Mathematical Basics Of Motion And Deformation In Computer Graphics

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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 : 49,5 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.

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 : 43,6 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 : Morgan & Claypool
Page : 95 pages
File Size : 53,5 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 Progress in Expressive Image Synthesis III

Yoshinori Dobashi,Hiroyuki Ochiai
Mathematical Progress in Expressive Image Synthesis III Book PDF

Author : Yoshinori Dobashi,Hiroyuki Ochiai
Publisher : Springer
Page : 152 pages
File Size : 41,5 Mb
Release : 2016-05-21
Category : Technology & Engineering
ISBN : 9789811010767

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Mathematical Progress in Expressive Image Synthesis III by Yoshinori Dobashi,Hiroyuki Ochiai Pdf

“Progress in Expressive Image Synthesis” (MEIS2015), was held in Fukuoka, Japan, September 25–27, 2015. The aim of the symposium was to provide a unique venue where various issues in computer graphics (CG) application fields could be discussed by mathematicians, CG researchers, and practitioners. Through the previous symposiums MEIS2013 and MEIS2014, mathematicians as well as CG researchers have recognized that CG is a specific and practical activity derived from mathematical theories. Issues found in CG broaden the field of mathematics and vice versa, and CG visualizes mathematical theories in an aesthetic manner. In this volume, the editors aim to provoke interdisciplinary research projects through the peer-reviewed papers and poster presentations at the this year’s symposium. This book captures interactions among mathematicians, CG researchers, and practitioners sharing important, state-of-the-art issues in graphics and visual perception. The book is suitable for all CG researchers seeking open problem areas and especially for those entering the field who have not yet selected a research direction.

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 : 48,8 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.

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 : 48,6 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 : 55,5 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.

Deformation Models

Manuel González Hidalgo,Arnau Mir Torres,Javier Varona Gómez
Deformation Models Book PDF

Author : Manuel González Hidalgo,Arnau Mir Torres,Javier Varona Gómez
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 45,8 Mb
Release : 2012-10-29
Category : Computers
ISBN : 9789400754461

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Deformation Models by Manuel González Hidalgo,Arnau Mir Torres,Javier Varona Gómez Pdf

The computational modelling of deformations has been actively studied for the last thirty years. This is mainly due to its large range of applications that include computer animation, medical imaging, shape estimation, face deformation as well as other parts of the human body, and object tracking. In addition, these advances have been supported by the evolution of computer processing capabilities, enabling realism in a more sophisticated way. This book encompasses relevant works of expert researchers in the field of deformation models and their applications. The book is divided into two main parts. The first part presents recent object deformation techniques from the point of view of computer graphics and computer animation. The second part of this book presents six works that study deformations from a computer vision point of view with a common characteristic: deformations are applied in real world applications. The primary audience for this work are researchers from different multidisciplinary fields, such as those related with Computer Graphics, Computer Vision, Computer Imaging, Biomedicine, Bioengineering, Mathematics, Physics, Medical Imaging and Medicine.

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 : 40,7 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.

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 : 46,9 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

Mathematical and Computer Programming Techniques for Computer Graphics

Peter Comninos
Mathematical and Computer Programming Techniques for Computer Graphics Book PDF

Author : Peter Comninos
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 53,7 Mb
Release : 2010-04-06
Category : Computers
ISBN : 9781846282928

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Mathematical and Computer Programming Techniques for Computer Graphics by Peter Comninos Pdf

Provides a comprehensive and detailed coverage of the fundamentals of programming techniques for computer graphics Uses lots of code examples, encouraging the reader to explore and experiment with data and computer programs (in the C programming language)

Fundamentals of Computer Graphics

Peter Shirley,Michael Ashikhmin,Steve Marschner
Fundamentals of Computer Graphics Book PDF

Author : Peter Shirley,Michael Ashikhmin,Steve Marschner
Publisher : CRC Press
Page : 784 pages
File Size : 42,6 Mb
Release : 2009-07-21
Category : Computers
ISBN : 9781439865521

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Fundamentals of Computer Graphics by Peter Shirley,Michael Ashikhmin,Steve Marschner Pdf

With contributions by Michael Ashikhmin, Michael Gleicher, Naty Hoffman, Garrett Johnson, Tamara Munzner, Erik Reinhard, Kelvin Sung, William B. Thompson, Peter Willemsen, Brian Wyvill. The third edition of this widely adopted text gives students a comprehensive, fundamental introduction to computer graphics. The authors present the mathematical fo

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 : 42,8 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.

Introduction to the Mathematics of Computer Graphics

Nathan Carter
Introduction to the Mathematics of Computer Graphics Book PDF

Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 55,8 Mb
Release : 2016-12-31
Category : Mathematics
ISBN : 9781614441229

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Introduction to the Mathematics of Computer Graphics by Nathan Carter Pdf

This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.

Sound Synthesis, Propagation, and Rendering

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

Author : Shiguang Liu,Dinesh Manocha
Publisher : Morgan & Claypool Publishers
Page : 110 pages
File Size : 47,5 Mb
Release : 2022-03-24
Category : Computers
ISBN : 9781636393216

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