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International Conference on Mathematical Methods for Curves and Surfaces

MMCS 2012: Mathematical Methods for Curves and Surfaces pp 442–455Cite as

A Theoretical Analysis of an Improved Rational Scheme for Spherical Camera Motions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8177))

Abstract

A rational C 1 Hermite interpolation scheme on the sphere is introduced, improving the method proposed in [15]. On the base of a careful asymptotic analysis, a new selection of the free parameters is suggested, leading to a fourth order approximation scheme. The resulting curve is also endowed with a C 1 rational rotation-minimizing directed frame, which interpolates prescribed end orientations. The spline extension of the scheme is investigated. This is useful, for instance, in the description of smoothly varying camera motions, when a fixed target object is being imaged. Several examples are considered in order to show the performance of the proposed approach.

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Author information

Authors and Affiliations

  1. Department of Information Engineering and Mathematics, University of Siena, Italy

    Maria Lucia Sampoli

  2. Department of Mathematics and Computer Science, University of Florence, Italy

    Alessandra Sestini

  3. Faculty of Mathematics and Physics, Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Slovenia

    Gašper Jaklič & Emil Žagar

Authors
  1. Maria Lucia Sampoli
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  2. Alessandra Sestini
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  3. Gašper Jaklič
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  4. Emil Žagar
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Editor information

Editors and Affiliations

  1. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  2. DMA, University of Oslo, P.O.Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lyche

  3. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  4. University of Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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Sampoli, M.L., Sestini, A., Jaklič, G., Žagar, E. (2014). A Theoretical Analysis of an Improved Rational Scheme for Spherical Camera Motions. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2012. Lecture Notes in Computer Science, vol 8177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54382-1_25

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  • DOI: https://doi.org/10.1007/978-3-642-54382-1_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54381-4

  • Online ISBN: 978-3-642-54382-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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