Coefficient-Based Spline Data Reduction by Hierarchical Spaces

摘要

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 TH B-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.