How to do quadratic interpolation in two dimensions on a plane

I'm working on a project which analyzes the air velocity in front of a fan. We took measurments at various positions on an x-y plane placed perpendicular to the air flow, and read velocity in the z-direction only. I tried to create a surface plot to help visually show what the flow is like, but since I only have a few data points it looked really jagged. I then tried to use the interp2 function to try and smooth out the points but it came out like this:

I realize the interp2 is a linear interpolation technique, but is there a way we could do a quadratic fit in two dimensions? Since this should look more like a bell curve, as you would expect. All of this data is recorded in matricies, with identical x and y matricies for the plane, and a U matrix for the velocities. I appreciate any help I can get!

[jessupj]

see https://www.mathworks.com/help/curvefit/fit.html, specifically the section on fitting polynomial surfaces.... you probably want 'poly22'

[Torsten]

Did you read this page ?

https://de.mathworks.com/help/matlab/visualize/representing-a-matrix-as-a-surface.html

[Kayson Christensen]

I just looked at both those pages, and it seems they only handle two dimensional interpolation, or they require an array of inputs instead of a matrix. If I'm just not seeing it I understand, but is there something we can do if I have data values in X, Y, and Z directions, all specified as their own vectors (u,v,w) and recorded in a 3D matrix? I did use the meshgrid function to create a successful plot with my data, its just more choppy than I want.

Thank you for your time!

[Matt J]

X, Y, and Z directions, all specified as their own vectors (u,v,w) and recorded in a 3D matrix?

You need to attach an example of this data. You seemed to be saying in your initial post that Z is a function of X,Y. They aren't all independent of each other.

[Kayson Christensen]

My data is just a grid of numbers, with each data point being a different x-y coordinate. There are three values of Z, 0.5, 0, and -0.5. Each value of Z has its own grid of numbers, representing different planes. I attached a sample of one x-y plane. The values recorded are direction dependent, where U is in the x-direction, V in the y-direction, and W in the Z direction (upward). So, U, V, and W are all dependent on X, Y, and Z. The cubic function of interp2 might work, I'll try that soon.

[Torsten]

As it seems, the planes are in the direction of the outcoming air and not perpendicular to it ? In 1.jpg, one velocity direction (U,V or W) is listed ?

[Kayson Christensen]

The planes are set parallel with the flow from the fans (as if you're looking down on the full setup). In that photo, the U velocity direction was shown. There are two more charts like in that photo recording the data for V and W at the same plane. It's a complicated setup, but I found it was the easiest way of recording accurate data.

Answer 1

[Matt J]

I realize the interp2 is a linear interpolation technique

No, you have several alternatives to linear interpolation with interp2,

https://www.mathworks.com/help/matlab/ref/interp2.html#btyq8s0-1-method

Maybe try with 'cubic'?

[Kayson Christensen]

That worked perfectly! Pardon my inexperience with the software, I didn't even realize you could use multiple methods with the interp2 command. Thank you!

[Matt J]

You're quite welcome but please Accept-click the answer to indicate that it worked.