Constructing B-spline representation of quadratic Sibson-Thomson splines

In this paper, we show how to construct a normalized B-spline basis for a special C 1 continuous splines of degree 2, defined on Sibson-Thomson refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The dilatation equation can be found by applying the dyadic subdivision scheme directly to the Sibson-Thomson spline basis functions. As an application, a quasi-interpolation method, based on this Sibson-Thomson B-spline representation, is described which can be used for the efficient visualization of gridded surface data. B-spline basis of Sibson-Thomson splines.Refinement equation.Quasi-interpolants.

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