Haar Wavelets on Spherical Triangulations

  • Daniela Roşca
Part of the Mathematics and Visualization book series (MATHVISUAL)


We construct piecewise constant wavelets on spherical triangulations, which are orthogonal with respect to a scalar product on L2(\(\mathbb{S}\)2). Our classes of wavelets include certain wavelets obtained by Bonneau and by Nielson et al. We also prove the Riesz stability and show some numerical experiments.


Scalar Product Compression Rate Haar Wavelet Piecewise Constant Function Orthogonal Wavelet 
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  1. 1.
    Bonneau, G-P.: Optimal Triangular Haar Bases for Spherical Data. In: IEEE Visualization '99, San Francisco, USA (1999).Google Scholar
  2. 2.
    Nielson, G., Jung, I., Sung, J.: Haar Wavelets over Triangular Domains with Applications to Multiresolution Models for Flow over a Sphere. In: IEEE Visualization '97, 143–150 (1997).Google Scholar
  3. 3.
    Roşca, D.: Locally Supported Rational Spline Wavelets on the Sphere, submitted.Google Scholar
  4. 4.
    Schaeben, H., Potts, D., Prestin, J.: Spherical Wavelets with Application in Preferred Crystallographic Orientation, IAMG '2001, Cancun (2001).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Daniela Roşca
    • 1
    • 2
  1. 1.Institute of MathematicsUniversity of LübeckGermany
  2. 2.Department of MathematicsTechnical University of Cluj-NapocaRomania

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