import "../core/noop";

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_areaRingU,

d3_geo_areaRingV;

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_areaRingU = 1, d3_geo_areaRingV = 0;

d3_geo_area.lineStart = d3_geo_areaRingStart;

},

polygonEnd: function() {

var area = 2 * Math.atan2(d3_geo_areaRingV, d3_geo_areaRingU);

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 two previous points

// 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,

u0 = d3_geo_areaRingU,

v0 = d3_geo_areaRingV,

u = cosφ0 * cosφ + k * Math.cos(dλ),

v = k * Math.sin(dλ);

// ∑ arg(z) = arg(∏ z), where z = u + iv.

d3_geo_areaRingU = u0 * u - v0 * v;

d3_geo_areaRingV = v0 * u + u0 * v;

// 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);

};

}