Advances in Computational Mathematics

, Volume 38, Issue 1, pp 63–82 | Cite as

An interpolation scheme for designing rational rotation-minimizing camera motions

  • Rida T. Farouki
  • Carlotta Giannelli
  • Alessandra Sestini
Article

Abstract

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.

Keywords

Camera orientation Directed frames Rotation-minimizing frames Angular velocity Pythagorean curves Quaternions Interpolation 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Rida T. Farouki
    • 1
  • Carlotta Giannelli
    • 2
  • Alessandra Sestini
    • 3
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaDavisUSA
  2. 2.Dipartimento di Sistemi e InformaticaUniversità degli Studi di FirenzeFirenzeItaly
  3. 3.Dipartimento di Matematica “Ulisse Dini”Università degli Studi di FirenzeFirenzeItaly

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