Logarithm-Based Methods for Interpolating Quaternion Time Series

Joshua Parker (), Dionne Ibarra and David Ober
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Joshua Parker: Geospatial Research Lab, US Army Corps of Engineers, 7701 Telegraph Rd, Alexandria, VA 22307, USA
Dionne Ibarra: School of Mathematics, Clayton Campus, Monash University, Melbourne, VIC 3800, Australia
David Ober: Geospatial Research Lab, US Army Corps of Engineers, 7701 Telegraph Rd, Alexandria, VA 22307, USA

Mathematics, 2023, vol. 11, issue 5, 1-13

Abstract: In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C 2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables θ and n ^ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude.

Keywords: quaternions; interpolation; rotations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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