Efficient computation of partition of unity interpolants through a block-based searching technique

In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weight functions. In particular we present a new space-partitioning data structure based on a partition of the underlying generic domain in blocks. This approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points, leading to an optimized searching routine. Complexity analysis and numerical experiments in two- and three-dimensional interpolation support our findings. Some applications to geometric modelling are also considered. Moreover, the associated software package written in \textsc{Matlab} is here discussed and made available to the scientific community

Fast algorithms for matching CCD images to a stellar catalogue

Two new algorithms are described for matching two dimensional coordinate lists of point sources that are signifcantly faster than previous methods. By matching rarely occurring triangles (or more complex shapes) in the two lists, and by ordering searches by decreasing probability of success, it is demonstrated that very few candidates need be considered to find a successful match. Moreover, by immediately testing the suitability of a potential match using an efficient mechanism, the need to process the entire candidate set is avoided, yielding considerable performance improvements. Triangles are described by a cosine metric that reduces the density of triangle space, permitting efficient searches. An alternative shape characterization method that reduces computational overhead in the construction phase is discussed. The algorithms are tested on a set of 10 063 wide-field survey images, with fields-of-view up to 4.8 x 3.6 deg, successfully matching 100% of the images in a mean elapsed time of 6 ms (2.4 GHz Athlon CPU). The elapsed time of the searching phase is shown to vary by less than 1 ms for list sizes between 10 and 200 points, demonstrating that fast, robust searches may be completed in nearly constant time, independent of list size.Comment: Accepted for publication in Publications of the Astronomical Society of Australi