I need help because I’m facing a problem that I’m struggling to solve.

I would like to create a non-linear interpolation between 2 given points on the surface of a mesh to obtain a point distribution on the object.

This example below shows the same problem but with a linear interpolation on the surface of a cube.

My goal is to obtain a distribution of points only on the surface of my object, whatever the shape of the surface.
For the moment I obtain a linear interpolation as in the image below:

Can you please describe your expectations in more detail?

If you have a cube and a straight line connecting two points on different faces, the line does not intersect any faces and thus you have not points on the surface (except of the start and end points).