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A theoretical analysis of an improved rational scheme for spherical camera motions
Sampoli, Maria Lucia ...
A rational ▫$C ^{1}$▫ Hermite interpolation scheme on the sphere is introduced, improving the method proposed in [Jaklič, G., Sampoli, M.L., Sestini, A., Žagar, E.: ▫$C ^{1}$▫ rational interpolation ...of spherical motions with rational rotation-minimizing directed frames. Comput. Aided Geom. Design 30, 159-173 (2013)]. On the base of a careful asymptotic analysis, a new selection of the free parameters is suggested, leading to a fourth order approximation scheme. The resulting curve is also endowed with a ▫$C ^{1}$▫ rational rotation-minimizing directed frame, which interpolates prescribed end orientations. The spline extension of the scheme is investigated. This is useful, for instance, in the description of smoothly varying camera motions, when a fixed target object is being imaged. Several examples are considered in order to show the performance of the proposed approach.
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