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.

This book presents revised versions of the best papers selected from the symposium Mathematical Progress in Expressive Image Synthesis (MEIS2013) held in Fukuoka, Japan, in 2013. The topics cover various areas of computer graphics (CG), such as surface deformation/editing, character animation, visual simulation of fluids, texture and sound synthesis and photorealistic rendering. From a mathematical point of view, the book also presents papers addressing discrete differential geometry, Lie theory, computational fluid dynamics, function interpolation and learning theory. This book showcases the latest joint efforts between mathematicians, CG researchers and practitioners exploring important issues in graphics and visual perception.The book provides a valuable resource for all computer graphics researchers seeking open problem areas, especially those now entering the field who have not yet selected a research direction."

The material included in this book provides selected presentations given at the international symposium MEIS2014. The book aims to provide a unique venue where various issues in computer graphics (CG) application fields are discussed by mathematicians as well as CG researchers and practitioners. The target audience is not limited to researchers in academia but also those in industries with a strong interest in digital media creation, scientific visualization and visual engineering.