Table-driven algorithms for generating space-filling curves
Computer-Aided Design
An algorithm for displaying a class of space-filling curves
Software—Practice & Experience
A new algorithm for generation hilbert curves
Software—Practice & Experience
Linear clustering of objects with multiple attributes
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
Euclidean Voronoi labelling on the multidimensional grid
Pattern Recognition Letters
A framework for generating distributed-memory parallel programs for block recursive algorithms
Journal of Parallel and Distributed Computing
Encoding and decoding the Hilbert order
Software—Practice & Experience
Algorithm 781: generating Hilbert's space-filling curve by recursion
ACM Transactions on Mathematical Software (TOMS)
Using Hilbert curve in image storing and retrieving
MULTIMEDIA '00 Proceedings of the 2000 ACM workshops on Multimedia
Vertex-labeling algorithms for the Hilbert spacefilling curve
Software—Practice & Experience
ACM Computing Surveys (CSUR)
Algorithms + Data Structures = Programs
Algorithms + Data Structures = Programs
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
An algorithm for encoding and decoding the 3-D Hilbert order
IEEE Transactions on Image Processing
All-nearest-neighbors finding based on the Hilbert curve
Expert Systems with Applications: An International Journal
Computational and methodological aspects of terrestrial surface analysis based on point clouds
Computers & Geosciences
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An iterative algorithm is described, based on the replication process of the Hilbert matrix, for encoding and decoding the Hilbert order. The time complexity of the proposed algorithm is smaller than those published previously, and the space complexity is bounded by a constant. Moreover, the new algorithm has a wider applicability when compared with existing algorithms for certain machine-word lengths. A new variant of the Hilbert curve is suggested to overcome a shortcoming of the traditional Hilbert curve for the mapping problem. The proposed coding algorithms for the traditional Hilbert curve are also applicable to the new variant without increasing the time and space complexities. Copyright © 2006 John Wiley & Sons, Ltd.