OCamlで、点と直線の距離、点と線分の距離、点と半直線の距離

distance.ml

(* ベクトルの内積 *)
let ( ** ) (x,y) (a,b) = x *. a +. y *. b

(* 2点間の距離 *)
let distance (x,y) (a,b) = sqrt ((x -. a) * (x -. a) + (y -. b) * (y -. b))

(* 点(px,py) と 直線(x1,y1)(x2,y2)の距離 *)
let distance_to_line (x1,y1) (x2,y2) (px,py) =
  let b, c = (x2-.x1,y2-.y1), (px-.x1,py-.y1) in
  let dotprod = b ** c in
  sqrt ((c ** c) -. dotprod *. dotprod /. (b ** b))

(* 点(px,py) と 線分(x1,y1)(x2,y2)の距離 *)
let distance_to_segment (px,py) (x1,y1) (x2,y2) =
  let b, c = (x2-.x1,y2-.y1), (px-.x1,py-.y1) in
  let dotprod = b ** c in
  if dotprod < 0 then
    distance (px,py) (x1,y1)
  else dotprod > c ** c then
    distance (px,py) (x2,y2)
  else
    sqrt ((c ** c) -. dotprod *. dotprod /. (b ** b))

(* 点(px,py) と (x1,y1)から伸びる半直線との距離 *)
let distance_to_halfline (px,py) (x1,y1) (x2,y2) =
  let b, c = (x2-.x1,y2-.y1), (px-.x1,py-.y1) in
  let dotprod = b ** c in
  if dotprod < 0 then
    distance (px,py) (x1,y1)
  else
    sqrt ((c ** c) -. dotprod *. dotprod /. (b ** b))