Numerical Methods For Linear Complementarity Problems In Physics Based Animation

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Numerical Methods for Linear Complementarity Problems in Physics-Based Animation

Sarah Niebe,Kenny Erleben
Numerical Methods for Linear Complementarity Problems in Physics Based Animation Book PDF

Author : Sarah Niebe,Kenny Erleben
Publisher : Springer Nature
Page : 151 pages
File Size : 55,9 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031795640

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Numerical Methods for Linear Complementarity Problems in Physics-Based Animation by Sarah Niebe,Kenny Erleben Pdf

Linear complementarity problems (LCPs) have for many years been used in physics-based animation to model contact forces between rigid bodies in contact. More recently, LCPs have found their way into the realm of fluid dynamics. Here, LCPs are used to model boundary conditions with fluid-wall contacts. LCPs have also started to appear in deformable models and granular simulations. There is an increasing need for numerical methods to solve the resulting LCPs with all these new applications. This book provides a numerical foundation for such methods, especially suited for use in computer graphics. This book is mainly intended for a researcher/Ph.D. student/post-doc/professor who wants to study the algorithms and do more work/research in this area. Programmers might have to invest some time brushing up on math skills, for this we refer to Appendices A and B. The reader should be familiar with linear algebra and differential calculus. We provide pseudo code for all the numerical methods, which should be comprehensible by any computer scientist with rudimentary programming skills. The reader can find an online supplementary code repository, containing Matlab implementations of many of the core methods covered in these notes, as well as a few Python implementations [Erleben, 2011]. Table of Contents: Introduction / Numerical Methods / Guide for Software and Selecting Methods / Bibliography / Authors' Biographies

Finite Element Method Simulation of 3D Deformable Solids

Eftychios Sifakis,Jernej Barbič
Finite Element Method Simulation of 3D Deformable Solids Book PDF

Author : Eftychios Sifakis,Jernej Barbič
Publisher : Springer Nature
Page : 57 pages
File Size : 47,5 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025853

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Finite Element Method Simulation of 3D Deformable Solids by Eftychios Sifakis,Jernej Barbič Pdf

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 graphics literature. This book is designed for readers familiar with numerical simulation in computer graphics, who would like to obtain a cohesive picture of the various FEM simulation methods available, their strengths and weaknesses, and their applicability in various simulation scenarios. The book is also a practical implementation guide for the visual effects developer, offering a lean yet adequate synopsis of the underlying mathematical theory. Chapter 1 introduces the quantitative descriptions used to capture the deformation of elastic solids, the concept of strain energy, and discusses how force and stress result as a response to deformation. Chapter 2 reviews a number of constitutive models, i.e., analytical laws linking deformation to the resulting force that has successfully been used in various graphics-oriented simulation tasks. Chapter 3 summarizes how deformation and force can be computed discretely on a tetrahedral mesh, and how an implicit integrator can be structured around this discretization. Finally, chapter 4 presents the state of the art in model reduction techniques for real-time FEM solid simulation and discusses which techniques are suitable for which applications. Topics discussed in this chapter include linear modal analysis, modal warping, subspace simulation, and domain decomposition.

An Introduction to Verification of Visualization Techniques

Tiago Etiene,Robert M. Kirby,Cláudio T. Silva
An Introduction to Verification of Visualization Techniques Book PDF

Author : Tiago Etiene,Robert M. Kirby,Cláudio T. Silva
Publisher : Springer Nature
Page : 80 pages
File Size : 46,6 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025877

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An Introduction to Verification of Visualization Techniques by Tiago Etiene,Robert M. Kirby,Cláudio T. Silva Pdf

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 what it is supposed to do. The goal of this book is to introduce the reader to software verification in the context of visualization. In the same way we became more dependent on commercial software, we have also increased our reliance on visualization software. The reason is simple: visualization is the lens through which users can understand complex data, and as such it must be verified. The explosion in our ability to amass data requires tools not only to store and analyze data, but also to visualize it. This book is comprised of six chapters. After an introduction to the goals of the book, we present a brief description of both worlds of visualization (Chapter 2) and verification (Chapter 3). We then proceed to illustrate the main steps of the verification pipeline for visualization algorithms. We focus on two classic volume visualization techniques, namely, Isosurface Extraction (Chapter 4) and Direct Volume Rendering (Chapter 5). We explain how to verify implementations of those techniques and report the latest results in the field of verification of visualization techniques. The last chapter concludes the book and highlights new research topics for the future.

