Adaptive hierarchical B-spline surface representation of large-scale scattered data

The representation of large scale scattered data is a difficult problem especially when various features of the representation such as C
²
-continuity are required. This paper describes a fast algorithm for large scale scattered data approximation and interpolation. The interpolation algorithm uses a coarse-to-fine hierarchical control lattice to fit the scattered data. The refinement process is only used in the regions where the error between the scattered data and the result in a surface is greater than a specified tolerance. A method to ensure C
²
-continuity is introduced to calculate the control lattice under constrained conditions. Experimental results show that this method can quickly represent large scale scattered data set.