Matlab：非单调散乱数据下griddata替代interp2的插值疑问

Great question! The key difference boils down to how each function is designed to handle input data and execute interpolation:

1. Why interp2 fails with non-monotonic data #

interp2 is built only for regular, structured grid data. It requires your x_measured and y_measured to be either:

• Strictly monotonic vectors (that can be expanded into a grid with meshgrid), or
• Pre-computed grid matrices where rows/columns follow a consistent, ordered, monotonic pattern

When your data is non-monotonic, interp2 can't map the points to a valid rectangular grid structure—it relies on the grid's ordered rows/columns to locate neighboring points for interpolation. Without that predictable structure, it can't determine which points are adjacent to your target (x,y), hence the error.

2. How griddata handles non-monotonic data (and delivers linear interpolation) #

griddata is purpose-built for unstructured/scattered data—exactly your scenario! Here's the breakdown of how its 'linear' option works:

• First, it runs a Delaunay triangulation on your x_measured, y_measured points. This splits the entire 2D region covered by your data into a set of non-overlapping triangles, using all your measured points as vertices.
• When you request interpolation at (x,y), it first finds which triangle contains the target point.
• Finally, it performs linear interpolation within that triangle: it calculates the barycentric coordinates of the target point relative to the triangle's three vertices, then combines the corresponding z_measured values to compute the interpolated z value.

This method doesn't care if your original x/y data is monotonic—it only needs a valid set of scattered points that can form a triangulation (which works for almost all cases unless points are colinear or duplicated).

Quick use case recap #

• Stick with interp2 when you have regular, monotonic grid data (it's faster and optimized for this structure).
• Use griddata for scattered, non-monotonic, or irregularly spaced data (it's flexible and handles these cases seamlessly).

内容的提问来源于stack exchange，提问作者Karl