Hi, my apologies if this is not the right place to ask this- I am not a mathematician (I'm a software engineer) and Im working on some 3D applications.

My situation is this- given an origin of 0,0,0 and any two points I need to be able to return the xyz coordinate of any point that is on the line between these two points- with the assumption being that the two points must fall on a symmetrical closed surface surrounding the origin, sphere or ellipsoid. So the line would follow the surface shortest distance between the two points.

So for example, I would need the xyz point that is 0.1 of the line length... but I have no idea how to get it...

Is this possible from 2 points and an origin only? I am implementing this in C# if that helps.

Thanks!