MATLAB: Distance between two points on the sphere.

Question

Greetings!

I have to make a script that build a sphere (radius is given by me), then the user inputs two coordinates (x,y,z) ON the sphere, and script shows the closest distance between these two points.

I have no clue how to do that (I was not taught such things on my classes), even though I have to do this…

I wish you help me 🙂

Answer 1

I guess you want to find the shortest distance along the surface of the sphere, not just the euclidean distance between the points. The shortest path between two points on a sphere is always located on a great circle, which is thus a "great arc". You can find Roger Staffords mathematically robust method here:

https://www.mathworks.com/matlabcentral/newsreader/view_thread/278872

For convenience I repeat it here too:

" P1 = [x1,y1,z1] and P2 = [x2,y2,z2] are two vectors pointing from the center of the sphere to the two given points (x1,y1,z1) and (x2,y2,z2) on the sphere, what is the shortest great circle distance d between them?"

 d = radius * atan2(norm(cross(P1,P2)),dot(P1,P2));

If you want an example of how to use this to generate points along a great arc, then see the Mfile colornames_cube in my FEX submission colornames. The nested function cncDemoClBk at the end of the file steps along a great arc, rotating the axes as it goes.