Abstract: Most algorithms for describing three-dimensional Hilbert curves calculate node coordinates from the start point to the end point recursively. Directing at the multiple iteration， a new algorithm was brought forth. By means of constructing moving frame， the invariants under rigid body motion are obtained， that is， discrete curvature and torsion. Considering moving frame， the nodes are recoded. Establishing a map between the inflection point location number and the discrete curvature and torsion of the inflection point， based on that， writing the corresponding algorithm to make it for any number n， the pairs of curvature torsion and the image structure corresponding to the inflection points can be output. Compared to the algorithm Hilbert3(n)， the proposed algorithm is not limited to the order of the curve and does not depend on the iteration between the coordinates. Experimental results show that the algorithm is more efficient.

Key words: moving frame, Hilbert curve, discrete curvature, discrete torsion, iteration