A Framework for Interpolating Scattered Data Using Space-Filling Curves

The analysis of spatial data occurs in many disciplines and covers a wide variety activities. Available techniques for such analysis include spatial interpolation which is useful for tasks such as visualization and imputation. This paper proposes a novel approach to interpolation using space-filling curves. Two simple interpolation methods are described and their ability to interpolate is compared to several interpolation techniques including natural neighbour interpolation. The proposed approach requires a Monte-Carlo step that requires a large number of iterations. However experiments demonstrate that the number of iterations will not change appreciably with larger datasets.