Voronoi on surface

Hello everyone
I am a beginner but I am very interested in parametric design.
I need to create a surface with the grid voronoi.
Could you give me directions on how to do it please?
Instead of pictures for better understanding.
The first image is what I would get to do.
- I came to have the voronoi grid on the surface but when I do the offset of the grid is not done at all and no joins. Because?
- Should I extrude the lines of offset along the perpendicular to the surface, how could I do? by the time I used as a vector the z-axis as shown in the image.
- To make it a volume, you should do the extrusion line-offset or offset of the surface and then dissect the lines extruded offset?

I have read and seen tutorials and post on the site but I could not find the solution, please help thanks !!