### Abstract

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.

Original language | English |
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Pages (from-to) | 1-85 |

Number of pages | 85 |

Journal | Synthesis Lectures on Computer Graphics and Animation |

Volume | 6 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Computer Graphics and Computer-Aided Design

### Cite this

**Mathematical basics of motion and deformation in computer graphics.** / Anjyo, Ken; Ochiai, Hiroyuki.

Research output: Contribution to journal › Article

*Synthesis Lectures on Computer Graphics and Animation*, vol. 6, no. 3, pp. 1-85. https://doi.org/10.2200/S00599ED1V01Y201409CGR017

}

TY - JOUR

T1 - Mathematical basics of motion and deformation in computer graphics

AU - Anjyo, Ken

AU - Ochiai, Hiroyuki

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

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U2 - 10.2200/S00599ED1V01Y201409CGR017

DO - 10.2200/S00599ED1V01Y201409CGR017

M3 - Article

AN - SCOPUS:84932637968

VL - 6

SP - 1

EP - 85

JO - Synthesis Lectures on Computer Graphics and Animation

JF - Synthesis Lectures on Computer Graphics and Animation

SN - 1933-8996

IS - 3

ER -