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, sdλ = dλ >= 0 ? 1 : -1, adλ = sdλ * dλ, cosφ = Math.cos(φ), sinφ = Math.sin(φ), k = sinφ0 * sinφ, u = cosφ0 * cosφ + k * Math.cos(adλ), v = k * sdλ * Math.sin(adλ); 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); }; }