area.js

import adder from "./adder";
import {atan2, cos, quarterPi, radians, sin, tau} from "./math";
import noop from "./noop";
import stream from "./stream";

export var areaRingSum = adder();

var areaSum = adder(),
    lambda00,
    phi00,
    lambda0,
    cosPhi0,
    sinPhi0;

export var areaStream = {
  point: noop,
  lineStart: noop,
  lineEnd: noop,
  polygonStart: function() {
    areaRingSum.reset();
    areaStream.lineStart = areaRingStart;
    areaStream.lineEnd = areaRingEnd;
  },
  polygonEnd: function() {
    var areaRing = +areaRingSum;
    areaSum.add(areaRing < 0 ? tau + areaRing : areaRing);
    this.lineStart = this.lineEnd = this.point = noop;
  },
  sphere: function() {
    areaSum.add(tau);
  }
};

function areaRingStart() {
  areaStream.point = areaPointFirst;
}

function areaRingEnd() {
  areaPoint(lambda00, phi00);
}

function areaPointFirst(lambda, phi) {
  areaStream.point = areaPoint;
  lambda00 = lambda, phi00 = phi;
  lambda *= radians, phi *= radians;
  lambda0 = lambda, cosPhi0 = cos(phi = phi / 2 + quarterPi), sinPhi0 = sin(phi);
}

function areaPoint(lambda, phi) {
  lambda *= radians, phi *= radians;
  phi = phi / 2 + quarterPi; // 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 dLambda = lambda - lambda0,
      sdLambda = dLambda >= 0 ? 1 : -1,
      adLambda = sdLambda * dLambda,
      cosPhi = cos(phi),
      sinPhi = sin(phi),
      k = sinPhi0 * sinPhi,
      u = cosPhi0 * cosPhi + k * cos(adLambda),
      v = k * sdLambda * sin(adLambda);
  areaRingSum.add(atan2(v, u));

  // Advance the previous points.
  lambda0 = lambda, cosPhi0 = cosPhi, sinPhi0 = sinPhi;
}

export default function(object) {
  areaSum.reset();
  stream(object, areaStream);
  return areaSum * 2;
}