Understanding 3D surface plot - matlab

Question

As in this link, I have:
| 0.1 0.2 0.3 0.4
----------------------
1 | 10 11 12 13
2 | 11 12 13 14
3 | 12 13 14 15
4 | 13 14 15 16
Y = [0.1 0.2 0.3 0.4];
X = [1 2 3 4];
Z = [10 11 12 13; 11 12 13 14; 12 13 14 15; 13 14 15 16];
I plotted the surface Z using the command "surf(X,Y,Z)" in matlab. I got:
But really I don't understand the plotted surface. Can someone explain to me in details (in a text) what happens in this surface? For example: how can we observe the point (2,0.2,12)?

Answer 1

Include some labels and a colorbar and everything should be clear:
Y = [0.1 0.2 0.3 0.4];
X = [1 2 3 4];
Z = [10 11 12 13; 11 12 13 14; 12 13 14 15; 13 14 15 16];
surf(X,Y,Z)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Z')
As suggested in the comments you can find your point on the surface by adding:
hold on;
plot3(2,0.2,12,'ro','MarkerSize',10,'MarkerFaceColor','r');
it then appears as a red dot.
Your table contains 16 points, these are plotted and the area inbetween, colored according to the applied colormap with the lowest z-value of the group of 4, which is according to the doc the surface height.
Actually it would be cleaner coding if you'd include the following line before the plot:
[X,Y] = meshgrid(X,Y);
this way all your input variables get the same dimensions:
X =
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
Y =
0.1 0.1 0.1 0.1
0.2 0.2 0.2 0.2
0.3 0.3 0.3 0.3
0.4 0.4 0.4 0.4
Z =
10 11 12 13
11 12 13 14
12 13 14 15
13 14 15 16
In case of surf the function does that for you, but other plotting functions are may not that tolerant.