research-article

Mathematical description of motion and deformation: from basics to graphics applications

Authors:

Hiroyuki Ochiai,

Ken AnjyoAuthors Info & Claims

SA '13: SIGGRAPH Asia 2013 Courses

Article No.: 2, Pages 1 - 47

https://doi.org/10.1145/2542266.2542268

Published: 19 November 2013 Publication History

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.

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Cited By

Anjyo KOchiai H(2022)Mathematical Basics of Motion and Deformation in Computer Graphics, Second EditionundefinedOnline publication date: 26-Mar-2022
Anjyo KOchiai H(2022)Mathematical Basics of Motion and Deformation in Computer GraphicsundefinedOnline publication date: 21-Mar-2022
Bansal STatu A(2019)Affine interpolation in a lie group frameworkACM Transactions on Graphics10.1145/3306346.332299738:4(1-16)Online publication date: 12-Jul-2019
Show More Cited By

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Mathematical description of motion and deformation: from basics to graphics applications

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Published In

cover image ACM Conferences

SA '13: SIGGRAPH Asia 2013 Courses

November 2013

1458 pages

ISBN:9781450326315

DOI:10.1145/2542266

Conference Chair:
Yizhou Yu
The University of Hong Kong, Hong Kong

Copyright © 2013 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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SIGCHI: ACM Special Interest Group on Computer-Human Interaction

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 November 2013

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SA '13

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SIGGRAPH

SA '13: SIGGRAPH Asia 2013

November 19 - 22, 2013

Hong Kong, Hong Kong

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Overall Acceptance Rate 178 of 869 submissions, 20%

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Cited By

Anjyo KOchiai H(2022)Mathematical Basics of Motion and Deformation in Computer Graphics, Second EditionundefinedOnline publication date: 26-Mar-2022
Anjyo KOchiai H(2022)Mathematical Basics of Motion and Deformation in Computer GraphicsundefinedOnline publication date: 21-Mar-2022
Bansal STatu A(2019)Affine interpolation in a lie group frameworkACM Transactions on Graphics10.1145/3306346.332299738:4(1-16)Online publication date: 12-Jul-2019
Ochiai H(2014)Mathematics: As an Infrastructure of Technology and ScienceA Mathematical Approach to Research Problems of Science and Technology10.1007/978-4-431-55060-0_1(3-15)Online publication date: 15-Jul-2014

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