# Finding surface height at x,y coordinates

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LMS on 19 Apr 2016
Commented: LMS on 19 Apr 2016
Dear all,
using the mapping toolbox, I've created an interpolated surface from a scattered dataset. x,y,z are read from a file.
[yi,xi] = meshgrid(min(y):0.5:max(y), min(x):0.5:max(x)); % sets up mesh grid for x/y coords, step-size=0.5
zi = griddata(y,x,z,yi,xi,'linear'); % interpolates z values
surfm(yi,xi,zi);
Now, I need to read out the interpolated zi value at a given location (say... -10, -50). I feel like there's a very simple solution, but half an hour of googling and reading up in the documentation hasn't led me to success. Could someone point me in the right direction? Thank you!
Stephen23 on 19 Apr 2016
What do you mean by "I need to read out the interpolated zi value": do you want to click on the figure and get the z value, or do you want to calculate the z value by passing the x,y location values?

Teja Muppirala on 19 Apr 2016
Instead of GRIDDATA, I think "scatteredInterpolant" is what you want. This creates an object that you can use to query points freely.
% Make some data
x = -30+60*rand(1000,1);
y = -30+60*rand(1000,1);
z = sin(x/10).*sin(y/15);
% set up the scatteredInterpolant object
method = 'linear';
extrap = 'none';
S = scatteredInterpolant(x,y,z,method,extrap)
% Evaluate on the grid
[yi,xi] = meshgrid(min(y):0.5:max(y), min(x):0.5:max(x)); % sets up mesh grid for x/y coords, step-size=0.5
zi = S(xi,yi); % <-- This is equivalent to zi = GRIDDATA(...)
% You can call S(x,y) to evaluate at specific points
S(-10,20)
LMS on 19 Apr 2016
Thank you SO MUCH! This works perfectly.

John D'Errico on 19 Apr 2016
You have already used griddata! It looks like you have found a code snippet, but have no clue as to what it does or why it works. So read the help for griddata.
Now you wish to interpolate at some general point. You can either use griddata again at that general point, or since you have apparently now formed a regular grid you COULD use interp2.
The latter seems logical, but it is in fact worse, because then you have two sources of interpolation error. So just use griddata, as you did already.
LMS on 19 Apr 2016
JFC John, you're killing me. This is my code and I absolutely do understand what it does. I've been through the documentation of "griddata", but it doesn't mention how to query for coordinates. I tried every phrasing I could come up with but I seem to be missing something. Would it kill you to get off your high horse and just give me the correct way to code this?

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