% trigfield8.m generates field values at random locations

numpoints= 100;
x        = 5*randn(numpoints,1);
y        = 5*rand(numpoints,1);
Z        = zeros(numpoints,1);

m        = 100;                                 % number of Fourier modes

A        = randn(1,m)*sqrt(2/m);                % amplitudes of Fourier modes
phi      = 2 * pi * rand(m,1);                  % random phase
norm     = sqrt(-2*log(rand(m,1)));             % magnitudes of wave numbers
theta    = 2 * pi * rand(m,1);                  % arguments of wave numbers
K        = [norm.*cos(theta) norm.*sin(theta)]; % isotropic wave numbers

for i=1:numpoints,
  Z(i) = A * cos(K*[x(i); y(i)] + phi);         % compute field value at x,y
end

figure(1)
clf

subplot(2,1,1)
plot(x,y,'*');
axis([min(x) max(x) min(y) max(y)]);
title('Locations at which the field is sampled');

subplot(2,1,2)
tag3(x,y,Z)
view(-10,30)
title('Data points in 3d')

rotate3d on