📏 欧氏距离（2D/3D）Euclidean Distance

使用说明与常见问题How-to & FAQ

「欧氏距离（2D/3D）」是什么？What is the Euclidean Distance tool?

2D 或 3D 两点距离。本地处理。可设置「维数」、「x₁」、「y₁」、「z₁」、「x₂」。2D or 3D distance between two points. Processed locally. Settings: Dimensions, x₁, y₁, z₁, x₂.

如何使用「欧氏距离（2D/3D）」？How do I use the Euclidean Distance tool?

在「欧氏距离（2D/3D）」中，填写「维数」、「x₁」、「y₁」、「z₁」、「x₂」等参数，结果会随输入实时计算并显示在下方。In the Euclidean Distance: Fill in "Dimensions", "x₁", "y₁", "z₁", "x₂"; results are recalculated instantly as you type.

能算曼哈顿距离吗？Can it give the Manhattan distance?

不能，本页只算欧氏（直线）距离 √(Δx² + Δy² (+ Δz²))。曼哈顿距离是各坐标差的绝对值之和 |Δx| + |Δy| (+ |Δz|)，可以用同样的坐标手算。No, it gives the Euclidean (straight-line) distance √(Δx² + Δy² (+ Δz²)) only. Manhattan distance is the sum of absolute differences |Δx| + |Δy| (+ |Δz|), easy to work out from the same coordinates.

能举个计算实例吗？Can you show a worked example?

例如在「欧氏距离（2D/3D）」中填 维数 = 2D，x₁ = 0，y₁ = 0，x₂ = 3，y₂ = 4，结果区显示：距离：5For example, entering Dimensions = 2D, x₁ = 0, y₁ = 0, x₂ = 3, y₂ = 4 in the Euclidean Distance gives: Distance: 5

哪些输入会被检查？Which inputs are validated?

「欧氏距离（2D/3D）」会检查这些输入——「x₁」、「y₁」、「x₂」、「y₂」：必须填写；「z₁」：所选方式用到时必须填写；「z₂」：可留空；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Euclidean Distance checks its inputs — "x₁", "y₁", "x₂", "y₂": required; "z₁": required when the chosen option uses it; "z₂": optional; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「欧氏距离（2D/3D）」的设置：「维数」可选 2D、3D（默认 2D）；「x₁」默认 0；「y₁」默认 0；「z₁」默认 0；「x₂」默认 3；「y₂」默认 4；「z₂」默认 12。每次生成结果都按当前设置处理。Settings in the Euclidean Distance — "Dimensions": 2D, 3D (default 2D); "x₁" default 0; "y₁" default 0; "z₁" default 0; "x₂" default 3; "y₂" default 4; "z₂" default 12. The result always uses the current settings.

计算精度如何？How precise are the results?

「欧氏距离（2D/3D）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Euclidean Distance uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「欧氏距离（2D/3D）」免费吗？需要注册吗？Is the Euclidean Distance free? Do I need an account?

「欧氏距离（2D/3D）」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 Euclidean Distance is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.