在Python中生成3D希尔伯特空间填充曲线的算法 [英] Algorithm for generating a 3D Hilbert space-filling curve in Python

问题描述

我想将RGB颜色立方体中的点映射到Python中的一维列表，以使颜色列表看起来美观且连续。

I'd like to map points in a RGB color cube to a one-dimensional list in Python, in a way that makes the list of colors look nice and continuous.

我相信使用3D希尔伯特空间填充曲线将是实现此目的的一种好方法，但是我进行了搜索，但没有找到非常有用的资源来解决此问题。尤其是Wikipedia仅提供了用于生成2D曲线的示例代码。

I believe using a 3D Hilbert space-filling curve would be a good way to do this, but I've searched and haven't found very helpful resources for this problem. Wikipedia in particular only provides example code for generating 2D curves.

推荐答案

本文似乎有很多讨论：
三维希尔伯特空间填充曲线的清单。

This paper seems to have quite a discussion: An inventory of three-dimensional Hilbert space-filling curves.

引用摘要：

希尔伯特的二维空间填充曲线因其
的良好局部性而受到赞赏适用于许多应用。但是，尚不清楚
概括此曲线以填充
高维空间的最佳方法是什么。我们认为使
希尔伯特曲线在两个维度上独一无二的属性由10694807
在三个维度上结构不同的空间填充曲线所共享。

Hilbert's two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that the properties that make Hilbert's curve unique in two dimensions, are shared by 10694807 structurally different space-filling curves in three dimensions.

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