Mathematical Basics of Motion and Deformation in Computer Graphics

Mathematical Basics of Motion and Deformation in Computer Graphics

Ken Anjyo, Hiroyuki Ochiai
ISBN: 9781627054447 | PDF ISBN: 9781627054454
Copyright © 2015 | 83 Pages | Publication Date: 10/01/2014

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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

About the Author(s)

Ken Anjyo, OLM Digital, Inc.
Ken Anjyo is an R&D supervisor at OLM Digital. He has been credited as R&D supervisor for recent Pokemon and several other movies. His research focuses on construction of mathematical and computationally tractable models. Dr. Anjyo's research includes recent SIGGRAPH and IEEE CG&A papers on art-directable specular highlights and shadows for anime, the Fourier method for editing motion capture, and direct manipulation blendshapes for facial animation. He is co-founder of the Digital Production Symposium (DigiPro) that started in 2012 and served as SIGGRAPH Asia 2015 Course co-chair, SIGGRAPH 2014 Computer Animation Festival jury, and co-chair of the 2014 Mathematical Progress in Expressive Image Synthesis symposium (MEIS2014). He is also a VES member since 2011.

Hiroyuki Ochiai, Kyushu University
Hiroyuki Ochiai is a Professor at Institute of Mathematics for Industry, Kyushu University, Japan. He received his Ph.D. in mathematics from the University of Tokyo in 1993. His research interests include representation theory of Lie groups and Lie algebras, algebraic analysis, and group theory. He has been joining the CREST project Mathematics for Computer Graphics led by Ken Anjyo since 2010.

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