Note: To follow this note and especially to get definitions of concepts as lower catchment basin, FOZ, dual geodesic reconstruction, I STRONGLY recommend to read the following documents available on my Web page (http://cmm.ensmp.fr/~beucher/publi.html): P algorithm, a dramatic enhancement of the waterfal transformation (http://cmm.ensmp.fr/~beucher/publi/P-Algorithm_SB_BM.pdf, in particular, pa...