三维网格插值的原理(a question about three-dimensional interpolation(interp3))

我想知道interp3是如何实现三维的插值的，是将空间划分为网格之后在三个坐标轴上分别对数据点插值吗？那坐标轴交点处的数据如何确定呢？（I am wondering how function 'interp3' does the three-dimensional interpolation? Does it divided the space into meshgrids and interpolate data points on each of the three axes? If so, how is the data at the intersection of the axes determined?)

Answer 1

[Raghav]

Hi,

Based on your question, I understand that you want to know about the working of interp3 function in MATLAB.

interp3 is a MATLAB function that performs 3D interpolation using various methods such as linear, nearest neighbour, and cubic interpolation. The function divides the 3D space into a regular grid of points and then interpolates the values of the function at these grid points based on the values at the input data points.

The data at the intersection of the axes, also known as the mesh points or grid points, are determined based on the interpolation method used. For example, in linear interpolation, the values at the mesh points are determined by connecting the input data points using straight lines, while in cubic interpolation, the values at the mesh points are determined using cubic polynomials that fit the input data points and their derivatives.

In general, the accuracy of the interpolated values at the mesh points depends on the density and distribution of the input data points, as well as the interpolation method used. Higher-order interpolation methods such as cubic interpolation can provide more accurate results than lower-order methods such as linear interpolation, but they may also require more input data points to achieve the same level of accuracy.

For more information you can refer to the below mentioned documentation:

https://www.mathworks.com/help/matlab/ref/interp3.html

Hope this helps.

Regards,

Raghav Bansal