The reproducing kernel Hilbert space (RKHS) method has been previously shown to be accurate and efficient in the construction of potential energy surfaces (PES) by interpolating fully gridded high level ab initio data. This paper extends the RKHS method to handle partially filled data calculated over arbitrarily shaped regions, while keeping nearly intact its accuracy and efficiency. The extension permits points or regions to be added to or removed from the grid as needed before doing expensive ab initio calculations, thus enabling the construction of RKHS PESs from the data distributions that are most likely to occur in practice. The utility of the new technique is demonstrated using data from the lowest global RKHS PES for the reaction O(D-1)+H-2, showing that ignoring the irrelevant regions of the PES does not adversely impact the accuracy of the surfaces if the relevant region is adequately sampled. (C) 2001 American Institute of Physics.