“Efficient, fair interpolation using Catmull-Clark surfaces” by Halstead, Kass and DeRose

  • ©Mark A. Halstead, Michael Kass, and Tony DeRose




    Efficient, fair interpolation using Catmull-Clark surfaces



    We describe an efficient method for constructing a smooth
    surface that interpolates the vertices of a mesh of arbitrary
    topological type. Normal vectors can also be interpolated at
    an arbitrary subset of the vertices. The method improves
    on existing interpolation techniques in that it is fast, robust
    and general.
    Our approach is to compute a control mesh whose
    Catmull-Clark subdivision surface interpolates the given
    data and minimizes a smoothness or “fairness” measure of
    the surface. Following Celniker and Gossard, the norm we
    use is based on a linear combination of thin-plate and membrane energies. Even though Catmull-Clark surfaces do not
    possess closed-form parametrizations, we show that the relevant properties of the surfaces can be computed efficiently
    and without approximation. In particular, we show that (1)
    simple, exact interpolation conditions can be derived, and
    (2) the fairness norm and its derivatives can be computed
    exactly, without resort to numerical integration.


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