% Farouki data
% 6-20-96  svd3dfars.m
% modification of bana3dn_herm.m
m1 = 6
n1 = 3		% number of data points in each direction: rows, columns
far=[-3.0 -1.2  0.0
-3.0  0.0  0.1
-2.7  1.3 -0.1
-2.0 -1.0 -0.2
-1.7  0.2  0.3
-1.5  1.6  0.0
-1.1 -1.5  1.0
-0.6 -0.1  1.1
-0.8  1.2  0.3
-0.4 -0.8 -0.3
 0.0  0.1  0.1
 0.2  1.0  0.5
 0.8 -1.0  0.3
 1.5 -0.3  0.4
 2.2  1.5  0.6
 2.3 -1.7  0.2
 3.0 -0.1  0.3
 3.3  1.2  0.5 ];
ax = far(:,1);ay = far(:,2);az = far(:,3);
axx=reshape(ax,n1,m1)';
ayy=reshape(ay,n1,m1)';
azz=reshape(az,n1,m1)';

%number of rows & columns in surface representation:
k=5;
n11=k*(n1-1)+1;
m11=k*(m1-1)+1;
xx=linspace(1,n1,n1)';yy=linspace(1,m1,m1)';
xxx=linspace(1,n1,n11)';yyy=linspace(1,m1,m11)';

[u,s,v]=svd(axx);
s = diag(s);
z = zeros(m11,n11);
for j=1:3
  spx = spline(xx,v(:,j), xxx);
  spy = spline(yy,u(:,j), yyy);
  z = z + s(j)*spy*spx';
end
splx=z;

[u,s,v]=svd(ayy);
s = diag(s);
z = zeros(m11,n11);
for j=1:3
  spx = spline(xx,v(:,j), xxx);
  spy = spline(yy,u(:,j), yyy);
  z = z + s(j)*spy*spx';
end
sply=z;

[u,s,v]=svd(azz);
s = diag(s);
z = zeros(m11,n11);
for j=1:3
  spx = spline(xx,v(:,j), xxx);
  spy = spline(yy,u(:,j), yyy);
  z = z + s(j)*spy*spx';
end
splz=z;

subplot(1,1,1)
plot3(axx,ayy,azz,'o')

subplot(1,2,1)
view(50,20)
subplot(1,2,2)
view(45,20)
clf

subplot(2,2,1)
surf(splx,sply,splz,splz)

subplot(2,2,2)
view(45,20)

subplot(2,2,3)
view(135,20)

subplot(2,2,4)
view(130,20)