Grouping 2D contour plots into a 3D Figure

HI,

I have recently used the contour plots to map the velocity of a wind tunnel at different distances from the inlet. I am wondering how I can add these 2D contours (screenshot 1) into a 3D plotshowing multiple 2D contours on the same figure. I have the data stored in 5*5 Matrices (Screenshot 2), would i need to change this data into a different form for 3D plotting. The third screenshot is a example, similar to what I am hoping to achieve.

I am quite new to matlab so any help would be much appriciated.

Thanks

Answer 1

[Cris LaPierre]

I would stack you 5x5 matrices together to create a volume V. I would then use meshgrid to create X, Y and Z arrays the same size as V. You might then be able to use contourslice or slice functions in MATLAB to create your desired figure.

x = [1945 2445 2945];
y = [-750	-375	0	375	750];
z = [230, 115, 0, -115, -230];
[X,Y,Z] = meshgrid(x,y,z);

V1=[3.649	5.354	5.208	5.441	3.456
3.264	5.725	5.679	5.728	2.667
2.931	5.7741	5.744	5.782	2.202
2.653	5.775	5.78	5.674	2.003
1.738	5.743	5.778	5.659	1.572];

V2 = V1 + rand(size(V1))*3-1.5;
V3 = V1 + rand(size(V1))*3-1.5;
V = cat(3,V1,V2,V3);
% Rearrange so columns = X, rows = Y, pages = Z
V = permute(V,[2,3,1]);
% contourslice
contourslice(X,Y,Z,V,[x],[],[])
xlabel('X Position')
ylabel('Y Position')
zlabel('Z Position')
colorbar
view(3)
grid on

% slice
slice(X,Y,Z,V,[x],[],[])
xlabel('X Position')
ylabel('Y Position')
zlabel('Z Position')
colorbar

The other option is to use hold on and add 3 contourf plots to your axes. (Adapted from here: https://www.mathworks.com/matlabcentral/answers/477979-plot-multiple-2d-contour-plots-in-one-3d-figure)

figure
[~,h] = contourf(squeeze(Y(:,1,:)),squeeze(Z(:,1,:)),squeeze(V(:,1,:)));
h.ContourZLevel = 1945;
hold on
[~,h]=contourf(squeeze(Y(:,2,:)),squeeze(Z(:,2,:)),squeeze(V(:,2,:)));
h.ContourZLevel = 2445;
[~,h]=contourf(squeeze(Y(:,3,:)),squeeze(Z(:,3,:)),squeeze(V(:,3,:)));
h.ContourZLevel = 2945;
hold off
xlabel('X Position')
ylabel('Y Position')
zlabel('Z Position')
colorbar
view(3)

[Marshall Boden]

That is brilliant thankyou very much for your help I will give these a go now

[Cris LaPierre]

Here's a way that gets a little closer to the picture you shared. It gets a bit complicated since you have to code much of the manipulation manually. This is adapted from here: https://www.mathworks.com/matlabcentral/answers/1910215-filled-contour-plot-on-other-planes-x-z-or-y-z

% create data 
x = [1945 2445 2945];
y = [-750	-375	0	375	750];
z = [230, 115, 0, -115, -230];

V1=[3.649	5.354	5.208	5.441	3.456
3.264	5.725	5.679	5.728	2.667
2.931	5.7741	5.744	5.782	2.202
2.653	5.775	5.78	5.674	2.003
1.738	5.743	5.778	5.659	1.572];
V2 = V1 + rand(size(V1))*2-1;
V3 = V1 + rand(size(V1))*2-1;

% Set up to rotate plots
ax = axes;
t = hgtransform('Parent',ax);
xlim([min(x) max(x)])
ylim([min(y) max(y)])
zlim([min(z) max(z)])

% create filled contour plots
[~,h1] = contourf(y,z,V1,'Parent',t);
h1.ZLocation = x(1);
t.Matrix=makehgtform('yrotate',pi/2)*makehgtform('zrotate',pi/2);

hold on
[~,h2] = contourf(y,z,V2,'Parent',t);
h2.ZLocation = x(2);
t.Matrix=makehgtform('yrotate',pi/2)*makehgtform('zrotate',pi/2);

[~,h3] = contourf(y,z,V3,'Parent',t);
h3.ZLocation = x(3);
t.Matrix=makehgtform('yrotate',pi/2)*makehgtform('zrotate',pi/2);
hold off

xlabel('X Position')
ylabel('Y Position')
zlabel('Z Position')
colorbar
view([25 25])
grid on

[Marshall Boden]

that has made my day, thankyou very much

[Cris LaPierre]

One more thought. The plot you shared shows some deformation in Z (what corresponds to X here). You could use multiple surf plots. You'd have to upsample your data, and you'd have to figure out a way to scale the deformation to make it visible and meaningful. Here's a quick attempt.

% create data 
x = [1945 2445 2945];
y = [-750	-375	0	375	750];
z = [230, 115, 0, -115, -230];

v1=[3.649	5.354	5.208	5.441	3.456
3.264	5.725	5.679	5.728	2.667
2.931	5.7741	5.744	5.782	2.202
2.653	5.775	5.78	5.674	2.003
1.738	5.743	5.778	5.659	1.572];
v2 = v1 + rand(size(v1));
v3 = v1 + rand(size(v1))*2-1;

% Upsample 5x5 grids using interp2
Y = linspace(min(y),max(y),25);
Z = linspace(min(z),max(z),25);
V1 = interp2(y,z,v1,Y,Z');
V2 = interp2(y,z,v2,Y,Z');
V3 = interp2(y,z,v3,Y,Z');

[Y,Z] = meshgrid(Y,Z);

% I opted to use the V1-3 to adjust X values to show displacement. 
% Given the scale, I multiplied by 20 so that it was visible.
surf(x(1)+V1*50,Y,Z,V1)

hold on
surf(x(2)+V2*50,Y,Z,V2)
surf(x(3)+V3*50,Y,Z,V3)
hold off

xlabel('X Position')
ylabel('Y Position')
zlabel('Z Position')
colorbar
view(3)
grid on