MATLAB: How to project a 3-D sphere onto a 2-D surface

Question

I got a matrix M with 3 col, n rows. The points created by the matrix are all on a sphere with radius r. In a seperate matrix, let's call it "U", same size. Has either 0's or the exact same row. (indicating parts of the the sphere that have been selected).

So a sphere where nothing has been selected is a 3xn matrix filled with 0's.

I want to project the sphere onto a 2D surface (lets ignore the z, and plot x and y), which gives me a "double" sphere, spanned by points. I used the scatter command to get this result. I shifted half of the circle down in y, so u would get two circles next to eachother.

Now… here's my question:

Can I create a memory efficient 2-D plot, in which the points are translated to "surface parts", in order to better indicate which parts of the sphere has been seen.

The reason for the memory efficient part is due to a constant refresh of the data.

See attached picture for an more visual explanation.

picture

Added question: say I don't cut the circle in half in the middle, but say at 1/3. What would be the most easy way to "fold" the data points outward that would otherwise be obscured by the datapoints that have the same x&y, but different z points.

(see explanation in the left down corner)

Thanks in advance,

Answer 1

This is called map projection. There are multiple methods. check any map projection resource.

The best resource is perhaps this:

Map Projections: A Working Manual By John Snydenr

MATLAB has a built-in command [x,y] = mfwdtran(lat,lon) There are some other command that might be helpful too, such as projfwd() .

These commands are part of "Mapping Toolbox".