A rational C1 Hermite interpolation scheme on the sphere is introduced, improving the method proposed in a previous work. 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 C1 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.
Sampoli, M.L., Sestini, A., Jaklic, G., Zagar, E. (2014). A theoretical analysis of an improved rational scheme for spherical camera motions. In Mathematical Methods for Curves and Surfaces (pp. 442-455). Berlin Heidelberg : SPRINGER-VERLAG [10.1007/978-3-642-54382-1_25].
A theoretical analysis of an improved rational scheme for spherical camera motions
SAMPOLI, MARIA LUCIA;
2014-01-01
Abstract
A rational C1 Hermite interpolation scheme on the sphere is introduced, improving the method proposed in a previous work. 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 C1 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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https://hdl.handle.net/11365/44615
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