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10.1145/2897826.2927338acmconferencesArticle/Chapter ViewAbstractPublication PagessiggraphConference Proceedingsconference-collections
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An elementary introduction to matrix exponential for CG

Published: 24 July 2016 Publication History

Abstract

This course presents an elementary, intuitive, and visual introduction to several mathematical basics for beginners in computer graphics. The mathematical concepts covered in this course include 2D/3D translation, rotation, affine transformation, quaternion, dual quaternion, exponential and logarithm. These are quite useful for various aspects of computer graphics, including curve/surface editing, deformation and animation of geometric objects. On one hand we don't assume that the audience has familiarity with such mathematical concepts. Elements of linear algebra and calculus at undergraduate level are sufficient for the attendees of this course. To clarify the relation between these concepts and computer graphics practice, several graphics techniques will also be demonstrated, such as morphing (ARAP), cage-based deformation and Poisson mesh editing.

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References

[1]
{Ochiail4} Ochiai and Anjyo: Mathematical Basics of Motion and Deformation in Computer Graphics, SIGGRAPH2014 Course Notes 19.
[2]
{Anjyol4} Anjyo and Ochiai: Mathematical Basics of Motion and Deformation in Computer Graphics, Synthesis Lectures on Computer Graphics and Animation, Morgan & Claypool Publishers 2014

Cited By

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  • (2017)Mathematical Basics of Motion and Deformation in Computer Graphics: Second EditionSynthesis Lectures on Visual Computing10.2200/S00766ED1V01Y201704VCP0279:1(1-95)Online publication date: 9-Apr-2017

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cover image ACM Conferences
SIGGRAPH '16: ACM SIGGRAPH 2016 Courses
July 2016
1735 pages
ISBN:9781450342896
DOI:10.1145/2897826
Permission to make digital or hard copies of part or all 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 third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 24 July 2016

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Cited By

View all
  • (2017)Mathematical Basics of Motion and Deformation in Computer Graphics: Second EditionSynthesis Lectures on Visual Computing10.2200/S00766ED1V01Y201704VCP0279:1(1-95)Online publication date: 9-Apr-2017

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