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N维Hilbert曲线生成算法

李晨阳1, 段雄文1, 冯玉才1(华中科技大学计算机学院,武汉 430074)

摘 要
Hilbert曲线描述了一种多维空间与1维空间—映射的方法,在图像处理、多维数据索引等领域有着重要的地位。但因为高维Hilbert曲线的复杂性,对高维Hilbert的相关算法研究很少。提出了产生N维Hilbert曲线的一个新算法。该算法基于静态演化规则,自底向上地分析N维Hilbert曲线编码规律,实现N维Hilbert曲线的编码生成。与现有的算法相比,本文算法易于实现。实验结果表明,该算法具有更好的计算性能。
关键词
Algorithm for Generating N-dimensional Hilbert Curve

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Abstract
The Hilbert curve is a way of mapping the multidimensional space into the one-dimensional space. Such mappings are of interest in a number of application domains including image processing and the indexing of multidimensional data. However, little has been discussed on its high dimensional algorithms due to the complexity. In this paper, a novel algorithm is presented for generating an N-dimensional Hilbert curve, which analyzes a Hilbert curve from bottom to top, based on a static evolvement rule table. The experimental results show that our method is easier to implement and faster in computation than other methods.
Keywords

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