Geometric and Discrete Path Planning for Interactive Virtual Worlds

Marcelo Kallmann,Mubbasir Kapadia
Geometric and Discrete Path Planning for Interactive Virtual Worlds Book PDF

Author : Marcelo Kallmann,Mubbasir Kapadia
Publisher : Springer Nature
Page : 181 pages
File Size : 50,5 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031025884

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Geometric and Discrete Path Planning for Interactive Virtual Worlds by Marcelo Kallmann,Mubbasir Kapadia Pdf

Path planning and navigation are indispensable components for controlling autonomous agents in interactive virtual worlds. Given the growing demands on the size and complexity of modern virtual worlds, a number of new techniques have been developed for achieving intelligent navigation for the next generation of interactive multi-agent simulations. This book reviews the evolution of several related techniques, starting from classical planning and computational geometry techniques and then gradually moving toward more advanced topics with focus on recent developments from the work of the authors. The covered topics range from discrete search and geometric representations to planning under different types of constraints and harnessing the power of graphics hardware in order to address Euclidean shortest paths and discrete search for multiple agents under limited time budgets. The use of planning algorithms beyond path planning is also discussed in the areas of crowd animation and whole-body motion planning for virtual characters.

Virtual Crowds

Mubbasir Kapadia,Nuria Pelechano,Jan Allbeck,Norm Badler
Virtual Crowds Book PDF

Author : Mubbasir Kapadia,Nuria Pelechano,Jan Allbeck,Norm Badler
Publisher : Springer Nature
Page : 248 pages
File Size : 52,7 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031025860

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Virtual Crowds by Mubbasir Kapadia,Nuria Pelechano,Jan Allbeck,Norm Badler Pdf

This volume presents novel computational models for representing digital humans and their interactions with other virtual characters and meaningful environments. In this context, we describe efficient algorithms to animate, control, and author human-like agents having their own set of unique capabilities, personalities, and desires. We begin with the lowest level of footstep determination to steer agents in collision-free paths. Steering choices are controlled by navigation in complex environments, including multi-domain planning with dynamically changing situations. Virtual agents are given perceptual capabilities analogous to those of real people, including sound perception, multi-sense attention, and understanding of environment semantics which affect their behavior choices. The roles and impacts of individual attributes, such as memory and personality are explored. The animation challenges of integrating a number of simultaneous behavior and movement demands on an agent are addressed through an open source software system. Finally, the creation of stories and narratives with groups of agents subject to planning and environmental constraints culminates the presentation.

Efficient Quadrature Rules for Illumination Integrals

Ricardo Marques,Christian Bouville,Luís Paulo Santos,Kadi Bouatouch
Efficient Quadrature Rules for Illumination Integrals Book PDF

Author : Ricardo Marques,Christian Bouville,Luís Paulo Santos,Kadi Bouatouch
Publisher : Springer Nature
Page : 82 pages
File Size : 40,7 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031795671

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Efficient Quadrature Rules for Illumination Integrals by Ricardo Marques,Christian Bouville,Luís Paulo Santos,Kadi Bouatouch Pdf

Rendering photorealistic images is a costly process which can take up to several days in the case of high quality images. In most cases, the task of sampling the incident radiance function to evaluate the illumination integral is responsible for an important share of the computation time. Therefore, to reach acceptable rendering times, the illumination integral must be evaluated using a limited set of samples. Such a restriction raises the question of how to obtain the most accurate approximation possible with such a limited set of samples. One must thus ensure that sampling produces the highest amount of information possible by carefully placing and weighting the limited set of samples. Furthermore, the integral evaluation should take into account not only the information brought by sampling but also possible information available prior to sampling, such as the integrand smoothness. This idea of sparse information and the need to fully exploit the little information available is present throughout this book. The presented methods correspond to the state-of-the-art solutions in computer graphics, and take into account information which had so far been underexploited (or even neglected) by the previous approaches. The intended audiences are Ph.D. students and researchers in the field of realistic image synthesis or global illumination algorithms, or any person with a solid background in graphics and numerical techniques.

