Abstract:

Multi-scale two-dimensional Hilbert curve is constructed, and specially the scale dimension is treated as the third dimension. The new structure embodies the multi-level characteristics and overcomes the drawback of Z sequence coding pattern, thus improving the continuity of the curve and advancing the spatial retrieval efficiency. The authors conducted two kinds of experiments based on the quad-tree model to compare the retrieval efficiency of Hilbert curve and Z curve. The consequence indicates that the multi-scale Hilbert curve performs better than Z curve, and the improvement on different data distributions vary from 15% to 30%.

Key words: multi-scale, Hilbert curve, spatial continuity

摘要：

将二维Hilbert编码和Z编码拓展到以尺度维作为第三维的三维填充曲线: 多尺度Hilbert曲线和Z曲线。在多尺度数据条件下, 这两种曲线能够提高空间填充曲线的空间连续性, 适应多尺度的需求。依托四叉树模型, 将多尺度的Hilbert曲线与按照相同思路设计的多尺度Z曲线进行两类对比试验, 验证了多尺度Hilbert曲线相对于Z曲线在空间连续性方面的优势, 提高的比例在15%~30%之间。

关键词: 多尺度, Hilbert曲线, 空间连续性