### Abstract

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.

Original language | English |
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Title of host publication | SIGGRAPH Asia 2013 Courses, SA 2013 |

DOIs | |

Publication status | Published - Dec 30 2013 |

Event | SIGGRAPH Asia 2013 Courses, SA 2013 - Hong Kong, Hong Kong Duration: Nov 19 2013 → Nov 22 2013 |

### Other

Other | SIGGRAPH Asia 2013 Courses, SA 2013 |
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Country | Hong Kong |

City | Hong Kong |

Period | 11/19/13 → 11/22/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Graphics and Computer-Aided Design
- Software

### Cite this

*SIGGRAPH Asia 2013 Courses, SA 2013*[2] https://doi.org/10.1145/2542266.2542268

**Mathematical description of motion and deformation - From basics to graphics applications.** / Ochiai, Hiroyuki; Anjyo, Ken.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*SIGGRAPH Asia 2013 Courses, SA 2013.*, 2, SIGGRAPH Asia 2013 Courses, SA 2013, Hong Kong, Hong Kong, 11/19/13. https://doi.org/10.1145/2542266.2542268

}

TY - GEN

T1 - Mathematical description of motion and deformation - From basics to graphics applications

AU - Ochiai, Hiroyuki

AU - Anjyo, Ken

PY - 2013/12/30

Y1 - 2013/12/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84890924893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890924893&partnerID=8YFLogxK

U2 - 10.1145/2542266.2542268

DO - 10.1145/2542266.2542268

M3 - Conference contribution

SN - 9781450326315

BT - SIGGRAPH Asia 2013 Courses, SA 2013

ER -