Efficient 3D Hilbert Curve Encoding and Decoding Algorithms

Hilbert curve describes a one-to-one mapping between multidimensional space and 1D space. Most traditional 3D Hilbert encoding and decoding algorithms work on order-wise manner and are not aware of the difference between different input data and spend equivalent computing costs on them, thus resulting in a low efficiency. To solve this problem, in this paper we design efficient 3D state views for fast encoding and decoding. Based on the state views designed, a new encoding algorithm (JFK-3HE) and a new decoding algorithm (JFK-3HD) are proposed. JFK-3HE and JFK-3HD can avoid executing iteratively encoding or decoding each order by skipping the first 0s in input data, thus decreasing the complexity and improving the efficiency. Experimental results show that JFK-3HE and JFK-3HD outperform the state-of-the-arts algorithms for both uniform and skew-distributed data.