论文标题
阿兹台克曲线：新的空间填充曲线的建议
Aztec curve: proposal for a new space-filling curve
论文作者
论文摘要
本文简要审查了不同的空间填充曲线（SFC），并提出了新的曲线。一个世纪已经过去了这类曲线的成立，从那以后，它们在计算机科学中被发现很有用，尤其是在数据存储和索引中，由于它们的聚类特性，成为希尔伯特曲线是分形家族中最知名的成员。本文介绍了提出的阿兹台克曲线，具有与希尔伯特曲线相似的特征，并伴随着语法描述。它产生了创建双维簇的可能性，不适合Hilbert和Peano曲线。除此之外，还实施了在压缩传感范围上应用的情况，其中希尔伯特曲线的使用与阿兹台克曲线形成鲜明对比，具有相似的性能，并将AZTEC曲线定位为可行的，并且将未来利用用于使用SFC的应用的新替代方案。
Different space-filling curves (SFCs) are briefly reviewed in this paper, and a new one is proposed. A century has passed between the inception of this kind of curves, since then they have been found useful in computer science, particularly in data storage and indexing due to their clustering properties, being Hilbert curve the most well-known member of the family of fractals. The proposed Aztec curve, with similar characteristics to the Hilbert's curve, is introduced in this paper, accompanied by a grammatical description for its construction. It yields the possibility of creating bi-dimensional clusters, not available for Hilbert nor Peano curves. Additional to this, a case of application on the scope of Compressed Sensing is implemented, in which the use of Hilbert curve is contrasted with Aztec curve, having a similar performance, and positioning the Aztec curve as viable and a new alternative for future exploitation on applications that make use of SFC's.
