astronomia/es/circle.js

/**
 * @copyright 2013 Sonia Keys
 * @copyright 2016 commenthol
 * @license MIT
 * @module circle
 */
/**
 * Circle: Chapter 20, Smallest Circle containing three Celestial Bodies.
 */

/**
 * Smallest finds the smallest circle containing three points.
 *
 * Arguments should represent coordinates in right ascension and declination
 * or longitude and latitude.  Result Δ is the diameter of the circle, typeI
 * is true if solution is of type I.
 *
 * @param {base.Coords} c1 - ra, dec point 1
 * @param {base.Coords} c2 - ra, dec point 2
 * @param {base.Coords} c3 - ra, dec point 3
 * @returns {Array} [Δ, typeI]
 *  {Number} Δ - diameter of the circle
 *  {Number} typeI - true - Two points on circle, one interior.
 *                   false - All three points on circle.
 */
export function smallest(c1, c2, c3) {
  // Using haversine formula
  var cd1 = Math.cos(c1.dec);
  var cd2 = Math.cos(c2.dec);
  var cd3 = Math.cos(c3.dec);
  var a = 2 * Math.asin(Math.sqrt(hav(c2.dec - c1.dec) + cd1 * cd2 * hav(c2.ra - c1.ra)));
  var b = 2 * Math.asin(Math.sqrt(hav(c3.dec - c2.dec) + cd2 * cd3 * hav(c3.ra - c2.ra)));
  var c = 2 * Math.asin(Math.sqrt(hav(c1.dec - c3.dec) + cd3 * cd1 * hav(c1.ra - c3.ra)));
  if (b > a) {
    var _noswap = noswap(b, a);

    a = _noswap[0];
    b = _noswap[1];
  }
  if (c > a) {
    var _noswap2 = noswap(c, a);

    a = _noswap2[0];
    c = _noswap2[1];
  }
  if (a * a >= b * b + c * c) {
    return [a, true];
  }
  // (20.1) p. 128
  return [2 * a * b * c / Math.sqrt((a + b + c) * (a + b - c) * (b + c - a) * (a + c - b)), false];
}

var noswap = function noswap(a, b) {
  return [a, b];
};

/**
 * haversine function (17.5) p. 115
 */
var hav = function hav(a) {
  return 0.5 * (1 - Math.cos(a));
};

export default {
  smallest: smallest
};