Space-filling curves are classical ways to reduce the dimensions of data. This paper first presents the mapping rules of the diagonal space-filling curve. Unique curve which exists under the rules and the number of grids on each dimensionality is not constrained. Then a new conception about equipotential surface was given, and the relationship between the number of grids on different equipotential surface was dirived. Table-based space-filling curve generation algorithms on the basis of the realtionship were presented. It is found that the algorithms have low running time and high scalability.
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吴国福,窦强,窦文华.基于查表的空间填充曲线映射算法[J].国防科技大学学报,2010,32(5):75-79. WU Guofu, DOU Qiang, DOU Wenhua. Table-based Space-filling Curve Generation[J]. Journal of National University of Defense Technology,2010,32(5):75-79.