Kurt

Thank you, LU! That's a great question. How concerned are you concerned with performance? If you can stomach an O(n ^ 2) algorithm, where n is the number of points output by GridSphere, then I think the following approach will be easiest.

1. Find the distance between all the pairs of points output by GridSphere.
2. Sort by these distances to find all the pairs of points that are closest to one another. There are at least three gotchas here: (1) you'll need to make sure that either you're not computing the distance between a point and itself or that you're filtering out the pairs with distance 0, (2) you'll probably want to avoid computing both the distance from point a to point b and the distance from point b to point a, and (3) you'll need to account for the imperfect precision of floating point arithmetic, which will result in clumps of distances that are very close but not quite equal. Some of the functions that come with GridSphere may be helpful to you, such as DistinctFromPrevious, which will find the boundaries between the aforementioned clumps.
3. Draw great circles (or just straight lines) connecting the pairs of points you found in step 2. Each of these pairs corresponds to one edge of a triangle. As Paul mentioned, you may need to call conversion functions like deg2rad and sph2cart on your great circle (or line) vectors to project them appropriately.

Thanks for pointing this out, Matt. I ran several of the options against each other, and profiled the results. I've updated the file with the version that consistently ran the fastest. You were right that using a persistent variable was not worth it.

I'm aware that the function is trivial to implement, but I felt it was an important enough constant that it should have come built in. Apparently other people did as well, because it's getting downloaded.

Hi Kurt, Wonderful program. I was just wondering if it is possible to connect the vertices with lines? Using Paul's example plots the vertiecs but i would like to display it as a mesh grid showing the edges of the triangles.

Thanks!

Blazingly fast and well documented. Only an example would not have been unbecoming, e.g. to illustrate the fact that returned values are in degrees (whereas Matlab's sph2cart requires radians).

[lat,long] = GridSphere(1000);
latrad = deg2rad(lat);
longrad = deg2rad(long);
[x,y,z] = sph2cart(longrad, latrad, 1);
scatter3(x, y, z, 22);
axis equal vis3d;