Plotting 4D with 3 vectors and 1 matrix

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Simao Nobrega
Simao Nobrega 2015-6-20
评论： Simao Nobrega 2015-6-21
Hello,
I am solving a problem where I have three vectors (one for each 3D dimension), with different lengths and unevenly spaced, and a temperature matrix where each entry corresponds to the temperature at the position (x(i),y(j),z(k)). My goal is to make a 4D plot where the forth dimension (temperature) is represented my a colour (see attached file).
I have searched for an answer but did not get any solution for the conditions that I presented (3 vectors with 1 matrix). What function or approach would you recommend me to try?
*Data type*
length of x = M
length of y = N
length of z = P
size of Temperature matrix = M x N x P
Thanks in advance.

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采纳的回答

Walter Roberson
Walter Roberson 2015-6-20
You can create a scattered interpolant and then sample it along grids. But as is hinted in your image, the outside is going to hide the inside when you plot. You can work with a voxel viewing routine or you can create isosurfaces to try to deal with that.
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Walter Roberson
Walter Roberson 2015-6-21
http://www.mathworks.com/help/matlab/ref/slice.html
[X, Y, Z] = ndgrid(x, y, z);
slice(X, Y, Z, temperature, [min(x), max(x)], [min(y), max(y)], [min(z), max(z)], 'cubic')
Simao Nobrega
Simao Nobrega 2015-6-21
Thank you Walter for your answer.
Worked like charm! Slice is a very nice function.
Best regards

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Hugo
Hugo 2015-6-20
You could use "patch" since the surface will hide the interior points. You can create a matrix containing the coordinates of each point on the surface and then another matrix containing the indexes of the vertices defining each face in the patch. Suppose you want to create the faces corresponding to the top. You can use
xaux = repmat(x(:),1,Ny);
yaux = repmat(y(:)',Nx,1);
zaux = repmat(zval,Nx,Ny);
vertices = [xaux(:),yaux(:),zaux(:)];
faces = [];
for indy = 1:Ny,
for indx=1:Nx,
faces=[faces;[indx,indx+1,indx+11,indx+10]+(indy-1)*10];
end,
end
patch('Vertices',vertices,'Faces',faces,'CData',reshape(temperature(:,:,end),Nx*Ny,1),'FaceColor','interp','EdgeColor','none');
You will need to repeat this for each side. You can use any grid you want. The interpolation may be rather unsatisfactory. Hope this helps.
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Simao Nobrega
Simao Nobrega 2015-6-21
Hello Hugo,
Thank you for your answer. In the attached image you can see the temperature distribution of the top plane using contourf and your code. Maybe the problem is the interpolation that is being made in your code.

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