C~1 rational interpolation of spherical motions with rational rotation-minimizing directed frames

摘要

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 C~1 continuous and are rational of degree 8, which, under suitable mild assumptions on angular velocity directions, can be reduced to 6 if only G~1 continuity is required.