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单词 Level curve
释义

Level curve

中文百科

水平集 Level set

（重定向自Level curve）
一个以不同方式表达的三页扭结.
Points at constant slices of x2 = f(x1).Lines at constant slices of x3 = f(x1, x2).Planes at constant slices of x4 = f(x1, x2, x3).(n − 1)-dimensional level sets for functions of the form f(x1, x2, ..., xn) = a1x1 + a2x2 + ... + anxn where a1, a2, ..., an are constants, in (n + 1)-dimensional Euclidean space, for n = 1, 2, 3.

在数学领域中, 一个具有n变量的实值函数f的水平集是具有以下形式的集合

{ (x1,...,xn) | f(x1,...,xn) = c }

其中 c 是常数. 即, 使得函数值具有给定常数的变量集合.

当具有两个变量时, 称为水平曲线(等高线), 如果有三个变量, 称为水平曲面, 更多变量时, 水平集被叫做水平超曲面.

集合

{ (x1,...,xn) | f(x1,...,xn) ≤ c }

被称为 f 的 子水平集 .

英语百科

Level set 水平集

（重定向自Level curve）
Points at constant slices of x2 = f(x1).Lines at constant slices of x3 = f(x1, x2).Planes at constant slices of x4 = f(x1, x2, x3).(n − 1)-dimensional level sets for functions of the form f(x1, x2, ..., xn) = a1x1 + a2x2 + ... + anxn where a1, a2, ..., an are constants, in (n + 1)-dimensional Euclidean space, for n = 1, 2, 3.
Points at constant slices of x2 = f(x1).Contour curves at constant slices of x3 = f(x1, x2).Curved surfaces at constant slices of x4 = f(x1, x2, x3).(n − 1)-dimensional level sets of non-linear functions f(x1, x2, ..., xn) in (n + 1)-dimensional Euclidean space, for n = 1, 2, 3.

In mathematics, a level set of a real-valued function f of n real variables is a set of the form

that is, a set where the function takes on a given constant value c.

When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline. So a level curve is the set of all real-valued solutions of an equation in two variables x1 and x2. When n = 3, a level set is called a level surface (see also isosurface), and for higher values of n the level set is a level hypersurface. So a level surface is the set of all real-valued roots of an equation in three variables x1, x2 and x3, and a level hypersurface is the set of all real-valued roots of an equation in n (n > 3) variables.
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更新时间：2025/6/22 4:53:11