Visualising Volume Object Data

Hey everyone,

I know there's a lot of questions on this problem but I can't find anything which quite works the way I'd like it to. I have a set of upper and lower bounds in spherical coordinates which as a pair each describe some small volume region. The result is 3 matrices R, Theta, Phi of size [Ntheta x Nphi x Nr] for both the upper and lower bounds. Corresponding to these individual bounds is then some scalar value in another matrix of size [Ntheta x Nphi x Nr].

What I would like to do is plot the individual volume elements i.e from [Tlow:Tup , Plow:Pup , Rlow : Rup] as filled blocks with color chosen by the value in the matrix. Some example code for the data I'm working with is given though these are just simplified pieces of data (I'm aware I can vectorise the for loops but again this is just example data):

Nr=3; Nt=20; Np=20;
Rq = linspace(0,1,Nr); Thetaq = linspace(0,pi,Nt); Phiq = linspace(-pi,pi,Np);
[Thetaq,Phiq,Rq] = meshgrid(Thetaq,Phiq,Rq);

delR = (max(Rq(:))-min(Rq(:)))./Nr;
delT = (max(Thetaq(:))-min(Thetaq(:)))./Nt;
delP = (max(Phiq(:))-min(Phiq(:)))./Np;

for Rind = 1:Nr
    for Tind = 1:Nt
        for Pind = 1:Np
            Rlow(Tind,Pind,Rind) = delR.*(Rind-1); Rup(Tind,Pind,Rind) = delR.*Rind;
            Tlow(Tind,Pind,Rind) = delT.*(Tind-1); Tup(Tind,Pind,Rind) = delT.*Tind;
            Plow(Tind,Pind,Rind) = delP.*(Pind-1); Pup(Tind,Pind,Rind) = delP.*Pind;
        end
    end
end

mockobjprop = ones(Nt,Np,Nr); %Object With Correct Sized Matrix
mockobjprop(:,:,1:2) = 10; %First 2 Radial Shells Have Value 10

The object I envisage here is a spherical object with 3 radial shells, such all volume elements in the inner two shells will have one colour and the 3rd shell will be a different colour. I'm hoping to utalise matlabs inbuilt colormaps as the general data is much more complicated than this two colour scheme. I have seen a few suggestions using the slice function however even if I convert my volume bounds to cartesian it finds the data to be defined on an invalid meshgrid.

The best solution I have so far is using a point at the centre of each volume chunk, converting to cartesian and plotting a scatter3 plot with the color set by the propety matrix. However visually this is appalling at best.

Xq = Rq.*sin(Thetaq).*cos(Phiq); Yq = Rq.*sin(Phiq).*sin(Thetaq); Zq =Rq.*cos(Thetaq);
scatter3(Xq(:),Yq(:),Zq(:),1e3,mockobjprop(:))

Any advise or suggestions would be greatly appreciated. Even if it isn't exactly what I'm searching for anything would be an improvement. I had one suggestion of exporting the data to paraviewer however I cannot figure out how to export this type of data mind render it within paraviewer.

[darova]

Did you try surf() or isosurface()? Can you attach the data?

[ADSW121365]

The code needed for some example data is given above. For a little more context imagine a unit sphere defined with 3 radial shells, 5 theta components and 5 phi components. The first two radial shells represent an object with density 10 totalling 50 volume elements which should be coloured. The final radial shell/25 volume elements then have a different density, 1, and therefore colour.

I have tried using both surf and isosurface but haven't managed to get a plot to produce for either. If you can see a way to produce plots using this type of data some example code would be greatly appreciated!

[darova]

You want small spheres instead of points? What do you mean by 'volume'?

[ADSW121365]

So I'm performing a 3D integral between limits Rlow:Rup, Tlow:Tup, Plow:Pup in spherical coordinates. This is done over a series of limits which cover the entire unit sphere. If you map that out on paper you'll see that effectivitely divided a sphere into a set of small 'wedges' i.e the space between the 3 limits. (The diagram here is probably helpful;http://citadel.sjfc.edu/faculty/kgreen/vector/block3/jacob/node14.html )

That bit of code is irrelevant, what I'm interested in is creating an image of the space these limits represent

What I would like to do is then plot each wedge from those limits and color the space it represents a color - this is where the variable mockobjprop comes in. It gives the associated colour to each volume wedge.

[darova]

I give up. Sorry

Answer 1

[Bjorn Gustavsson]

You could work with surf on each radial layer and set the surface property facealpha to something transparent. Perhaps something like this:

for iR = 1:Nr,
    ph{iR} = surf(Xq(:,:,iR),Yq(:,:,iR),Zq(:,:,iR),mockobjprop(:,:,iR));
    hold on
    shading flat
    set(ph{iR},'facealpha',.45) % this you might modify...
end

You might modify the facealpha value to be proportional to the value of mockobjprop or something suitable to illustrate your volume. Another trick to do is to do this in all three dimensions with surfaces also for all theta and phi values, but that is just an extension of the general idea...

HTH

[ADSW121365]

Brilliant basically exactly what I was looking for. Thankyou!