Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition [electronic resource] /
by Ken Anjyo, Hiroyuki Ochiai.
- 2nd ed. 2017.
- XVI, 79 p. online resource.
- Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging, 2469-4223 .
- Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging, .
Preface -- Preface to the Second Edition -- 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.
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.