Rational Interpolation of Rigid-Body Motions

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Let g 1, g 2,...,g n be a sequence of elements of a Lie group, (knot points). Our problem is to find a smooth, parameterised curve in the group that passes through these elements at parameter values t 1, t 2,...,t n . There are many variations on this basic problem. For example we could take account of velocities. Perhaps we might only require the curve to be near the knot points.