Compaction Techniques for Raster Scan Graphics using Space-filling Curves

Using Space-filling Curves for Computation Reordering

Space-filling curves have been widely used in mathematics and to transform multi-dimensional problems into one-dimensional forms. For scientific applications, ordering data or computation along spacefilling curves can be useful for exploiting locality when partitioning onto parallel systems or when restructuring to exploit memory hierarchy. In this paper, we present an efficient approach for en...

Dynamic Load Balancing Using Space-Filling Curves

Space-filling curves (SFCs) provide a continuous mapping from a one-dimensional to a d-dimensional space and have been used to linearize spatially distributed data for partitioning, memory management and image processing. This paper gives a short introduction to the concept of SFCs and highlights some of the applications found in computer science. The main focus will be on dynamic distribution ...

Unconventional Space-filling Curves

A 2-dimensional space-filling curve, here, is a surjective continuous map from an interval to a 2-dimensional space. To construct a new space-filling curve distinct and much different from Hilbert’s, Peano’s, and the Z-order, we first observe that all three of these curves are based on self-similar fractals–in particular, the recursive definition of the sequences of functions that converge to t...

Using Space-Filling Curves for Multi-dimensional Indexing

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 compa...