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Rethinking Quaternions
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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.
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Morgan & Claypool Publishers; May 2010
176 pages; ISBN 9781608454211
Read online, or download in secure PDF format
176 pages; ISBN 9781608454211
Read online, or download in secure PDF format
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1608454215
9781608454204
9781608454211