An interpolation scheme for designing rational rotation-minimizing camera motions

When a moving (real or virtual) camera images a stationary object, the use of a rotation-minimizing directed frame (RMDF) to specify the camera orientation along its path yields the least apparent rotation of the image. The construction of such motions, using curves that possess rational RMDFs, is considered herein. In particular, the construction entails interpolation of initial/final camera positions and orientations, together with an initial motion direction. To achieve this, the camera path is described by a rational space curve that has a rational RMDF and interpolates the prescribed data. Numerical experiments are used to illustrate implementation of the method, and sufficient conditions on the two end frame orientations are derived, to ensure the existence of exactly one interpolant. By specifiying a sequence of discrete camera positions/orientations and an initial motion direction, the method can be used to construct general rotation-minimizing camera motions. Communicated by Helmut Pottmann. R. T. Farouki (B) Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA e-mail: [email protected] C. Giannelli Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Viale Morgagni 65, 50134 Firenze, Italy e-mail: [email protected] A. Sestini Dipartimento di Matematica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67a, 50134 Firenze, Italy e-mail: [email protected] 64 R.T. Farouki et al.