Obtaining volume of 3d-shape from crossection points

Hi everyone,

I have the following problem: For a set of given crossection points of a shape in 3d, how can I calculate/approximate the volume of the shape? The shape from which the crossection points are obtained is not necessarily convex, hence convhull volume would be too big. I know the shape looks somewhat ovaloid.

Here are some x y z sample points roughly showing the problem I am dealing with:

intervalPhi = 100;
RadiusA = [5 20 16 20 20 10 3];
RadiusB = [3 10 10 15 12 7 2];
X = [-15 -10 -5 0 5 10 15];
phi = 0:2*pi/intervalPhi:2*pi; phi(end) = [];
x=[]; y=[]; z=[];
for i = 1:length(RadiusA);
  rA = RadiusA(i); rB = RadiusB(i);
  for p = phi
      x(end+1,1) = X(i); y(end+1,1) = rA*cos(p); z(end+1,1) = rB*sin(p);
  end
end
plot3(x,y,z,'.'); grid on; xlim([-20 20]); ylim([-20 20]); zlim([-20 20])

Any help is welcome!

Thanks in advance, Florian