How to generate a curve describing a contour on 3D scatter plot

Hey,

I need some help defining the equation of the contour profile at a specified elevation from a list of 3D coordinates.

• I have a matrix A = [448100, 3] coordinates of X, Y, Z.
• Z ranges from 600 to 650 meters.
• I would like to mathematically describe the contours so I can extract a table of coordinate values at that specific elevation (Xs and Ys).
• Then I would be computing the contours at every meter interval so I have 'contour equations'

Does MATLAB have a function or does anyone have some idea on how I could do that?

The reason I would like to do this, is because I have two (2) data sets and I would like to measure movement between the two. If I define the same elevation contours on both data sets, I can cacluate the distance change of each contour line by generating points on each of the curves and then I can measure the average distance moved.

I have been able to isolate a fixed curve of the points, but I believe I am encountering issues generating a fitted curve on the values because it violates the principle definition of a function (only one y for every valid x).

Any ideas to overcome this?

*on the attached screenshot, all x and y have the same z value.

Answer 1

[Star Strider]

I’m not certain what you want to do, however it is possible (although not straightforward) to extract the various contours using the M contour matrix output. Specify the contour levels using the levels input argument.

Defining the function as might be an option.

[Brent Majcher]

Thank you so much for responding and offering some advice.

The contour function is confusing to me. I have been able to generate the contours with:

[M,c] = contour(X,Y,Z);

This plots the attached photo... Matrix M is a size 2x10271... and I don't know where the Z values are stored. Can you offer some advice to what this function does? Are the z values stored in the c object?

Thanks again

[Star Strider]

The ‘z’ values are the values of the contour.

This illustrates how to get the levels from a contour plot —

[X,Y,Z] = peaks(50);

figure
[M,C] = contour(X, Y, Z, 'ShowText',1);

Levels = C.LevelList                                                    % These Are The 'Z' Values For Each Contour

Levels = 1×8

-6 -4 -2 0 2 4 6 8

for k = 1:numel(Levels)
    idx = find(M(1,:) == Levels(k));
    ValidV = rem(M(2,idx),1) == 0;
    StartIdx{k,:} = idx(ValidV);
    VLen{k,:} = M(2,StartIdx{k});
end

figure
k1 = 4;                                                                 % Index For Levels 'k1'
hold on
for k2 = 1:numel(StartIdx{k1})
    idxv = StartIdx{k1}(k2)+1 : StartIdx{k1}(k2)+VLen{k1}(k2);          % Index For Contour 'k1'
    xv = M(1,idxv);
    yv = M(2,idxv);
    plot(xv, yv)
end
hold off
xlabel('M(1,:)')
ylabel('M(2,:)')
title(sprintf('Contour Level %.1f', Levels(k1)))
axis('equal')

Since the levels are functions of both ‘x’ and ‘y’, there will be a value of ‘z’ for each (x,y) pair for each section of the contour.

I am not certain how to create a mathematical model for each contour, since that depends on the surface being contoured.

.