〰 生成希尔伯特曲线Generate Hilbert Curve

使用说明与常见问题How-to & FAQ

「生成希尔伯特曲线」是什么？What is the Generate Hilbert Curve tool?

生成希尔伯特空间填充曲线。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Hilbert space-filling curve. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.

如何使用「生成希尔伯特曲线」？How do I use the Generate Hilbert Curve tool?

在「生成希尔伯特曲线」中，按需设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」等选项，然后点击「绘制」、「下载 PNG」按钮即可。In the Generate Hilbert Curve: Set "Width", "Height", "Padding", "Line width", "Iterations", then click "Draw", "Download PNG".

希尔伯特曲线有什么性质？What are its properties?

第 n 次迭代的曲线恰好经过 2^n × 2^n 网格的全部 4^n 个格子各一次，每步只走到相邻格子，从不自交。相邻的格子在曲线上大多也相邻，所以常用于数据库和图像的空间索引、把二维数据排成一维。At iteration n the curve passes through every one of the 4^n cells of a 2^n × 2^n grid exactly once, always stepping to a neighbouring cell and never crossing itself. Cells that are close in the plane are mostly close along the curve, which is why it is used for spatial indexing in databases and images.

和摩尔曲线有何不同？How does it differ from the Moore curve?

摩尔曲线是希尔伯特曲线的闭合版本，终点回到起点旁边；本页是开放曲线，起点和终点在正方形底边两角。规则是 L → +RF-LFL-FR+，R → -LF+RFR+FL-，转角 90°。The Moore curve is the closed version, ending next to its start; this page draws the open curve, which starts and ends at the two bottom corners. The rule is L → +RF-LFL-FR+, R → -LF+RFR+FL- with 90° turns.

有哪些选项可以调整？What options can I adjust?

「生成希尔伯特曲线」的设置：「宽度」默认 512，范围 64–2048；「高度」默认 512，范围 64–2048；「边距」默认 20，范围 0–256；「线宽」默认 2，范围 0.5–40；「迭代次数」默认 5，范围 1–8；「背景」默认 #ffffff；「线条」默认 #1e3a8a。每次生成结果都按当前设置处理。Settings in the Generate Hilbert Curve — "Width" default 512, range 64–2048; "Height" default 512, range 64–2048; "Padding" default 20, range 0–256; "Line width" default 2, range 0.5–40; "Iterations" default 5, range 1–8; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.

「生成希尔伯特曲线」免费吗？需要注册吗？Is the Generate Hilbert Curve free? Do I need an account?

「生成希尔伯特曲线」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Generate Hilbert Curve is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.