Rethinking Quaternions (Record no. 85274)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 04371nam a22004935i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-79549-7 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240730164054.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 220601s2010 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783031795497 |
| -- | 978-3-031-79549-7 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 510 |
| 100 1# - AUTHOR NAME | |
| Author | Goldman, Ron. |
| 245 10 - TITLE STATEMENT | |
| Title | Rethinking Quaternions |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2010. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XVIII, 157 p. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Synthesis Lectures on Computer Graphics and Animation, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Preface -- Theory -- Computation -- Rethinking Quaternions and Clif ford Algebras -- References -- Further Reading -- Author Biography. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Quaternion multiplication can be used to rotate vectors in three-dimensions. Therefore, in computer graphics, quaternions have three principal applications: to increase speed and reduce storage for calculations involving rotations, to avoid distortions arising from numerical inaccuracies caused by floating point computations with rotations, and to interpolate between two rotations for key frame animation. Yet while the formal algebra of quaternions is well-known in the graphics community, the derivations of the formulas for this algebra and the geometric principles underlying this algebra are not well understood. The goals of this monograph are to provide a fresh, geometric interpretation for quaternions, appropriate for contemporary computer graphics, based on mass-points; to present better ways to visualize quaternions, and the effect of quaternion multiplication on points and vectors in three dimensions using insights from the algebra and geometry of multiplication in the complex plane; to derive the formula for quaternion multiplication from first principles; to develop simple, intuitive proofs of the sandwiching formulas for rotation and reflection; to show how to apply sandwiching to compute perspective projections. In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolatebetween two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text. Table of Contents: Preface / Theory / Computation / Rethinking Quaternions and Clif ford Algebras / References / Further Reading / Author Biography. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| General subdivision | Digital techniques. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1007/978-3-031-79549-7 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2010. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Image processing |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer vision. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer Imaging, Vision, Pattern Recognition and Graphics. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 1933-9003 |
| 912 ## - | |
| -- | ZDB-2-SXSC |
No items available.