Minkowski products of unit quaternion sets

• Published in: Advances in computational mathematics Vol. 45; no. 3; pp. 1607 - 1629
• Main Authors: Farouki, Rida T., Gentili, Graziano, Moon, Hwan Pyo, Stoppato, Caterina
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2019; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Lie groups; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Quaternions; Rotation; Spherical caps; Visualization; Unit quaternions; 65G30; 30G35; Minkowski products; 3-sphere; Stereographic projection; Lie algebra; Boundary evaluation; Spatial rotations

The Minkowski product of unit quaternion sets is introduced and analyzed, motivated by the desire to characterize the overall variation of compounded spatial rotations that result from individual rotations subject to known uncertainties in their rotation axes and angles. For a special type of unit q...