point-to-segment.cpp

typedef pair<double, double> pdb;

double pt2segment(pdb A, pdb B, pdb E) {
  pdb AB = {B.fst - A.fst, B.snd - A.snd};
  pdb BE = {E.fst - B.fst, E.snd - B.snd};
  pdb AE = {E.fst - A.fst, E.snd - A.snd};

  double AB_BE = AB.fst * BE.fst + AB.snd * BE.snd;
  double AB_AE = AB.fst * AE.fst + AB.snd * AE.snd;

  double ans;
  if (AB_BE > 0) {
    double y = E.snd - B.snd;
    double x = E.fst - B.fst;
    ans = hypot(x, y);
  } else if (AB_AE < 0) {
    double y = E.snd - A.snd;
    double x = E.fst - A.fst;
    ans = hypot(x, y);
  } else {
    auto [x1, y1] = AB;
    auto [x2, y2] = AE;
    double mod = hypot(x1, y1);
    ans = abs(x1 * y2 - y1 * x2) / mod;
  }

  return ans;
}