scatter plot and definition of contour levels in z coordinate

Dear all,

I have created a scatter plot from x, y and z coordinates for a bed topography characterization around vertical structures. In plane, they have different colors according to the z range of values. The scatter plot do not seem to be a discrete representation of the data due to the high number of points.

Now, I would like to know if it is possible or not to create a contour plot, i.e., to define contour lines in the same plot (within the scatter plot). If yes, how can I do it? I have tried the contour and contourf functions but it always returns an error as the x and the y coordinates are columns of data and not matrices.

Thank you in advance!

Kind regards

Answer 1

[Kelly Kearney]

An alternative to gridding your data would be to use one of the scattered-data contouring functions from the File Exchange. These work best when your data is not too noisy (relative to the contour levels you choose):

% Fake data

x = randn(500,1);
y = randn(500,1);

z =  3*(1-x).^2.*exp(-(x.^2) - (y+1).^2) ...
   - 10*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2) ...
   - 1/3*exp(-(x+1).^2 - y.^2); % peaks

% Plot

tri = delaunay(x,y);
tricontour(tri,x,y,z,-6:6);
hold on;
scatter(x,y,[],z,'filled');

[Ana Alves]

Thanks. But, how can I adapt that code to my values? The x and y are not random values, and how do you calculate the z values?They should be given data.

Thanks

[Kelly Kearney]

I assumed that you already have your x, y, and z values, read from whatever data source you're using into equal-sized vectors. But I don't have access to your data, so I created some fake points. The z equation there is simply the peaks one used in a lot of Matlab examples (surf, contour, etc.).

[Ana Alves]

Hi Kelly,

Thanks for your answer...I replaced the fake data by my values in x, y and z. When I run the code I returned the following error:

Undefined function 'tricontour' for input arguments of type 'double'.

Error in code (line 17) tricontour(tri,x,y,z,v);

Then Ithought that there was sth wrong with the tricontour function, so I tried to run another case, the one available in this link:http://www.mathworks.com/matlabcentral/fileexchange/38858-contour-plot-for-scattered-data/content/tricontour.m

But, a similar error I received:

Undefined function 'tricontour' for input arguments of type 'double'.

Error in code_example (line 21) [C,h]=tricontour(tri,x,y,z,v);

Do you have an idea of what is the source of the problem?

Thank you very much!

[Mike Garrity]

It sounds like you don't have tricontour installed. It's not actually a part of MATLAB. It was written by Duane Hanselman, and you can get it from the File Exchange:

http://www.mathworks.com/matlabcentral/fileexchange/38858-contour-plot-for-scattered-data/content/tricontour.m

[Ana Alves]

So, if I unzip that file in the same directory of my code, it will work? Thanks

[Ana Alves]

It runs now, but I am not sure about if this do what I want, what I am looking for is for an image like the attached here.

Thanks

[Kelly Kearney]

Well, that's not a contour plot. I think using a scattered interpolant and pcolor/image will get what you want. I chose natural neighbor interpolation with no extrapolation, which looks similar to your example:

% Fake data

x = randn(500,1);
y = randn(500,1);

z =  3*(1-x).^2.*exp(-(x.^2) - (y+1).^2) ...
   - 10*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2) ...
   - 1/3*exp(-(x+1).^2 - y.^2);

% Plot

xg = linspace(min(x), max(x), 100);
yg = linspace(min(y), max(y), 100);
[xg,yg] = meshgrid(xg,yg);
F = scatteredInterpolant([x y], z, 'natural', 'none');
zg = F(xg,yg);

hp = pcolor(xg,yg,zg);
shading flat;
hold on;

hs = scatter(x,y,2,z,'filled');
set(hs, 'markeredgecolor', 'w');

[Lihuang Zhu]

Exactly what I am looking for. I just don't know the terminology of this kind of plot. Thank you!

Answer 2

[Walter Roberson]

Assuming that you have a column of data corresponding to each (x, y, z) triple... call the matrix xyzV

xspacing = 0.01;
yspacing = 0.01;
zspacing = 0.001; 
x = xyzV(:,1);
y = xyzV(:,2);
z = xyzV(:,3);
V = xyzV(:,4);
xidx = 1 + round((x - x(1))/xspacing);
yidx = 1 + round((y - y(1))/yspacing);
zidx = 1 + round((z - z(1))/zspacing);
Vcuboid = accumarray([xidx, yidx, zidx], V);

After that you are left with the question of how you want to take a contour plot of a cuboid of values. You might want to use isosurface() or you might want to use slice()

[Ana Alves]

Hi Walter,

Thanks for your reply. However, when I tried it I received an error message concerning the line (V=xyz(:,4)); I understand that in this line as well as in the previous three lines you are identifying the variables, so I created a fourth colums of the file of zero values, but It doesn't work also.

Why did you defined a spacing for z different for the other two coordinates? They should be all of 1cm distant from each other.

What does this code exactly? it creates a cube of values? But if I want to represent in plan like a uniform surface with x and y values, and then the z coordinate as different colors and isolines...

Thanks in advance.

[Walter Roberson]

Your z has values such as -0.083 and -0.084 so the difference between z is 0.001 . Your other values are only 0.01 apart.

Before my answer I wrote "Assuming that you have a column of data corresponding to each (x, y, z) triple... call the matrix xyzV". This would be for the case where there is a value at each distinct (x,y,z) triple. It appears that I was misreading the data.

xspacing = 0.01;
yspacing = 0.01;
x = xyz(:,1);
minx = min(x);
y = xyz(:,2);
miny = min(y);
z = xyz(:,3);
xidx = 1 + round((x - minx)/xspacing);
yidx = 1 + round((y - miny)/yspacing);
zrectangle = accumarray([xidx, yidx], z);

xvals = (0:size(zrectangle,1)-1)*xspacing + minx;
yvals = (0:size(zrectangel,2)-1)*yspacing + ymin;

contour(xvals, yvals, zrectangle);  %if you want a contour plot

[Ana Alves]

Hi Walter,

This code:

%codigo_forum
close all
clear all
clc
L1=load('data_1cm_1cm.dat');
L2=L1/0.05;

xspacing = 0.01;
yspacing = 0.01;
x = L2(:,1);
minx = min(x);
y = L2(:,2);
miny = min(y);
z = L2(:,3);
xidx = 1 + round((x - minx)/xspacing);
yidx = 1 + round((y - miny)/yspacing);
zrectangle = accumarray([xidx, yidx], z);
xvals = (0:size(zrectangle,1)-1)*xspacing + minx;
yvals = (0:size(zrectangle,2)-1)*yspacing + miny;
contour(xvals, yvals, zrectangle);

returns an error:

Error using contour (line 81)
The size of X must match the size of Z or the
number of columns of Z.

Error in codigo_forum (line 20)
contour(xvals, yvals, zrectangle);  %if you want a
contour plot

Could you please help me?

Thank you very much,

[Walter Roberson]

contour(xvals, yvals, zrectangle.');

[Ana Alves]

Hi Walter,

Thanks,it is working now, but I am not sure if is this what I am looking for...I obtained the plot attached.

Kind regards,

[Ana Alves]

Hi, I am looking for sth like this (see attached file), Thanks!