How to make a surface plot of imported data of a numerical function z=f(x,y)

Hi!

I'm completely new to MatLab and I might not understand the coding ecosystem that MatLab is built upon. What I'm trying to do is really simple in my mind, but I still don't have the know-how of MatLab to do it efficiently.

Here is my issue: I have a python code that calculates a number z that takes two variables x and y, so z = f(x,y). The x-y plane is a rectangle divided up into many equally spaced points, and z would then be the height over each point when plotted. Accordingly, the data is arranged according to equally spaced coordinates x and y, followed by the corresponding z value. Assume there are N x-values and M y-values, each x-y pair is listed on the same row with its corresponding z-value, so something like:

x1 y1 z11

x1 y2 z12

....

x1 yM z1M

x2 y1 z21

x2 y2 z22

...

x2 yM z2M

and so on until the final x-coordinate:

xN y1 zN1

xN y2 zN2

...

xN yM zNM

So, it's essentially a file with NxM rows and 3 columns, with each number separated by a space.

How do I make a surface plot out of this data, where each (xi,yj) is a point on the x-y plane and the corresponding zij is the height above that point?

I feel a little lost even after consulting the help pages, since none of those seem to apply to my case. Particularly, it seems I don't know how to make the surf command know how to interpred the first two columns as coordinate pairs row-by-row, over which the third column is the corresponding height. Maybe surf or surface are not the right ways to think about this problem?

Any help on this would be greatly appreaciated!

[Daniel Bozi]

Interestingly, the surf command returns a figure which is entirely non-sensical, where the only numbers I recognise are the ones on the right hand side of the picture below, which seems to enumerate the rows 1-3456 for each of the 3456 rows of my file.

Answer 1

[Chad Greene]

Just to be clear, you already have the data, and it takes this form

M = [x y z]; 

where x, y, and z are columns?

My next question is, are x and y spaced in some type of grid, like

M =[1 1 5;
    1 2 3; 
    1 3 7; 
    2 1 9; 
    2 2 1; 
    2 3 2; 
    3 1 2; 
    3 2 9; 
    3 3 8]

What I'm asking is, do the first to columns have some kind of repeating pattern that creates a regular grid of points x,y? If so, an easy solution is to use my xyz file functions. Check out the examples on that page. Syntax would be

[X,Y,Z] = xyz2grid(M(:,1),M(:,2),M(:,3); 
surf(X,Y,Z) 
shading interp

If your data are not already in some regular type of grid, let me know and we can discuss that solution.

[Daniel Bozi]

Hi! Thanks for your answer!

Before I look into your link, I just wanted to answer your questions.

• Yes I already have all the numerical data
• Yes, what I understand you're calling x, y and z are indeed columns. I include a screengrab from notepad of what the structure typically looks like (you are only seeing the first x-coordinate here due to the sheer size of the file, and yes the y-coordinate descends from 0 to negative numbers). Notice how the third element in each row is the z-coordinate.
• Hopefully the screengrab will answer your question on the type of grid you are asking about?

So, see below for a typical screengrab from the data file. Thanks very much for your help!

[Chad Greene]

Oh, perfect. It looks like x and y are on regular intervals of 0.05, so it might even be able to do everything in one step:

[X,Y,Z] = xyzread('expo-largeu.dat'); 
surf(X,Y,Z) 
shading interp