How can I calculate the angle between two surfaces?

I have two planes with 50x50 points and I want to find the angle between them. The first is a reference plane at z = 0 and the second is a measured surface sample (see graph). I can get matlab to display the surface normal using surfnorm but it doesn't seem to output that data anywhere.

Any help would be very appreciated!

Answer 1

[Roger Stafford]

The command

[Nx,Ny,Nz] = surfnorm(Z)

will return surface normals to surface Z. See:

https://www.mathworks.com/help/matlab/ref/surfnorm.html

However these normals will change from point to point. You need the equation of the best fit plane to obtain a single over-all normal to your points. For a plane with equation

a*x+b*y+c*z+d = 0

its normal is the vector v = [a,b,c]. To make it of unit length do:

v = v/norm(v);

As I think you are aware, the angle between the normals to two planes is the same as the angle between those planes. The angle between two 3D vectors v1 and v2 is:

   ang = atan2(norm(cross(v1,v2)),dot(v1,v2));

[Tobias Reichold]

Thank you very much for your time and help! This has helped a lot!

Answer 2

[David Goodmanson]

Hi Tobias, You get the components of the unit normals with [nx ny nz] = surfnorm(x,y,z) so if you have two surfaces z1 and z2, then

[nx1 ny1 nz1] = surfnorm(x,y,z1);   % each is 50 x 50 in your case
[nx2 ny2 nz2] = surfnorm(x,y,z2);
n1dotn2 = nx1.*nx2 + ny1.*ny2 + nz1.*nz2;
theta = acos(n1dotn2)             % 50 x 50, in radians

In your case the lower surface is the xy plane with n2 = (0,0,1) so you could just use theta = acos(nz1)

[Tobias Reichold]

Here is my code so far:

p00 =   4.234e-05;
p10 =   5.574e-07;
p01 =  -7.654e-08;

for x = 1:50
    for y = 1:50
        f(x,y) = p00 + p10*x + p01*y;
        y = y + 1;
        if y > 50
            x = x+1;
        end
    end
end
figure
surfnorm(f)
hold on
zero_plane = zeros(50,50);
surfnorm(zero_plane)
hold on

f is the tilted plane in a 50x50 matrix. zero_plane is the 50x50 reference plane against which I want to find the tilt angle. When I run the surfnorm I get the normal vectos displayed as shown in the graph:

But I'm not sure how to get the data from the red vectors and turn them into the angle.

I want to get an angle for each vector pair from the reference and the tilted plane, so I will end up with 50x50 angles (2500 seperate values).

[David Goodmanson]

I see what you mean, see the edited answer above with details added.