C1C1 rational interpolation of spherical motions with rational rotation-minimizing directed frames

An interpolation method for constructing rational curves on the unit sphere with rational directed rotation-minimizing frames is presented. This type of curves is useful, for instance, in the description of smoothly varying camera motions. The proposed scheme uses as input data the initial and the final curve positions and tangents on the sphere, together with the associated end frame orientations. Both the curve and the rotation-minimizing directed frame produced by the scheme are C1C1 continuous and are rational of degree 8, which, under suitable mild assumptions on angular velocity directions, can be reduced to 6 if only G1G1 continuity is required.

► A scheme for constructing rational rotation-minimizing spherical motions had been developed.
► The method is based on interpolation of initial/final curve positions, orientations, and compatible motion directions.
► The resulting curve segments possess C1C1 continuity and therefore can be used to construct a C1C1 spline by interpolation.
► The degree of obtained curves is usually eight, as well as the degree of the associated rational rotation-minimizing frames.