Geometric Continuity of Curves and Surfaces

Przemysław Kiciak
Geometric Continuity of Curves and Surfaces Book PDF

Author : Przemysław Kiciak
Publisher : Springer Nature
Page : 233 pages
File Size : 44,8 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031025907

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Geometric Continuity of Curves and Surfaces by Przemysław Kiciak Pdf

This book is written for students, CAD system users and software developers who are interested in geometric continuity—a notion needed in everyday practice of Computer-Aided Design and also a hot subject of research. It contains a description of the classical geometric spline curves and a solid theoretical basis for various constructions of smooth surfaces. Textbooks on computer graphics usually cover the most basic and necessary information about spline curves and surfaces in order to explain simple algorithms. In textbooks on geometric design, one can find more details, more algorithms and more theory. This book teaches how various parts of the theory can be gathered together and turned into constructions of smooth curves and smooth surfaces of arbitrary topology. The mathematical background needed to understand this book is similar to what is necessary to read other textbooks on geometric design; most of it is basic linear algebra and analysis. More advanced mathematical material is introduced using elementary explanations. Reading Geometric Continuity of Curves and Surfaces provides an excellent opportunity to recall and exercise necessary mathematical notions and it may be your next step towards better practice and higher understanding of design principles.

Digital Heritage Reconstruction Using Super-resolution and Inpainting

Milind G. Padalkar,Manjunath V. Joshi
Digital Heritage Reconstruction Using Super resolution and Inpainting Book PDF

Author : Milind G. Padalkar,Manjunath V. Joshi
Publisher : Springer Nature
Page : 150 pages
File Size : 48,9 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025914

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Digital Heritage Reconstruction Using Super-resolution and Inpainting by Milind G. Padalkar,Manjunath V. Joshi Pdf

Heritage sites across the world have witnessed a number of natural calamities, sabotage and damage from visitors, resulting in their present ruined condition. Many sites are now restricted to reduce the risk of further damage. Yet these masterpieces are significant cultural icons and critical markers of past civilizations that future generations need to see. A digitally reconstructed heritage site could diminish further harm by using immersive navigation or walkthrough systems for virtual environments. An exciting key element for the viewer is observing fine details of the historic work and viewing monuments in their undamaged form. This book presents image super-resolution methods and techniques for automatically detecting and inpainting damaged regions in heritage monuments, in order to provide an enhanced visual experience. The book presents techniques to obtain higher resolution photographs of the digitally reconstructed monuments, and the resulting images can serve as input to immersive walkthrough systems. It begins with the discussion of two novel techniques for image super-resolution and an approach for inpainting a user-supplied region in the given image, followed by a technique to simultaneously perform super-resolution and inpainting of given missing regions. It then introduces a method for automatically detecting and repairing the damage to dominant facial regions in statues, followed by a few approaches for automatic crack repair in images of heritage scenes. This book is a giant step toward ensuring that the iconic sites of our past are always available, and will never be truly lost.

Design, Representations, and Processing for Additive Manufacturing

Marco Attene,Marco Livesu,Sylvain Lefebvre
Design Representations and Processing for Additive Manufacturing Book PDF

Author : Marco Attene,Marco Livesu,Sylvain Lefebvre
Publisher : Springer Nature
Page : 136 pages
File Size : 52,6 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025969

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Design, Representations, and Processing for Additive Manufacturing by Marco Attene,Marco Livesu,Sylvain Lefebvre Pdf

The wide diffusion of 3D printing technologies continuously calls for effective solutions for designing and fabricating objects of increasing complexity. The so called "computational fabrication" pipeline comprises all the steps necessary to turn a design idea into a physical object, and this book describes the most recent advancements in the two fundamental phases along this pipeline: design and process planning. We examine recent systems in the computer graphics community that allow us to take a design idea from conception to a digital model, and classify algorithms that are necessary to turn such a digital model into an appropriate sequence of machining instructions.

