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Cubic spline algorithms for orientation interpolation
Author(s) -
Kang I. G.,
Park F. C.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990910)46:1<45::aid-nme662>3.0.co;2-k
Subject(s) - quaternion , mathematics , spline interpolation , invariant (physics) , algorithm , rotation (mathematics) , differentiable function , spline (mechanical) , knot (papermaking) , orientation (vector space) , geometry , mathematical analysis , bilinear interpolation , structural engineering , engineering , statistics , chemical engineering , mathematical physics
This article presents a class of spline algorithms for generating orientation trajectories that approximately minimize angular acceleration. Each algorithm constructs a twice‐differentiable curve on the rotation group SO(3) that interpolates a given ordered set of rotation matrices at specified knot times. Rotation matrices are parametrized, respectively, by the unit quaternion, canonical co‐ordinate, and Cayley–Rodrigues representations. All the algorithms share the common feature of (i) being invariant with respect to choice of fixed and moving frames ( bi‐invariant ), and (ii) being cubic in the parametrized co‐ordinates. We assess the performance of these algorithms by comparing the resulting trajectories with the minimum angular acceleration curve. Copyright © 1999 John Wiley & Sons, Ltd.