Abstract: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.