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Rigid-Body Pose and Position Interpolation using Geometric Algebra

This paper presents a method of interpolating between two or more general displacements (rotation and translation). The resulting interpolated path is smooth and possesses a number of desirable properties. It differs from existing algorithms which require factorising the pose into separate rotation and translation components and is derived from an intuitively appealing framework – i.e. a natural extension of the standard interpolation scheme for pure rotations. The mathematical framework used for the derivation is that of geometric algebra. While this paper presents the theory behind the interpolation and its description as a tool, we also outline the possible advantages of using this technique for vision and graphics applications.