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

Hiroyuki Ochiai, Ken Anjyo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationSIGGRAPH Asia 2013 Courses, SA 2013
DOIs
Publication statusPublished - Dec 30 2013
EventSIGGRAPH Asia 2013 Courses, SA 2013 - Hong Kong, Hong Kong
Duration: Nov 19 2013Nov 22 2013

Other

OtherSIGGRAPH Asia 2013 Courses, SA 2013
CountryHong Kong
CityHong Kong
Period11/19/1311/22/13

Fingerprint

Computer graphics
Animation
Geometry

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design
  • Software

Cite this

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

SIGGRAPH Asia 2013 Courses, SA 2013. 2013. 2.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ochiai, H & Anjyo, K 2013, Mathematical description of motion and deformation - From basics to graphics applications. in 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
@inproceedings{08e7087832304e92b8ff36d4451e4859,
title = "Mathematical description of motion and deformation - From basics to graphics applications",
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.",
author = "Hiroyuki Ochiai and Ken Anjyo",
year = "2013",
month = "12",
day = "30",
doi = "10.1145/2542266.2542268",
language = "English",
isbn = "9781450326315",
booktitle = "SIGGRAPH Asia 2013 Courses, SA 2013",

}

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 -