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Interpolating Camera Configurations

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Computer Analysis of Images and Patterns (CAIP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2756))

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Abstract

A surprisingly rich variety of tools has been developed for interpolating camera orientations, including traditional methods based on charts, corner-cutting schemes from computer graphics, and Riemannian cubic interpolants. Piecewise geodesic and generalized deCastlejau interpolants are described in sufficient detail to permit implementation. Experimental comparisons are made between generalized deCastlejau curves and Riemannian cubics.

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References

  1. Ahlberg, J.H., Nilson, E.N., Walsh, J.H.: The Theory of Splines and Their Applications. Mathematics in Science and Engineering, vol. 38. Academic Press, London (1967)

    Book  MATH  Google Scholar 

  2. Angeles, J., Akras, R.: Cartesian Trajectory Planning for 3-DOF Spherical Wrists. In: IEEE Conference on Robotics and Automation, Scottsdale, AZ, May 1989, pp. 68–74 (1989)

    Google Scholar 

  3. Barr, A.H., Currin, B., Gabriel, S., Hughes, J.F.: Smooth Interpolation of Orientations with Angular Velocity Constraints Using Quaternions. Computer Graphics 26(2), 313–320 (1992)

    Article  Google Scholar 

  4. Brady, J.M., Hollerbach, J.M., Johnson, T.L., Lozano-Perez, T., Masson, M.T.: Robot Motion: Planning and Control. MIT Press, Cambridge (1982)

    Google Scholar 

  5. Camarinha, M., Silva Leite, F., Crouch, P.: On the Geometry of Riemannian Cubic Polynomials. Differential Geom. Appl. 15(2), 107–135 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Camarinha, M., Silva Leite, F., Crouch, P.: Splines of Class C k on Non-Euclidean Spaces. IMA J. Math. Control & Information 12(4), 399–410 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chapman, P.B., Noakes, L.: Singular Perturbations and Interpolation - a Problem in Robotics. Nonlinear Analysis TMA 16(10), 849–859 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  8. Crouch, P., Silva Leite, F.: The Dynamic Interpolation Problem: on Riemannian Manifolds, Lie Groups, and Symmetric Spaces. J. Dynam. Control Systems 1(2), 177–202 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Crouch, P., Kun, G., Silva Leite, F.: The De Castlejau Algorithm on Lie Groups and Spheres. J. Dynam. Control Systems 5(3), 397–429 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Duff, T.: Quaternion Splines for Animating Rotations. In: Second Summer Graphics Workshop, Monterey, CA, December 12-13, pp. 54–62 (1985) (Usenix Association)

    Google Scholar 

  11. Gabriel, S.A., Kajiya, J.T.: Spline Interpolation in Curved Manifolds (1985) (unpublished manuscript)

    Google Scholar 

  12. Goldman, R.N.: Recursive Triangles. In: Dahmen, W., Gasca, M., Micchelli, C.A. (eds.) Computations of Curves and Surfaces. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol. 307, pp. 27–72. Kluwer, Dordrecht (1989)

    Google Scholar 

  13. Jost, J.: Riemannian Geometry and Geometrical Analysis. Springer, Heidelberg (1995)

    Google Scholar 

  14. Keller, H.B.: Numerical Methods for Two-Point Boundary-Value Problems. Blaisdell, Waltham Mass (1968)

    MATH  Google Scholar 

  15. Krakowski, K.: PhD Thesis, University of Western Australia (submitted 2002)

    Google Scholar 

  16. Silva Leite, F., Camarinha, M., Crouch, P.: Elastic Curves as Solutions of Riemannian and Sub-Riemannian Control Problems. Math. Control Signals Systems 13(2), 140–155 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Milnor, J.: Morse Theory. Annals of Math Studies, vol. 51. Princeton UP, Princeton (1963)

    MATH  Google Scholar 

  18. Noakes, L.: Asymptotically Smooth Splines. World Scientific Series in Approximations and Decompositions, vol. 4, pp. 131–137 (1994)

    Google Scholar 

  19. Noakes, L.: Riemannian Quadratics. In: Le Méhauté, A., Rabut, C., Schumaker, L.L. (eds.) Curves and Surfaces with Applications in CAGD, vol. 1, pp. 319–328. Vanderbilt University Press (1997)

    Google Scholar 

  20. Noakes, L.: Nonlinear Corner-Cutting. Advances in Computational Math. 8, 165–177 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  21. Noakes, L.: Accelerations of Riemannian Quadratics. Proc. Amer. Math. Soc. 127, 1827–1836 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  22. Noakes, L.: Quadratic Interpolation on Spheres. Advances in Computational Math. (in-press)

    Google Scholar 

  23. Noakes, L., Heinzinger, G., Paden, B.: Cubic Splines on Curved Spaces. J. Math. Control & Information 6, 465–473 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  24. Noakes, L.: Null Cubics and Lie Quadratics. J. Math. Physics (in-press)

    Google Scholar 

  25. Paul, R.P.: Manipulator Path Control. IEEE Trans. Syst. Man. Cybern. SMC-9, 702–711 (1979)

    Article  Google Scholar 

  26. Shoemake, K.: Animating Rotation with Quaternion Curves. SIGGRAPH 19(3), 245–254 (1985)

    Article  Google Scholar 

  27. Tan, H.H., Potts, R.B.: A Discrete Path/Trajectory Planner for Robotic Arms. J. Austral. Math. Soc. Series B 31, 1–28 (1989)

    Google Scholar 

  28. Taylor, R.H.: Planning and Execution of Straight-Line Manipulator Trajectories. IBM J. Res. Develop. 23, 424–436 (1979)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics & Statistics, The University of Western Australia, 35 Stirling Highway, 6009 WA, Crawley, Perth, Australia

    Lyle Noakes

Authors
  1. Lyle Noakes
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computing Science, University of Groningen, P.O.Box 800, 9700 AV, Groningen, The Netherlands

    Nicolai Petkov

  2. Institute of Mathematics and Computing Science, University of Groningen, Blauwborgje 3, 9747 AC, Groningen, The Netherlands

    Michel A. Westenberg

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© 2003 Springer-Verlag Berlin Heidelberg

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Noakes, L. (2003). Interpolating Camera Configurations. In: Petkov, N., Westenberg, M.A. (eds) Computer Analysis of Images and Patterns. CAIP 2003. Lecture Notes in Computer Science, vol 2756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45179-2_87

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  • DOI: https://doi.org/10.1007/978-3-540-45179-2_87

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40730-0

  • Online ISBN: 978-3-540-45179-2

  • eBook Packages: Springer Book Archive

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