligent robots and autonomous systems depend on algorithms that efficiently realize functionalities ranging from perception to decision making, from motion planning to control. The works collected in this SPAR book represent the state of the art in algorithmic robotics. They originate from papers accepted to the 14th Interna...
Virtual Crowds
There are many applications of computer animation and simulation where it is necessary to model virtual crowds of autonomous agents. Some of these applications include site planning, education, entertainment, training, and human factors analysis for building evacuation. Other applications include simulations of scenarios where masses of people gather, flow, and disperse, such as transportation centers, sporting events, and concerts. Most crowd simulations include only basic locomotive behaviors possibly coupled with a few stochastic actions. Our goal in this survey is to establish a baseline of techniques and requirements for simulating large-scale virtual human populations. Sometimes, these...
Gazing at Games
Eye tracking is a process that identifies a specific point in both space and time that is being looked at by the observer. This information can also be used in real-time to control applications using the eyes. Recent innovations in the video game industry include alternative input modalities to provide an enhanced, more immersive user experience. In particular, eye gaze control has recently been explored as an input modality in video games. This book is an introduction for those interested in using eye tracking to control or analyze video games and virtual environments. Key concepts are illustrated through three case studies in which gaze control and voice recognition have been used in combi...
Mathematical Basics of Motion and Deformation in Computer Graphics
This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation. Table of Contents: Preface / Symbols and Notations / Introduction / Rigid Transformation / Affine Transformation / Exponential and Logarithm of Matrices / 2D Affine Transformation between Two Triangles / Global 2D Shape Interpolation / Parametrizing 3D Positive Affine Transformations / Further Readings / Bibliography / Authors' Biographies
Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration
The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate w...
Stochastic Partial Differential Equations for Computer Vision with Uncertain Data
In image processing and computer vision applications such as medical or scientific image data analysis, as well as in industrial scenarios, images are used as input measurement data. It is good scientific practice that proper measurements must be equipped with error and uncertainty estimates. For many applications, not only the measured values but also their errors and uncertainties, should be—and more and more frequently are—taken into account for further processing. This error and uncertainty propagation must be done for every processing step such that the final result comes with a reliable precision estimate. The goal of this book is to introduce the reader to the recent advances from...
