Mathematics: As an Infrastructure of Technology and Science

Chapter
Part of the Mathematics for Industry book series (MFI, volume 5)

Abstract

One of the roles of mathematics is to serve as a language to describe science and technology. The terminology is often common over several branches of science and technology. In this chapter, we describe several basic notions with the emphasis on what is the point of a definition and what are key properties. The objects are taken from set theory, groups and algebras.

Keywords

Group Lie algebra Exponential map Spherical linear interpolation Unit quaternion  

References

  1. 1.
    M. Alexa, D. Cohen-Or, D. Levin, As-rigid-as-possible shape interpolation, in Proceedings of ACM SIGGRAPH (2000), pp. 157–164Google Scholar
  2. 2.
    D.A. Cox, J. Little, D. O’Shea Ideals, Varieties, and Algorithms, An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd edn. (Springer, New York, 2007)Google Scholar
  3. 3.
    S. Kaji, S. Hirose, H. Ochiai, K. Anjyo, A Lie theoretic parameterization of affine transformation, in Mathematical Progress in Expressive Image Synthesis, MI Lecture Note, vol. 50, (Kyushu University, 2013), pp. 134–140Google Scholar
  4. 4.
    S. Kaji, S. Hirose, S. Sakata, Y. Mizoguchi, K. Anjyo, Mathematical analysis on affine maps for 2D shape interpolation. in Proceedings of SCA2012 (2012), pp. 71–76Google Scholar
  5. 5.
    M. Koecher, R. Remmert, Hamilton’s Quaternions, in Numbers, (Springer, New York, 1991)Google Scholar
  6. 6.
    G. Matsuda, S. Kaji, H. Ochiai, Anti-commutative dual complex numbers and 2D rigid transformation, in Mathematical Progress in Expressive Image Synthesis, MI Lecture Note, vol. 50, (Kyushu University, 2013), pp. 128–133Google Scholar
  7. 7.
    H. Ochiai, K. Anjyo, Mathematical Description of Motion and Deformation—From Basics to Graphics Applications—, SIGGRAPH Asia 2013 Course, http://portal.acm.org, (Revised course notes are also available at http://mcg.imi.kyushu-u.ac.jp/english/index.php ) (2013)
  8. 8.
    F. Reinhardt, H. Soeder, G. Falk, in dtv-Atlas zur Mathematik, Deutscher Taschenbuch (Springer, New York, 1978)Google Scholar
  9. 9.
    J. Vince, in Quaternions for Computer Graphics (Springer, New York, 2011)Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

Personalised recommendations