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Journal for Geometry and Graphics 22 (2018), No. 1, 087--098
Copyright Heldermann Verlag 2018

From A to B: New Methods to Interpolate Two Poses

Hans-Peter Schröcker
Dept. of Basic Sciences in Engineering, University of Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria

We present two methods to interpolate between two given rigid body displacements. Both are based on linear interpolation in the ambient space of well-known curved point models for the group of rigid body displacements. The resulting motions are either vertical Darboux motions or cubic circular motions. Both are rational of low degree and lie in the cylinder group defined by the two input poses. We unveil the essential parameters in the construction of these motions and discuss some of their properties.

Keywords: Darboux motion, cubic circular motion, motion interpolation, line-symmetric motion.

MSC: 70B10; 53A17, 65D17, 14R25

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