SULJE VALIKKO

Englanninkielisten kirjojen poikkeusaikata... LUE LISÄÄ

avaa valikko

Rethinking Quaternions
35,10 €
Springer International Publishing AG
Sivumäärä: 157 sivua
Asu: Pehmeäkantinen kirja
Julkaisuvuosi: 2010, 10.10.2010 (lisätietoa)
Kieli: Englanti
Tuotesarja: Synthesis Lectures on Computer Graphics and Animation
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

Tuotetta lisätty
ostoskoriin kpl
Siirry koriin
LISÄÄ OSTOSKORIIN
Tilaustuote | Arvioimme, että tuote lähetetään meiltä noin 4-5 viikossa
Myymäläsaatavuus
Helsinki
Tapiola
Turku
Tampere
Rethinking Quaternions
Näytä kaikki tuotetiedot
ISBN:
9783031795480
Sisäänkirjautuminen
Kirjaudu sisään
Rekisteröityminen
Oma tili
Omat tiedot
Omat tilaukset
Omat laskut
Lisätietoja
Asiakaspalvelu
Tietoa verkkokaupasta
Toimitusehdot
Tietosuojaseloste