Coefficient–based spline data reduction by hierarchical spaces

Abstract

We present a data reduction scheme for efficient surface storage, by introducing a coefficient–based least squares spline operator that does not require any pointwise evaluation to approximate (in a lower dimension spline space) a given bivariate B–spline function. In order to define an accurate approximation of the target spline with a significant reduction of the space dimension, this operator is subsequently combined with the hierarchical spline framework to design an adaptive method that exploits the capabilities of truncated hierarchical B–splines (THB–splines). The resulting THB–spline simplification approach is validated by several numerical tests. The target B–spline surfaces include approximations of functions whose analytical expression is available, reconstructions of geographic data and parametric surfaces.