Adaptive hierarchical b-spline surface approximation of large-scale scattered data

Abstract

A fast algorithm for large scale scattered data approximation is described. The algorithm exploits a coarse-to-fine hierarchical control lattice to fit the scattered data. In this algorithm, the refinement process is only located in the regions where the error between the scattered data and the resulting surface is greater than a specified tolerance. A recursive algorithm is used to find these regions. In order to ensure the C/sup 2/-continuity of the resulting surfaces, we introduce an additional method to get the boundary control points around the subcontrol lattice. Experimental results are included to show that this method can approximate large scale scattered data sets quickly.