smallest function

({double diameter, bool typeI}) smallest(double ra1, double dec1, double ra2, double dec2, double ra3, double dec3,)

Smallest circle containing three celestial bodies.

All arguments in radians. Returns diameter in radians and whether the solution is Type I (two points on circle, third inside).

Implementation

({double diameter, bool typeI}) smallest(
    double ra1, double dec1,
    double ra2, double dec2,
    double ra3, double dec3) {
  var a = sep(ra1, dec1, ra2, dec2);
  var b = sep(ra2, dec2, ra3, dec3);
  var c = sep(ra3, dec3, ra1, dec1);

  // Sort so a >= b >= c
  if (a < b) { final t = a; a = b; b = t; }
  if (a < c) { final t = a; a = c; c = t; }
  if (b < c) { final t = b; b = c; c = t; }

  if (a >= math.sqrt(b * b + c * c)) {
    return (diameter: a, typeI: true);
  }
  // Type II: all three on circle
  final d = 2 * a * b * c /
      math.sqrt((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c));
  return (diameter: d, typeI: false);
}