Function to return Interpolated Value at one query point

I have created an interpolation surface of my experimental data (xA,yA,zA) to a grid with the code below, and now would like to create a function to return the interpolated value at a given single querry point, for example (.001237, .002954).

How can I create an F(x,y) that will return a single value, the interpolated value of z at the point (x,y)?

!---------------------------------------------

[xq,yq] = meshgrid(.001:.00005:.005);

z2 = griddata(xA,yA,zA,xq,yq,'cubic');

!-----------------------------------------------

Answer 1

[Star Strider]

Use the griddedInterpolant function, and then experiment with the actual data to see what gives the best results —

xA = (rand(20,1))*0.005;
yA = (rand(20,1))*0.005;
zA = (rand(20,1))*0.005;

[xq,yq] = meshgrid(.001:.00005:.005);
z2 = griddata(xA,yA,zA,xq,yq,'cubic')

z2 = 81×81

0.0020 0.0019 0.0019 0.0018 0.0018 0.0017 0.0016 0.0018 0.0021 0.0021 0.0020 0.0020 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0014 0.0013 0.0012 0.0010 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0004 0.0020 0.0020 0.0019 0.0019 0.0018 0.0017 0.0019 0.0021 0.0021 0.0021 0.0020 0.0019 0.0019 0.0018 0.0018 0.0017 0.0016 0.0015 0.0014 0.0014 0.0012 0.0011 0.0010 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0004 0.0021 0.0020 0.0020 0.0019 0.0018 0.0021 0.0022 0.0022 0.0021 0.0021 0.0020 0.0019 0.0019 0.0018 0.0017 0.0016 0.0016 0.0015 0.0014 0.0013 0.0012 0.0011 0.0010 0.0009 0.0008 0.0007 0.0005 0.0005 0.0004 0.0004 0.0021 0.0021 0.0020 0.0019 0.0022 0.0023 0.0022 0.0022 0.0021 0.0020 0.0020 0.0019 0.0018 0.0018 0.0017 0.0016 0.0015 0.0015 0.0014 0.0013 0.0012 0.0011 0.0010 0.0009 0.0008 0.0006 0.0005 0.0005 0.0004 0.0004 0.0022 0.0021 0.0021 0.0023 0.0023 0.0022 0.0022 0.0021 0.0021 0.0020 0.0019 0.0019 0.0018 0.0017 0.0016 0.0016 0.0015 0.0014 0.0013 0.0013 0.0012 0.0011 0.0010 0.0009 0.0008 0.0006 0.0005 0.0005 0.0004 0.0004 0.0022 0.0022 0.0024 0.0023 0.0023 0.0022 0.0022 0.0021 0.0020 0.0020 0.0019 0.0018 0.0017 0.0017 0.0016 0.0015 0.0014 0.0014 0.0013 0.0012 0.0011 0.0010 0.0010 0.0009 0.0007 0.0006 0.0005 0.0004 0.0004 0.0004 0.0023 0.0024 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.0018 0.0018 0.0017 0.0016 0.0015 0.0015 0.0014 0.0013 0.0012 0.0012 0.0011 0.0010 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0004 0.0003 0.0025 0.0024 0.0024 0.0023 0.0022 0.0022 0.0021 0.0020 0.0019 0.0019 0.0018 0.0017 0.0016 0.0016 0.0015 0.0014 0.0013 0.0013 0.0012 0.0011 0.0010 0.0010 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0004 0.0003 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0020 0.0020 0.0019 0.0018 0.0017 0.0016 0.0016 0.0015 0.0014 0.0013 0.0013 0.0012 0.0011 0.0011 0.0010 0.0009 0.0008 0.0008 0.0007 0.0006 0.0005 0.0004 0.0004 0.0003 0.0025 0.0024 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.0018 0.0017 0.0017 0.0016 0.0015 0.0014 0.0014 0.0013 0.0012 0.0011 0.0011 0.0010 0.0009 0.0009 0.0008 0.0007 0.0007 0.0006 0.0005 0.0004 0.0004 0.0003

F = griddedInterpolant(z2);
xp = 0.001237;
yp = 0.002954;
zp1 = F(xp, yp)

zp1 = 0.0020

% zp2 = F(yp, xp)

figure
surf(xq,yq,z2)
hold on
stem3(xp, yp, zp1, '^r', 'MarkerSize',10, 'MarkerFaceColor','r')
% stem3(yp, xp, zp2, '^g', 'MarkerSize',10, 'MarkerFaceColor','g')
hold off
xlabel('x')
ylabel('y')
view(-45,30)

It would help to have the actual data.

.

[Thomas Kane]

Thank you! This is just what I was looking for. Yes, I will experiment with the interpolation type to fine tune. Your code and the beautiful graphic are wonderfully illustrative. Thanks again.

[Star Strider]

As always, my pleasure!

I very much appreciate your compliment!