import “../core/noop”; import “../math/adder”; import “../math/trigonometry”; import “geo”; import “stream”;

d3.geo.area = function(object) {

d3_geo_areaSum = 0;
d3.geo.stream(object, d3_geo_area);
return d3_geo_areaSum;

};

var d3_geo_areaSum,

d3_geo_areaRingSum = new d3_adder;

var d3_geo_area = {

sphere: function() { d3_geo_areaSum += 4 * π; },
point: d3_noop,
lineStart: d3_noop,
lineEnd: d3_noop,

// Only count area for polygon rings.
polygonStart: function() {
  d3_geo_areaRingSum.reset();
  d3_geo_area.lineStart = d3_geo_areaRingStart;
},
polygonEnd: function() {
  var area = 2 * d3_geo_areaRingSum;
  d3_geo_areaSum += area < 0 ? 4 * π + area : area;
  d3_geo_area.lineStart = d3_geo_area.lineEnd = d3_geo_area.point = d3_noop;
}

};

function d3_geo_areaRingStart() {

var λ00, φ00, λ0, cosφ0, sinφ0; // start point and previous point

// For the first point, …
d3_geo_area.point = function(λ, φ) {
  d3_geo_area.point = nextPoint;
  λ0 = (λ00 = λ) * d3_radians, cosφ0 = Math.cos(φ = (φ00 = φ) * d3_radians / 2 + π / 4), sinφ0 = Math.sin(φ);
};

// For subsequent points, …
function nextPoint(λ, φ) {
  λ *= d3_radians;
  φ = φ * d3_radians / 2 + π / 4; // half the angular distance from south pole

  // Spherical excess E for a spherical triangle with vertices: south pole,
  // previous point, current point.  Uses a formula derived from Cagnoli’s
  // theorem.  See Todhunter, Spherical Trig. (1871), Sec. 103, Eq. (2).
  var dλ = λ - λ0,
      cosφ = Math.cos(φ),
      sinφ = Math.sin(φ),
      k = sinφ0 * sinφ,
      u = cosφ0 * cosφ + k * Math.cos(dλ),
      v = k * Math.sin(dλ);
  d3_geo_areaRingSum.add(Math.atan2(v, u));

  // Advance the previous points.
  λ0 = λ, cosφ0 = cosφ, sinφ0 = sinφ;
}

// For the last point, return to the start.
d3_geo_area.lineEnd = function() {
  nextPoint(λ00, φ00);
};

}