Product of Exponentials (POE) Splines on Lie‐Groups: Limitations, Extensions, and Application to SO(3) $$ SO(3) $$and SE(3) $$ SE(3)

Existing methods for constructing splines and Bézier curves on a Lie group G $$ G $$involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of G $$ G...

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Bibliographic Details
Published in:	International journal for numerical methods in engineering 2025-07, Vol.126 (14), p.n/a
Main Author:	Müller, Andreas
Format:	Article
Language:	English
Subjects:	Algorithms Boundary conditions bézier curves cosserat continua Curves de casteljau algorithm Fields (mathematics) Geodesy Initial conditions Lie groups magnus expansion Poisson equation Polynomials product of exponentials Rods SE$$ SE SO$$ SO Spline functions splines
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