Page 313 - Numerical Analysis Using MATLAB and Excel

Interpolation with MATLAB

a. Denoting the width as the x – axis , the depth as the y – axis and the height as the z – axis ,
plot the given data to form a rectangular grid.

b. Interpolate the value of at x = 108 m, and y = 177 m.
z
c. Compute the maximum height and its location on the x – y plane.
Solution:

The MATLAB script and plot are shown below and explanations are provided with comment
statements.

% This script is for Example_7_15
%
x=0: 25: 175; % x−axis varies across the rows of z
y=0: 25: 275; % y−axis varies down the columns of z
z=[500.08 500.15 500.05 500.08 500.14 500.13 500.09 500.15;
500.12 500.01 500.11 500.18 500.15 500.12 500.05 500.15;
500.13 500.12 500.09 500.11 500.11 500.05 500.15 500.02;
500.09 500.17 500.17 500.14 500.16 500.09 500.02 500.11;
500.08 500.09 500.13 500.18 500.14 500.14 500.14 500.15;
500.15 500.10 500.11 500.11 500.12 500.13 500.14 500.12;
500.17 500.12 500.13 500.18 500.13 500.15 500.17 500.11;
500.13 500.14 500.13 500.09 500.14 500.16 500.17 500.14;
500.15 500.09 500.14 500.18 500.17 500.08 500.13 500.09;
500.12 500.15 500.14 500.01 500.16 500.12 500.11 500.10;
500.02 500.19 500.01 500.08 500.12 500.02 500.16 500.12;
500.19 500.21 500.17 500.03 500.17 500.09 500.14 500.17];
%
mesh(x,y,z); axis([0 175 0 275 500 502]); grid off; box off
xlabel('x−axis, m'); ylabel('y−axis, m'); zlabel('Height, meters above sea level'); title('Parcel
map')
% The pause command below stops execution of the program for 10 seconds
% so that we can see the mesh plot
pause(10);
z_int=interp2(x,y,z,108,177,'cubic');
disp('Interpolated z is:'); z_int
[xx,yy]=meshgrid(x,y);
xi=0: 2.5: 175; % Make x−axis finer
% size(xi); % Returns a row vector containing the size of xi where the
% first element denotes the number of rows and the second is the number
% of columns. Here, size(xi) = 1 71
disp('size(xi)'); size(xi)
yi=0: 2.5: 275; % Make y−axis finer
disp('size(yi)'); size(yi)
[xxi,yyi]=meshgrid(xi,yi); % Forms grid of all combinations of xi and yi

Numerical Analysis Using MATLAB® and Excel®, Third Edition 7−35
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