Fast and accurate normalization of vectors and quaternions

We present fast and accurate ways to normalize two and three-dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the computational geometry and computer-aided design communities are not aw...

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Veröffentlicht in:	Computation and applied mathematics 2018-09, Vol.37 (4), p.4649-4660
1. Verfasser:	Mascarenhas, Walter F.
Format:	Artikel
Sprache:	eng
Schlagworte:	ACCURACY ALGEBRA Applications of Mathematics Applied physics CAD Computational geometry Computational mathematics Computational Mathematics and Numerical Analysis COMPUTER-AIDED DESIGN EFFICIENCY GEOMETRY Linear algebra Mathematical analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences MATHEMATICAL METHODS AND COMPUTING Mathematics Mathematics and Statistics Quaternions THREE-DIMENSIONAL CALCULATIONS Vectors (mathematics)
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Beschreibung
Zusammenfassung:	We present fast and accurate ways to normalize two and three-dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the computational geometry and computer-aided design communities are not aware of the possibility of speeding up these fundamental operations in the robust way proposed here.
ISSN:	0101-8205 2238-3603 1807-0302
DOI:	10.1007/s40314-018-0594-6