Mathematical Description of Motion and Deformation: From Basics to Graphics Applications

    Tuesday, 19 November

    09:00 - 12:45

    Room S222

    While many technical terms, such as Euler angle, quaternion, and affine transformation, now become quite popular in computer graphics, their graphical meanings are sometimes a bit far from the original mathematical entities, which might cause misunderstanding or misuse of the mathematical techniques. This course presents an intuitive introduction to several mathematical concepts that are quite useful for describing motion and deformation of geometric objects.

    The concepts are inherited mostly from differential geometry and Lie theory, and now commonly used in various aspects of computer graphics, including curve/surface editing, deformation and animation of geometric objects. The objective of this course is to fill the gap between the original mathematical concepts and the practical meanings in computer graphics without assuming any prior knowledge of pure mathematics. We then illustrate practical usefulness of deep understanding of the mathematical concepts. Moreover this course demonstrates our current/ongoing research work, which is benefited from our mathematical formulation.



    Intended Audience

    This course will serve as a good introduction to mathematics (differential geometry and Lie theory) for the beginners who work for geometric modeling and animation. For the experienced developers and researchers will find the course a comprehensive overview of the geometric methods.


    Elementary geometry, linear algebra, and calculus.


    Hiroyuki Ochiai, Kyushu University
    Ken Anjyo, OLM Digital, Inc.

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

    Ken Anjyo; R&D supervisor of OLM Digital; research interest focuses on construction of the mathematical and computationally tractable models, several of which were presented with his SIGGRAPH/ IEEE CG&A papers. He is also a VES member.