matlab 3d surface plot from scatter3 data

Question

I want to plot a 3d scatter plot with a surface plot on the same figure, so that I end up with something like this:

I would have thought that the code below might have achieved what I wanted but obviously not. I have x, y and z data to plot a scatter3:

x = [1 1 1 1 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 0.8 0.8 0.8 0.8 0.75 0.75 0.75 0.75]';
y = [0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1]';
z = [0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3]';

scatter3(x,y,z)
hold on

And now add a surface??

p = [x y z];
surf(p)

Any ideas? Thanks.

Answer 1

The problem is that surf is treating your matrix p as a 2D array of z values, with integer values for x & y. Fortunately, surf has more than one way to enter values (see http://au.mathworks.com/help/matlab/ref/surf.html).

Try this:

x = [1 1 1 1 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 0.8 0.8 0.8 0.8 0.75 0.75 0.75 0.75]';
y = [0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1]';
z = [0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3]';

xr = reshape(x, 4, 5);
yr = reshape(y, 4, 5);
zr = reshape(z, 4, 5);

surf(xr, yr, zr)

xlabel('x')
ylabel('y')
zlabel('z')

In this case, surf expects a 2D array of x, y, and z values (as they would appear if looking at them top down). This way, surf knows which vertices to connect into a surface. Fortunately this can be easily achieved with your data by simply reshaping the vectors into matrices.

In future, if all your points lie on the same x and y coordinates, you could replace xr with [1, 0.95, 0.85, 0.8, 0.75] and yr with [0.3, 0.2, 0.15, 0.1] and surf will convert them into arrays for you.

Answer 2

I had to deal with the same problem; I thought it might be still useful to answer this question

You need to create a compatible z-axis/matrix. I wrote scatt2surfto convert scatter data to surfaces. I hope it helps.

clear all;clc

xx = [1 1 1 1 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 0.8 0.8 0.8 0.8 0.75 0.75 0.75 0.75];
yy= [0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1];
zz= [0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3 0.1 0.15 0.2 0.3];


[x1,y1,z_surf]=scatt2surf(xx,yy,zz);
figure(3)
surf(x1,y1,z_surf);
xlabel('\it X');ylabel('\it Y');zlabel('\it Z');
colormap(hot)

hold on
scatter3(xx,yy,zz,[],zz,'o','filled','MarkerEdgeColor','none');
grid on;


function [x1,y1,z_surf]=scatt2surf(xx,yy,zz)   
    x1= unique(round(xx,7));
    y1=unique(round(yy,7));
    z_surf=ones(length(x1),length(y1));
    for i=1:length(x1)
        for j=1:length(y1) 
        indx=[xx==x1(i) & yy==y1(j)];
        z_surf(i,j)=zz(indx);   
        end
    end
    z_surf=z_surf';
end