Page 314 - Numerical Analysis Using MATLAB and Excel

Chapter 7 Finite Differences and Interpolation

% size(xxi) = size(yyi) = size(zzi) = 111 71
disp('size(xxi)'); size(xxi); disp('size(yyi)'); size(yyi); disp('size(zzi)'); size(zzi)
size(xxi), size(yyi), size(zzi)
zzi=interp2(x,y,z,xxi,yyi,'cubic'); % Cubic interpolation − interpolates
% all combinations of xxi and yyi and constructs the matrix zzi
mesh(xxi,yyi,zzi); % Plot smoothed data
hold on;
[xx,yy]=meshgrid(x,y); % Grid with original data
plot3(xx,yy,z,'*k'); axis([0 175 0 275 500 503]); grid off; box off
xlabel('x−axis, m'); ylabel('y−axis, m'); zlabel('Height, meters above sea level');
title('Map of Rectangular Land Parcel')
hold off;
% max(x) returns the largest element of vector x
% max(A) returns a row vector which contains the maxima of the columns
% in matrix A. Likewise max(zzi) returns a row vector which contains the
% maxima of the columns in zzi. Observe that size(max(zzi)) = 1 71
% and size(max(max(zzi))) = 1 1
zmax=max(max(zzi)) % Estimates the peak of the terrain
% The 'find' function returns the subscripts where a relational expression
% is true. For Example,
% A=[a11 a12 a13; a21 a22 a23; a31 a32 a33] or
% A=[−1 0 3; 2 3 −4; −2 5 6];
% [i,j]=find(A>2)
% returns
% i =
%
% 2
% 3
% 1
% 3
%
%
% j =
%
% 2
% 2
% 3
% 3
% That is, the elements a22=3, a32=5, a13=3 and a33=6
% satisfy the condition A>2
% The == operator compares two variables and returns ones when they
% are equal, and zeros when they are not equal
%
[m,n]=find(zmax==zzi)
% m =

7−36 Numerical Analysis Using MATLAB® and Excel®, Third Edition
Copyright © Orchard Publications