Hilbert Space-Filling by Piecewise-Linear Index Transformation

Due to its locality-preserving property, the Hilbert space-filling curve is used in a variety of applications, where data mapping from multiple-dimensions to one-dimension is required. An efficient algorithm to calculate the data indexes along the curve can then be considered as an address generation unit. We present two index transformation methods using simple bit operations. A counter-based transformation is derived first. Utilizing the regular structure of the transform matrix, a significant complexity reduction is achieved by basing the transform on Gray indexes. The proposed methods lend themselves to a simple and straightforward hardware implementation.