rhinoshortpath can creat a shortpath curve on a face.
I also need creat a shortpath curve on a mesh,how can i do?

The Rhino SDK does not have a function to create the shortest possible curve (geodesic) between two points on a mesh.

but I need these function right now,can you give me some ideas how to write this
function myself?

I am sorry, but I cannot help you. This is not a feature of Rhino.

You might [check this][1] out to write your own.

[1]: http://www.cs.technion.ac.il/~vitus/geolib.html