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单词 Linear interpolation
释义

Linear interpolation

中文百科

线性插值

Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.
In this geometric visualisation, the value at the green circle multiplied by the distance between the red and blue circles is equal to the sum of the value at the red circle multiplied by the distance between the green and blue circles, and the value at the blue circle multiplied by the distance between the green and red circles.

线性插值是数学、计算机图形学等领域广泛使用的一种简单插值方法。

假设我们已知坐标 (x0, y0) 与 (x1, y1)，要得到 [x0, x1] 区间内某一位置 x 在直线上的值。根据图中所示，我们得到

\frac{y - y_0}{x - x_0} = \frac{y_1 - y_0}{x_1 - x_0}. \,\!

由于 x 值已知，所以可以从公式得到 y 的值

y = y_0 + (x-x_0)\frac{y_1 - y_0}{x_1-x_0} = y_0 + \frac{(x-x_0) y_1 - (x-x_0) y_0}{x_1-x_0}

已知 y 求 x 的过程与以上过程相同，只是 x 与 y 要进行交换。

英语百科

Linear interpolation 线性插值

Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.
In this geometric visualisation, the value at the green circle multiplied by the distance between the red and blue circles is equal to the sum of the value at the red circle multiplied by the distance between the green and blue circles, and the value at the blue circle multiplied by the distance between the green and red circles.
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines).
Example of bilinear interpolation on the unit square with the z-values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by colour.

In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
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更新时间：2025/8/10 17:16:03