CODEWITHSUNDEEP
matlab3dgeometry2dprojection
user2066183
user2066183

Reputation:

project a sphere to a plane using matlab

This is probably very basic matlab, so forgive me. I use the command sphere to create a 3D sphere and have the x,y,z matrices that will produce it using surf. For example:

[x,y,z]=sphere(64);

I'd like to project (or sum) this 3D sphere into one of the Cartesian 2D planes (for example X-Y plane) to obtain a 2D matrix that will be the projection of that sphere. Using imshow or imagesc on the output should look something like this:

enter image description here

simple summing obviously doesn't work, how can I accomplish that in Matlab?

Upvotes: 5

Views: 6588

Answers (3)

Floris
Floris

Reputation: 46375

It is possible that I completely misunderstand your question, in which case I apologize; but I think one of the following three methods may in fact be what you need. Note that method 3 gives an image that looks a lot like the example you provided... but I got there with a very different route (not using the sphere command at all, but computing "voxels inside" and "voxels outside" by working directly with their distance from the center). I inverted the second image compared to the third on since it looked better that way - filling the sphere with zeros made it look almost like a black disk.

enter image description here

%% method 1: find the coordinates, and histogram them
[x y z]=sphere(200);
xv = linspace(-1,1,40);
[xh xc]=histc(x(:), xv);
[yh yc]=histc(y(:), xv);

% sum the occurrences of coordinates using sparse:
sm = sparse(xc, yc, ones(size(xc)));
sf = full(sm);

figure; 
subplot(1,3,1);
imagesc(sf); axis image; axis off
caxis([0 sf(19,19)]) % add some clipping
title 'projection of point density'

%% method 2: fill a sphere and add its volume elements:
xv = linspace(-1,1,100);
[xx yy zz]=meshgrid(xv,xv,xv);
rr = sqrt(xx.^2 + yy.^2 + zz.^2);
vol = zeros(numel(xv)*[1 1 1]);
vol(rr<1)=1;
proj = sum(vol,3);
subplot(1,3,2)
imagesc(proj); axis image; axis off; colormap gray
title 'projection of volume'

%% method 3: visualize just a thin shell:
vol2 = ones(numel(xv)*[1 1 1]);
vol2(rr<1) = 0;
vol2(rr<0.95)=1;
projShell = sum(vol2,3);
subplot(1,3,3);
imagesc(projShell); axis image; axis off; colormap gray
title 'projection of a shell'

Upvotes: 1

comingstorm
comingstorm

Reputation: 26107

I would look at map projections, which are designed for this purpose.

A search on "map projections matlab" yields documentation on a Matlab mapping toolbox. However, if you want or need to roll your own, there is a good summary at the USGS website, as well as a wikipedia article.

Upvotes: 0

reverse_engineer
reverse_engineer

Reputation: 4269

You can project on the X-Y plane in Matlab by using:

[x,y,z] = sphere(64);
surf(x,y,zeros(size(z)));

But I think you should not use Matlab for this, because the problem is so simple you can do this analytically...

Upvotes: 0

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