| Description |
1 online resource (xviii, 157 pages) : illustrations |
| Series |
Synthesis lectures on computer graphics and animation, 1933-9003 ; #13 |
|
Synthesis lectures in computer graphics and animation ; #13. 1933-8996
|
| Contents |
Preface -- I. Theory -- 1. Complex numbers -- 2. A brief history of number systems and multiplication -- Multiplication in dimensions greater than two -- 3. Modeling quaternions -- Mass-points: a classical model for contemporary computer graphics -- Arrows in four dimensions -- Mutually orthogonal planes in four dimensions -- 4. The algebra of quaternion multiplication -- 5. The geometry of quaternion multiplication -- 6. Affine, semi-affine, and projective transformations in three dimensions -- Rotation -- Mirror image -- Perspective projection -- Perspective projection and singular 4 x 4 matrices -- Perspective projection by sandwiching with quaternions -- Rotorperspectives and rotoreflections -- 7. Recapitulation: insights and results |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (page 153) |
| Subject |
Quaternions.
|
|
Quaternions
|
| Form |
Electronic book
|
| ISBN |
9781608454211 |
|
1608454215 |
|
9783031795497 |
|
3031795490 |
|
