Octave Error: surface: rows (Z) must be the same as length (Y) and columns (Z) must be the same as length (X)

Octave shows this error when trying to mesh a matrix:

>error: surface: rows (Z) must be the same as length (Y) and columns (Z) must be the same as length (X)*

N =

        0        0   0.0057
   1.0000        0   0.0165
   1.0000   1.0000   0.0145
        0   1.0000   0.0038
   0.5000   0.5000        0
   0.6667   0.5000   0.0001
   0.3333   0.5000   0.4560
   0.6443   0.5833   0.8280
   0.5833   0.6443   0.5774
   0.5000   0.6667   0.0000
   0.4167   0.6443   0.0001
   0.3557   0.5833   0.5898
   0.3557   0.4167   0.6540
   0.4167   0.3557   0.6016
   0.5000   0.3333   0.0000
   0.5833   0.3557   0.0001
   0.6443   0.4167   0.7667
   0.5000   0.2083   0.1617
   0.2083   0.5000   0.1576
   0.5000   0.7917   0.0048
   0.7917   0.5000   1.0050
   0.2961   0.7039   1.0004
   0.7039   0.2961   1.0027
   0.7039   0.7039   1.0024
   0.2961   0.2961   1.0008

tx= N(:,1);
ty= N(:,2);
tz= N(:,3);

length(tx);
length(ty);
length(tz);

figure(1)
[x,y] = meshgrid (tx, ty);
mesh(tx,ty,tz);
xlabel ("tx");
ylabel ("ty");
zlabel ("tz");

I am trying to mesh the matrix N using mesh but it keeps showing up the above error. I've already checked the size of X, Y and Z using the command length and it they all are the exact same size. So I don't understand what is the reason behind the error.

Also I have tried changing the command mesh(tx,ty,tz) to mesh(x,y,tz) but it is still the same.

Pd: I used the reference page from Octave to learn about the mesh command in this link: https://docs.octave.org/v6.2.0/Three_002dDimensional-Plots.html and also checked the code for the mesh of the example given.

Thanks in advance if someone can answer me.

The problem is that you don't have a surface here, but a (x,y) irregular scatter with the z values on it. You need first to interpolate your available z values onto on regular (x,y) grid: for this, you can use the griddata function:

N =[
        0        0   0.0057
   1.0000        0   0.0165
   1.0000   1.0000   0.0145
        0   1.0000   0.0038
   0.5000   0.5000        0
   0.6667   0.5000   0.0001
   0.3333   0.5000   0.4560
   0.6443   0.5833   0.8280
   0.5833   0.6443   0.5774
   0.5000   0.6667   0.0000
   0.4167   0.6443   0.0001
   0.3557   0.5833   0.5898
   0.3557   0.4167   0.6540
   0.4167   0.3557   0.6016
   0.5000   0.3333   0.0000
   0.5833   0.3557   0.0001
   0.6443   0.4167   0.7667
   0.5000   0.2083   0.1617
   0.2083   0.5000   0.1576
   0.5000   0.7917   0.0048
   0.7917   0.5000   1.0050
   0.2961   0.7039   1.0004
   0.7039   0.2961   1.0027
   0.7039   0.7039   1.0024
   0.2961   0.2961   1.0008]

tx= N(:,1);
ty= N(:,2);
tz= N(:,3);

txi = linspace(0,1,101);
tyi = linspace(0,1,101);
[x,y] = meshgrid (txi, tyi);
z =  griddata (tx, ty, tz, x, y)

figure(1)
mesh(x,y,z);
xlabel ("tx");
ylabel ("ty");
zlabel ("tz");

Alternatively, you can use plot3 to directly plot your scatter in in the (x,y,z) space. But floating points in a 3D space are difficult to visualize, so it can help for instance plotting also some bars from the (x,y) plane to each point:

figure(2)
plot3(tx,ty,tz,'o')
hold on
for k = 1:length(tx)
    plot3([tx(k) tx(k)],[ty(k) ty(k)],[0 tz(k)],'b')
endfor
hold off
xlabel ("tx");
ylabel ("ty");
zlabel ("tz");