Total force acting on open surface: How do I integrate a 3D vector field?

Hi,

I would like to calculate the total force acting on a 3D open surface. Initially, I have a 3D ellipsoid section created by stretching a spheric section along x,y, and z.

    phi = linspace(0,2*pi,100);
    theta = linspace(-pi/4,pi/2,100); %-pi/2 to pi/2 would give a closed sphere
    rho = 1;
    [theta2,phi2] = meshgrid(theta,phi);
    [X,Y,Z] = sph2cart(theta2,phi2,rho);
    X2 = X; % no stretching along X
    Y2 = 1.5*Y % stretching along Y
    Z2 = Z*0.5-min(Z(:)*0.5); % stretching along Z and alingin bottom of ellipsoid with z=0
  surf(X2,Y2,Z2);

The result is a set of 100*100 XYZ coordinates that define my ellipsoid section. The corresponding force values are contained in a 100x100 matrix f, so each XYZ coordinate is assigned a force value from f.

How can the total force acting on the entire surface of the ellipsoid section be calculated from the X2,Y2,Z2,f values? I have tried to work my way through trapz, isosurface, and alphatriangulation, but couldn't solve the problem.

Thanks for you help...