Visit our Christmas Gift Finder
Click & Collect from 2 Hours*
Last Christmas delivery dates
Free UK Standard Delivery On all orders £20 and over Order in time for Christmas 19th December 2nd Class | 20th December 1st Class Free Click & Collect to UK shops From 2 hours of your order*
Rethinking Quaternions - Synthesis Lectures on Computer Graphics and Animation (Paperback)
  • Rethinking Quaternions - Synthesis Lectures on Computer Graphics and Animation (Paperback)
zoom

Rethinking Quaternions - Synthesis Lectures on Computer Graphics and Animation (Paperback)

(author), (series editor)
£45.50
Paperback 157 Pages / Published: 30/10/2010
  • We can order this

Usually dispatched within 3 weeks

  • This item has been added to your basket
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 interpolate between 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.

Publisher: Morgan & Claypool Publishers
ISBN: 9781608454204
Number of pages: 157
Weight: 314 g
Dimensions: 235 x 187 x 9 mm

You may also be interested in...

A Project Guide to UX Design
Added to basket
Build Your Own Website
Added to basket
Don't Make Me Think, Revisited
Added to basket
Apache 2 Pocket Reference
Added to basket
Designing the Internet of Things
Added to basket
Letting Go of the Words
Added to basket
Building a Web Site For Dummies
Added to basket
Web Design All-in-One For Dummies
Added to basket
Web Design in easy steps
Added to basket
The Elements of User Experience
Added to basket
Creating and Consuming Rich PDFs
Added to basket
The Content Strategy Toolkit
Added to basket
Unity Game Development Essentials
Added to basket
Build Your First Website In Simple Steps
Added to basket

Please sign in to write a review

Your review has been submitted successfully.