000			04221nam a2200421 i 4500
999			_c387693 _d387693
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003			ES-MaUEC
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007			cr nn 008mamaa
008			220601s2010 sz | o |||| 0|eng d
020			_a9783031795497
024	7		_a10.1007/978-3-031-79549-7 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aQA188 _b2010 EB
100	1		_aGoldman, Ron _d1947- _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9687766
245	1	0	_aRethinking Quaternions _cby Ron Goldman
250			_a1st edition 2010
264		1	_aCham _bSpringer International Publishing _c2010
300			_a1 recurso en línea (XVIII, 157 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Computer Graphics and Animation _x1933-9003
505	0		_aPreface -- Theory -- Computation -- Rethinking Quaternions and Clif ford Algebras -- References -- Further Reading -- Author Biography.
520			_aQuaternion 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. Table of Contents: Preface / Theory / Computation / Rethinking Quaternions and Clif ford Algebras / References / Further Reading / Author Biography.
988			_aSynthesis Collection of Technology_2010
650		7	_2embne _9142711 _aMatrices (Matemáticas)
650		7	_2embne _9140933 _aÁlgebra lineal
650		7	_2embne _9141143 _aGráficos de ordenador
776	0	8	_iPrinted edition: _z9783031795480
776	0	8	_iPrinted edition: _z9783031795503
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-79549-7 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b03/2023 _dz _eb _zSI