📍 线段端点与中点计算器（二维、三维）Endpoint & Midpoint Calculator (2D, 3D)

使用说明与常见问题How-to & FAQ

「线段端点与中点计算器（二维、三维）」是什么？What is the Endpoint & Midpoint Calculator (2D, 3D) tool?

已知中点和一个端点，求另一个端点：B = 2M − A；或反过来由两个端点求中点 M = (A + B) ÷ 2。支持二维和三维坐标。本地处理。Find the other endpoint from the midpoint and one endpoint, B = 2M − A, or the midpoint of two endpoints, M = (A + B) ÷ 2. Works in 2D and 3D. Processed locally.

如何使用「线段端点与中点计算器（二维、三维）」？How do I use the Endpoint & Midpoint Calculator (2D, 3D) tool?

在「线段端点与中点计算器（二维、三维）」中，填写「计算」、「维度」、「端点 A（如 0, 1 或 0, 1, 2）」、「中点 M（求端点时）或端点 B（求中点时）」等参数，结果会随输入实时计算并显示在下方。In the Endpoint & Midpoint Calculator (2D, 3D): Fill in "Calculate", "Dimensions", "Endpoint A (e.g. 0, 1 or 0, 1, 2)", "Midpoint M (for the endpoint) or endpoint B (for the midpoint)"; results are recalculated instantly as you type.

怎么由中点求端点？How is the endpoint found from the midpoint?

中点是两个端点的平均值，所以另一个端点 B = 2M − A，每个坐标分别计算。例如 A = (0, 1)、M = (2, 3) 时 B = (4, 5)。The midpoint is the average of the two endpoints, so the other endpoint is B = 2M − A, coordinate by coordinate. For A = (0, 1) and M = (2, 3), B = (4, 5).

可以算中点吗？Can it find the midpoint?

可以，把「计算」改为“由两个端点求中点”，M = (A + B) ÷ 2，同时给出线段长度。Yes: choose Midpoint of two endpoints; M = (A + B) ÷ 2, and the segment length is shown too.

坐标怎么写？How do I write coordinates?

用“逗号 + 空格”或空格分隔，可以带括号，例如 (1, 2) 或 1 2；三维写三个数。逗号后没有空格的 1,2 可能是千位或小数逗号，页面会提示改写。Separate them with a comma and a space, or with spaces, with or without parentheses, such as (1, 2) or 1 2; in 3D write three numbers. A comma with no space after it, as in 1,2, could be a thousands or decimal comma, so the page asks you to rewrite it.

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

例如在「线段端点与中点计算器（二维、三维）」中填 计算 = 由中点和端点 A 求端点 B，维度 = 二维 (x, y)，端点 A（如 0, 1 或 0, 1, 2） = 0, 0，中点 M（求端点时）或端点 B（求中点时） = 2, 2，结果区显示：端点 B：(4, 4)；线段长度 |AB|：5.65685425；ℹ B = 2M − AFor example, entering Calculate = Endpoint B from the midpoint…, Dimensions = 2D (x, y), Endpoint A (e.g. 0, 1 or 0, 1, 2) = 0, 0, Midpoint M (for the endpoint) or endpoint B (for the midpoint) = 2, 2 in the Endpoint & Midpoint Calculator (2D, 3D) gives: Endpoint B: (4, 4); Segment length |AB|: 5.65685425; ℹ B = 2M − A

有哪些选项可以调整？What options can I adjust?

「线段端点与中点计算器（二维、三维）」的设置：「计算」可选 由中点和端点 A 求端点 B、由两个端点求中点（默认 由中点和端点 A 求端点 B）；「维度」可选 二维 (x, y)、三维 (x, y, z)（默认 二维 (x, y)）；「端点 A（如 0, 1 或 0, 1, 2）」默认 0, 1；「中点 M（求端点时）或端点 B（求中点时）」默认 2, 3。每次生成结果都按当前设置处理。Settings in the Endpoint & Midpoint Calculator (2D, 3D) — "Calculate": Endpoint B from the midpoint and endpoint A, Midpoint of two endpoints (default Endpoint B from the midpoint and endpoint A); "Dimensions": 2D (x, y), 3D (x, y, z) (default 2D (x, y)); "Endpoint A (e.g. 0, 1 or 0, 1, 2)" default 0, 1; "Midpoint M (for the endpoint) or endpoint B (for the midpoint)" default 2, 3. The result always uses the current settings.

计算精度如何？How precise are the results?

「线段端点与中点计算器（二维、三维）」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 Endpoint & Midpoint Calculator (2D, 3D) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「线段端点与中点计算器（二维、三维）」免费吗？需要注册吗？Is the Endpoint & Midpoint Calculator (2D, 3D) free? Do I need an account?

「线段端点与中点计算器（二维、三维）」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 Endpoint & Midpoint Calculator (2D, 3D) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.