Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2018, Vol. 54 ›› Issue (2): 331-335.DOI: 10.13209/j.0479-8023.2017.147

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Research on Continuity of Multi-Scale Space-Filling Curves

ZHAI Weixin1, CHEN Bo2, TONG Xiaochong3, CHENG Chengqi2,†   

  1. 1. Institute of Remote Sensing and Geographic Information System, Peking University, Beijing 100871
    2. Aerospace Information Engineering Research Center, Peking University, Beijing 100871
    3. Institute of Survey and Mapping, Information Engineering University, Zhengzhou 450001
  • Received:2016-12-12 Revised:2017-10-17 Online:2018-03-20 Published:2018-03-20
  • Contact: CHENG Chengqi, E-mail: ccq(at)


翟卫欣1, 陈波2, 童晓冲3, 程承旗2,†   

  1. 1. 北京大学遥感与地理信息系统研究所, 北京 100871
    2. 北京大学工学院空天信息工程研究中心, 北京 100871
    3. 信息工程大学地理空间信息空间学院, 郑州 450001
  • 通讯作者: 程承旗, E-mail: ccq(at)
  • 基金资助:
    国家科技重大专项(11-Y20A02-9001-16/17, 30-Y20A01-9003-16/17, 30-Y30B13-9003-14/16)和公益性行业(测绘地理信息)科研专项(201512020)资助


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


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

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