Heterogeneous Spatial Data

Giuseppe Patanè,Michela Spagnuolo
Heterogeneous Spatial Data Book PDF

Author : Giuseppe Patanè,Michela Spagnuolo
Publisher : Springer Nature
Page : 129 pages
File Size : 53,9 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031025891

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Heterogeneous Spatial Data by Giuseppe Patanè,Michela Spagnuolo Pdf

New data acquisition techniques are emerging and are providing fast and efficient means for multidimensional spatial data collection. Airborne LIDAR surveys, SAR satellites, stereo-photogrammetry and mobile mapping systems are increasingly used for the digital reconstruction of the environment. All these systems provide extremely high volumes of raw data, often enriched with other sensor data (e.g., beam intensity). Improving methods to process and visually analyze this massive amount of geospatial and user-generated data is crucial to increase the efficiency of organizations and to better manage societal challenges. Within this context, this book proposes an up-to-date view of computational methods and tools for spatio-temporal data fusion, multivariate surface generation, and feature extraction, along with their main applications for surface approximation and rainfall analysis. The book is intended to attract interest from different fields, such as computer vision, computer graphics, geomatics, and remote sensing, working on the common goal of processing 3D data. To this end, it presents and compares methods that process and analyze the massive amount of geospatial data in order to support better management of societal challenges through more timely and better decision making, independent of a specific data modeling paradigm (e.g., 2D vector data, regular grids or 3D point clouds). We also show how current research is developing from the traditional layered approach, adopted by most GIS softwares, to intelligent methods for integrating existing data sets that might contain important information on a geographical area and environmental phenomenon. These services combine traditional map-oriented visualization with fully 3D visual decision support methods and exploit semantics-oriented information (e.g., a-priori knowledge, annotations, segmentations) when processing, merging, and integrating big pre-existing data sets.

GPU Ray Tracing in Non-Euclidean Spaces

Tiago Novello,Vinícius da Silva,Luiz Velho
GPU Ray Tracing in Non Euclidean Spaces Book PDF

Author : Tiago Novello,Vinícius da Silva,Luiz Velho
Publisher : Morgan & Claypool Publishers
Page : 129 pages
File Size : 41,6 Mb
Release : 2022-03-21
Category : Computers
ISBN : 9781636393278

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GPU Ray Tracing in Non-Euclidean Spaces by Tiago Novello,Vinícius da Silva,Luiz Velho Pdf

This book explores the visualization of three-dimensional non-Euclidean spaces using raytracing techniques in Graphics Processing Unit (GPU). This is a trending topic in mathematical visualization that combines the mathematics areas of geometry and topology, with visualization concepts of computer graphics. Several conditions made this a special moment for such topic. On one hand, the development of mathematical research, computer graphics, and algorithms have provided the necessary theoretical framework. On the other hand, the evolution of the technologies and media allows us to be immersed in three-dimensional spaces using Virtual Reality. The content of this book serves both experts in the areas and students. Although this is a short book, it is self-contained since it considers all the ideas, motivations, references, and intuitive explanations of the required fundamental concepts.

Stochastic Partial Differential Equations for Computer Vision with Uncertain Data

Tobias Preusser,Robert M. Kirby,Torben Pätz
Stochastic Partial Differential Equations for Computer Vision with Uncertain Data Book PDF

Author : Tobias Preusser,Robert M. Kirby,Torben Pätz
Publisher : Springer Nature
Page : 150 pages
File Size : 48,7 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025945

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Stochastic Partial Differential Equations for Computer Vision with Uncertain Data by Tobias Preusser,Robert M. Kirby,Torben Pätz Pdf

