Triangulate mesh reversed

Hi there,

So I have a doubly-curved surface that I want to turn into planar triangular mesh surfaces. The initial surface is built with a 21 x 21 point grid, with varying z-values. I can create a mesh from this point grid and then use Triangulate Mesh, but this does not give me the desired layout of the triangles. I basically want to flip all diagonals (see image attached). Does anyone know of a way to get better control over this?

triangulated (14.2 KB)

Have a look at this wonderful thread: Mesh Triangulation
It could be a solution for you.
The first attachment by Daniel Piker should be good for you.

Brilliant, thanks!