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

1. Front Matter

   Pages i-xvi

   PDF

2. Introduction

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 1-3

3. Rigid Transformation

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 5-21

4. Affine Transformation

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 23-28

5. Exponential and Logarithm of Matrices

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 29-40

6. 2D Affine Transformation between Two Triangles

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 41-44

7. Global 2D Shape Interpolation

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 45-52

8. Parametrizing 3D Positive Affine Transformations

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 53-61

9. Further Readings

   • Ken Anjyo, Hiroyuki Ochiai

   Pages 63-65

10. Back Matter

    Pages 67-79

    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.

• OLM Digital, Inc., Japan

  Ken Anjyo

• Kyushu University, Japan

  Hiroyuki Ochiai

Ken Anjyo is the R&D supervisor at OLM Digital. He has been credited as R&D supervisor for the recent Pokemon and several other movies. His research focuses on construction of mathematical and computationally tractable models. Dr. Anjyos 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 and 2015 Computer Animation Festival juror, and co-founder of the Mathematical Progress in Expressive Image Synthesis symposium (MEIS). He is appointed as the SIGGRAPH Asia 2018 conference chair. He is also a VES member since 2011.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. He was a lecturer of courses at SIGGRAPH Asia 2013, SIGGRAPH2014 and 2016.