Voronoi Cells on Curved Surface

Im looking to take the surface (in attached image) and create a voronoi algorithm so that the resulting cells are planar.

I have been able to create a mesh, or set of triangles using the delaunay command.

From what I understand, in a 2d voronoi, you take the midpoint of the resulting lines of the delaunay and draw perpendicular lines which in turn create a cell's edge. The intersection of the perpendicular lines create the corners to a cell.

I suppose that the next step is to create the correct planes for each cell to lie on. Any input would be much appreciated.