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_areaRing;

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_areaRing = 0;

d3_geo_area.lineStart = d3_geo_areaRingStart;

},

polygonEnd: function() {

d3_geo_areaSum += d3_geo_areaRing < 0 ? 4 * π + d3_geo_areaRing : d3_geo_areaRing;

d3_geo_area.lineStart = d3_geo_area.lineEnd = d3_geo_area.point = d3_noop;

}

};

function d3_geo_areaRingStart() {

var λ00, φ00, λ1, λ0, φ0, cosφ0, sinφ0; // start point and two previous points

// For the first point, …

d3_geo_area.point = function(λ, φ) {

d3_geo_area.point = nextPoint;

λ1 = λ0 = (λ00 = λ) * d3_radians, φ0 = (φ00 = φ) * d3_radians, cosφ0 = Math.cos(φ0), sinφ0 = Math.sin(φ0);

};

// For subsequent points, …

function nextPoint(λ, φ) {

λ *= d3_radians, φ *= d3_radians;

// If both the current point and the previous point are polar, skip this point.

if (Math.abs(Math.abs(φ0) - π / 2) < ε && Math.abs(Math.abs(φ) - π / 2) < ε) return;

var cosφ = Math.cos(φ), sinφ = Math.sin(φ);

// If the previous point is at the north pole, then compute lune area.

if (Math.abs(φ0 - π / 2) < ε) d3_geo_areaRing += (λ - λ1) * 2;

// Area of spherical triangle with vertices at south pole, previous point

// and current point = ER², where E is the spherical excess, and in our

// case, R = 1.

else {

var dλ = λ - λ0,

cosdλ = Math.cos(dλ),

// Distance from previous point to current point, well-conditioned

// for all angles.

d = Math.atan2(Math.sqrt((d = cosφ * Math.sin(dλ)) * d + (d = cosφ0 * sinφ - sinφ0 * cosφ * cosdλ) * d), sinφ0 * sinφ + cosφ0 * cosφ * cosdλ),

// Half the semiperimeter (a + b + c) / 2, where a, b and c are the

// lengths of the triangle sides.

s = (d + π + φ0 + φ) / 4;

// Compute the spherical excess E using l’Huilier’s theorem,

// tan(E / 4) = √[tan(s)tan(s - a / 2)tan(s - b / 2)tan(s - c / 2)].

d3_geo_areaRing += (dλ < 0 && dλ > -π || dλ > π ? -4 : 4) * Math.atan(Math.sqrt(Math.abs(Math.tan(s) * Math.tan(s - d / 2) * Math.tan(s - π / 4 - φ0 / 2) * Math.tan(s - π / 4 - φ / 2))));

}

// Advance the previous points.

λ1 = λ0, λ0 = λ, φ0 = φ, cosφ0 = cosφ, sinφ0 = sinφ;

}

// For the last point, return to the start.

d3_geo_area.lineEnd = function() {

nextPoint(λ00, φ00);

};

}