(* horizontal normal at (x1,y1) *)

nx={0,1,y1}/Sqrt[1+y1 y1];

(* vertical normal at (x1,y1) *)

ny = {1,0,x1}/Sqrt[1+x1 x1];


(*horizontal hover*)

Hx=2 (y1-y2)/Sqrt[1+y1 y1]/(1+x2 x2 + y2 y2)

(*horizontal hover*)

Hy=2 (x1-x2)/Sqrt[1+x1 x1]/(1+x2 x2 + y2 y2)

(*true distance*)

R=4 ((x1-x2) (x1-x2) + (y1-y2) (y1-y2))/Sqrt[1+x1 x1 + y1 y1]/Sqrt[1+x2 x2 + y2 y2]