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Digital, three-dimensional models of real world objects are required for many applications. These can be obtained by fitting global radial basis functions to point cloud data captured using laser scanners, a process that can be computationally intensive for large data sets. A faster approach is to evaluate a number of local radial basis functions and combine these into a complete representation. This paper demonstrates a partition of unity approach to this problem, adapted from a method outlined in Tobor et al. [Journal of WSCG, Vol.12, No.1-3, 2004]. Results are presented for synthetic and real point cloud data captured with a FastSCANtrade laser scanner, using standard and novel isosurfacing methods.