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From A to B: new methods to interpolate two poses. (English) Zbl 1426.70003
Summary: 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.

70B10 Kinematics of a rigid body
51N10 Affine analytic geometry
53A17 Differential geometric aspects in kinematics
65D17 Computer-aided design (modeling of curves and surfaces)
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