Function closest_point

code/geometry/lines.cpp:6–12

bool parallel(L(a, b), L(p, q)) {
  return abs(cross(b - a, q - p)) < EPS; }
point closest_point(L(a, b), P(c), bool segment = false) {
  if (segment) {
    if (dot(b - a, c - b) > 0) return b;
    if (dot(a - b, c - a) > 0) return a;
  }
  double t = dot(c - a, b - a) / norm(b - a);
  return a + t * (b - a); }
double line_segment_distance(L(a,b), L(c,d)) {
  double x = INFINITY;
  if (abs(a - b) < EPS && abs(c - d) < EPS) x = abs(a - c);