Mathematical Basics Of Motion And Deformation In Computer Graphics Second Edition

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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 : 54,9 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.

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 : Springer Nature
Page : 118 pages
File Size : 45,6 Mb
Release : 2014-10-22
Category : Mathematics
ISBN : 9783031795619

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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. 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 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
Page : 95 pages
File Size : 52,5 Mb
Release : 2017-04-13
Category : Mathematics
ISBN : 1627056971

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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.

Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition

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

Author : Ken Anjyo,Hiroyuki Ochiai
Publisher : Springer Nature
Page : 79 pages
File Size : 42,6 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031025921

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Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition 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.

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 : 43,9 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.

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 : 55,5 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.

Virtual Material Acquisition and Representation for Computer Graphics

Dar'ya Guarnera,Giuseppe Claudio Guarnera
Virtual Material Acquisition and Representation for Computer Graphics Book PDF

Author : Dar'ya Guarnera,Giuseppe Claudio Guarnera
Publisher : Springer Nature
Page : 93 pages
File Size : 46,8 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031025952

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Virtual Material Acquisition and Representation for Computer Graphics by Dar'ya Guarnera,Giuseppe Claudio Guarnera Pdf

This book provides beginners in computer graphics and related fields a guide to the concepts, models, and technologies for realistic rendering of material appearance. It provides a complete and thorough overview of reflectance models and acquisition setups, along with providing a selection of the available tools to explore, visualize, and render the reflectance data. Reflectance models are under continuous development, since there is still no straightforward solution for general material representations. Every reflectance model is specific to a class of materials. Hence, each has strengths and weaknesses, which the book highlights in order to help the reader choose the most suitable model for any purpose. The overview of the acquisition setups will provide guidance to a reader who needs to acquire virtual materials and will help them to understand which measurement setup can be useful for a particular purpose, while taking into account the performance and the expected cost derived from the required components. The book also describes several recent open source software solutions, useful for visualizing and manipulating a wide variety of reflectance models and data.

3D Computer Graphics

Samuel R. Buss
3D Computer Graphics Book PDF

Author : Samuel R. Buss
Publisher : Cambridge University Press
Page : 397 pages
File Size : 53,9 Mb
Release : 2003-05-19
Category : Computers
ISBN : 9781139440387

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3D Computer Graphics by Samuel R. Buss Pdf

This textbook, first published in 2003, emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, Bézier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site.

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 : 41,6 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.

Fundamentals of Computer Graphics, Fourth Edition

Steve Marschner,Peter Shirley
Fundamentals of Computer Graphics Fourth Edition Book PDF

Author : Steve Marschner,Peter Shirley
Publisher : CRC Press
Page : 734 pages
File Size : 42,6 Mb
Release : 2016-04-08
Category : Computers
ISBN : 9781498785907

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Fundamentals of Computer Graphics, Fourth Edition by Steve Marschner,Peter Shirley Pdf

Drawing on an impressive roster of experts in the field, Fundamentals of Computer Graphics, Fourth Edition offers an ideal resource for computer course curricula as well as a user-friendly personal or professional reference. Focusing on geometric intuition, the book gives the necessary information for understanding how images get onto the screen by using the complementary approaches of ray tracing and rasterization. It covers topics common to an introductory course, such as sampling theory, texture mapping, spatial data structure, and splines. It also includes a number of contributed chapters from authors known for their expertise and clear way of explaining concepts. Highlights of the Fourth Edition Include: Updated coverage of existing topics Major updates and improvements to several chapters, including texture mapping, graphics hardware, signal processing, and data structures A text now printed entirely in four-color to enhance illustrative figures of concepts The fourth edition of Fundamentals of Computer Graphics continues to provide an outstanding and comprehensive introduction to basic computer graphic technology and theory. It retains an informal and intuitive style while improving precision, consistency, and completeness of material, allowing aspiring and experienced graphics programmers to better understand and apply foundational principles to the development of efficient code in creating film, game, or web designs.

An Introduction to Laplacian Spectral Distances and Kernels

Giuseppe Patanè
An Introduction to Laplacian Spectral Distances and Kernels Book PDF

Author : Giuseppe Patanè
Publisher : Springer Nature
Page : 120 pages
File Size : 52,5 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031025938

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An Introduction to Laplacian Spectral Distances and Kernels by Giuseppe Patanè Pdf

In geometry processing and shape analysis, several applications have been addressed through the properties of the Laplacian spectral kernels and distances, such as commute time, biharmonic, diffusion, and wave distances. Within this context, this book is intended to provide a common background on the definition and computation of the Laplacian spectral kernels and distances for geometry processing and shape analysis. To this end, we define a unified representation of the isotropic and anisotropic discrete Laplacian operator on surfaces and volumes; then, we introduce the associated differential equations, i.e., the harmonic equation, the Laplacian eigenproblem, and the heat equation. Filtering the Laplacian spectrum, we introduce the Laplacian spectral distances, which generalize the commute-time, biharmonic, diffusion, and wave distances, and their discretization in terms of the Laplacian spectrum. As main applications, we discuss the design of smooth functions and the Laplacian smoothing of noisy scalar functions. All the reviewed numerical schemes are discussed and compared in terms of robustness, approximation accuracy, and computational cost, thus supporting the reader in the selection of the most appropriate with respect to shape representation, computational resources, and target application.

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 : 47,5 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.

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 : 42,5 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.

Mathematics for Computer Graphics

John A. Vince
Mathematics for Computer Graphics Book PDF

Author : John A. Vince
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 43,7 Mb
Release : 2010-01-26
Category : Computers
ISBN : 9781849960236

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Mathematics for Computer Graphics by John A. Vince Pdf

John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics. Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed. All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry. Plus – and unusually in a student textbook – a chapter on geometric algebra is included.

Mathematics for Computer Graphics

John Vince
Mathematics for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Nature
Page : 573 pages
File Size : 41,6 Mb
Release : 2022-04-26
Category : Computers
ISBN : 9781447175209

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Mathematics for Computer Graphics by John Vince Pdf

John Vince explains a comprehensive range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, special effects, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded sixth edition. The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on determinants, vectors, matrix algebra, complex numbers, geometric transforms, quaternion algebra, quaternions in space, interpolation, curves and patches, analytical geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new subject of geometric algebra, followed by two chapters that introduce differential and integral calculus. Finally, there is a chapter on worked examples. Mathematics for Computer Graphics covers all of the key areas of the subject, including: • Number sets • Algebra • Trigonometry • Complex numbers • Coordinate systems • Determinants • Vectors • Quaternions • Matrix algebra • Geometric transforms • Interpolation • Curves and surfaces • Analytic geometry • Barycentric coordinates • Geometric algebra • Differential calculus • Integral calculus This sixth edition contains approximately 150 worked examples and over 330 colour illustrations, which are central to the author’s descriptive writing style. Mathematics for Computer Graphics provides a sound understanding of the mathematics required for computer graphics software and setting the scene for further reading of more advanced books and technical research papers