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 the field of uncertainty quantification and error propagation for computer vision, image processing, and image analysis that are based on partial differential equations (PDEs). It presents a concept with which error propagation and sensitivity analysis can be formulated with a set of basic operations. The approach discussed in this book has the potential for application in all areas of quantitative computer vision, image processing, and image analysis. In particular, it might help medical imaging finally become a scientific discipline that is characterized by the classical paradigms of observation, measurement, and error awareness. This book is comprised of eight chapters. After an introduction to the goals of the book (Chapter 1), we present a brief review of PDEs and their numerical treatment (Chapter 2), PDE-based image processing (Chapter 3), and the numerics of stochastic PDEs (Chapter 4). We then proceed to define the concept of stochastic images (Chapter 5), describe how to accomplish image processing and computer vision with stochastic images (Chapter 6), and demonstrate the use of these principles for accomplishing sensitivity analysis (Chapter 7). Chapter 8 concludes the book and highlights new research topics for the future.

Mathematical Basics of Motion and Deformation in Computer Graphics

Ken Anjyo,Hiroyuki Ochiai
Mathematical Basics of Motion and Deformation in Computer Graphics Book PDF

Author : Ken Anjyo,Hiroyuki Ochiai
Publisher : Morgan & Claypool Publishers
Page : 97 pages
File Size : 49,7 Mb
Release : 2017-04-13
Category : Computers
ISBN : 9781627059848

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Mathematical Basics of Motion and Deformation in Computer Graphics by Ken Anjyo,Hiroyuki Ochiai Pdf

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.

Sound Synthesis, Propagation, and Rendering

Liu Shiguang,Manocha Dinesh
Sound Synthesis Propagation and Rendering Book PDF

Author : Liu Shiguang,Manocha Dinesh
Publisher : Springer Nature
Page : 96 pages
File Size : 44,5 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031792144

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Sound Synthesis, Propagation, and Rendering by Liu Shiguang,Manocha Dinesh Pdf

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 planning, building construction, and automotive applications. Moreover, plausible or realistic sound effects can improve the sense of presence in a virtual environment or a game. In these applications, sound can provide important clues such as source directionality and spatial size. The book first surveys various sound synthesis methods, including harmonic synthesis, texture synthesis, spectral analysis, and physics-based synthesis. Next, it provides an overview of sound propagation techniques, including wave-based methods, geometric-based methods, and hybrid methods. The book also summarizes various techniques for sound rendering. Finally, it surveys some recent trends, including the use of machine learning methods to accelerate sound simulation and the use of sound simulation techniques for other applications such as speech recognition, source localization, and computer-aided design.

Cloth Simulation for Computer Graphics

Tuur Stuyck
Cloth Simulation for Computer Graphics Book PDF

Author : Tuur Stuyck
Publisher : Springer Nature
Page : 110 pages
File Size : 53,6 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025976

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Cloth Simulation for Computer Graphics by Tuur Stuyck Pdf

Physics-based animation is commonplace in animated feature films and even special effects for live-action movies. Think about a recent movie and there will be some sort of special effects such as explosions or virtual worlds. Cloth simulation is no different and is ubiquitous because most virtual characters (hopefully!) wear some sort of clothing. The focus of this book is physics-based cloth simulation. We start by providing background information and discuss a range of applications. This book provides explanations of multiple cloth simulation techniques. More specifically, we start with the most simple explicitly integrated mass-spring model and gradually work our way up to more complex and commonly used implicitly integrated continuum techniques in state-of-the-art implementations. We give an intuitive explanation of the techniques and give additional information on how to efficiently implement them on a computer. This book discusses explicit and implicit integration schemes for cloth simulation modeled with mass-spring systems. In addition to this simple model, we explain the more advanced continuum-inspired cloth model introduced in the seminal work of Baraff and Witkin [1998]. This method is commonly used in industry. We also explain recent work by Liu et al. [2013] that provides a technique to obtain fast simulations. In addition to these simulation approaches, we discuss how cloth simulations can be art directed for stylized animations based on the work of Wojan et al. [2016]. Controllability is an essential component of a feature animation film production pipeline. We conclude by pointing the reader to more advanced techniques.