topogram/build/topogram.js

Create continuous area cartograms with TopoJSON and D3

(function (global, factory) {
	typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
	typeof define === 'function' && define.amd ? define(['exports'], factory) :
	(factory((global.topogram = global.topogram || {})));
}(this, function (exports) { 'use strict';

	function ascending(a, b) {
	  return a < b ? -1 : a > b ? 1 : a >= b ? 0 : NaN;
	}

	function bisector(compare) {
	  if (compare.length === 1) compare = ascendingComparator(compare);
	  return {
	    left: function(a, x, lo, hi) {
	      if (lo == null) lo = 0;
	      if (hi == null) hi = a.length;
	      while (lo < hi) {
	        var mid = lo + hi >>> 1;
	        if (compare(a[mid], x) < 0) lo = mid + 1;
	        else hi = mid;
	      }
	      return lo;
	    },
	    right: function(a, x, lo, hi) {
	      if (lo == null) lo = 0;
	      if (hi == null) hi = a.length;
	      while (lo < hi) {
	        var mid = lo + hi >>> 1;
	        if (compare(a[mid], x) > 0) hi = mid;
	        else lo = mid + 1;
	      }
	      return lo;
	    }
	  };
	}

	function ascendingComparator(f) {
	  return function(d, x) {
	    return ascending(f(d), x);
	  };
	}

	var ascendingBisect = bisector(ascending);

	function merge(arrays) {
	  var n = arrays.length,
	      m,
	      i = -1,
	      j = 0,
	      merged,
	      array;

	  while (++i < n) j += arrays[i].length;
	  merged = new Array(j);

	  while (--n >= 0) {
	    array = arrays[n];
	    m = array.length;
	    while (--m >= 0) {
	      merged[--j] = array[m];
	    }
	  }

	  return merged;
	}

	function sum(array, f) {
	  var s = 0,
	      n = array.length,
	      a,
	      i = -1;

	  if (f == null) {
	    while (++i < n) if (a = +array[i]) s += a; // Note: zero and null are equivalent.
	  }

	  else {
	    while (++i < n) if (a = +f(array[i], i, array)) s += a;
	  }

	  return s;
	}

	// Adds floating point numbers with twice the normal precision.
	// Reference: J. R. Shewchuk, Adaptive Precision Floating-Point Arithmetic and
	// Fast Robust Geometric Predicates, Discrete & Computational Geometry 18(3)
	// 305–363 (1997).
	// Code adapted from GeographicLib by Charles F. F. Karney,
	// http://geographiclib.sourceforge.net/

	function adder() {
	  return new Adder;
	}

	function Adder() {
	  this.reset();
	}

	Adder.prototype = {
	  constructor: Adder,
	  reset: function() {
	    this.s = // rounded value
	    this.t = 0; // exact error
	  },
	  add: function(y) {
	    add(temp, y, this.t);
	    add(this, temp.s, this.s);
	    if (this.s) this.t += temp.t;
	    else this.s = temp.t;
	  },
	  valueOf: function() {
	    return this.s;
	  }
	};

	var temp = new Adder;

	function add(adder, a, b) {
	  var x = adder.s = a + b,
	      bv = x - a,
	      av = x - bv;
	  adder.t = (a - av) + (b - bv);
	}

	var epsilon = 1e-6;
	var pi = Math.PI;
	var halfPi = pi / 2;
	var quarterPi = pi / 4;
	var tau = pi * 2;

	var degrees = 180 / pi;
	var radians = pi / 180;

	var abs = Math.abs;
	var atan = Math.atan;
	var atan2 = Math.atan2;
	var cos = Math.cos;
	var sin = Math.sin;
	var sign = Math.sign || function(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; };
	var sqrt = Math.sqrt;
	function acos(x) {
	  return x > 1 ? 0 : x < -1 ? pi : Math.acos(x);
	}

	function asin(x) {
	  return x > 1 ? halfPi : x < -1 ? -halfPi : Math.asin(x);
	}

	function noop() {}

	function streamGeometry(geometry, stream) {
	  if (geometry && streamGeometryType.hasOwnProperty(geometry.type)) {
	    streamGeometryType[geometry.type](geometry, stream);
	  }
	}

	var streamObjectType = {
	  Feature: function(object, stream) {
	    streamGeometry(object.geometry, stream);
	  },
	  FeatureCollection: function(object, stream) {
	    var features = object.features, i = -1, n = features.length;
	    while (++i < n) streamGeometry(features[i].geometry, stream);
	  }
	};

	var streamGeometryType = {
	  Sphere: function(object, stream) {
	    stream.sphere();
	  },
	  Point: function(object, stream) {
	    object = object.coordinates;
	    stream.point(object[0], object[1], object[2]);
	  },
	  MultiPoint: function(object, stream) {
	    var coordinates = object.coordinates, i = -1, n = coordinates.length;
	    while (++i < n) object = coordinates[i], stream.point(object[0], object[1], object[2]);
	  },
	  LineString: function(object, stream) {
	    streamLine(object.coordinates, stream, 0);
	  },
	  MultiLineString: function(object, stream) {
	    var coordinates = object.coordinates, i = -1, n = coordinates.length;
	    while (++i < n) streamLine(coordinates[i], stream, 0);
	  },
	  Polygon: function(object, stream) {
	    streamPolygon(object.coordinates, stream);
	  },
	  MultiPolygon: function(object, stream) {
	    var coordinates = object.coordinates, i = -1, n = coordinates.length;
	    while (++i < n) streamPolygon(coordinates[i], stream);
	  },
	  GeometryCollection: function(object, stream) {
	    var geometries = object.geometries, i = -1, n = geometries.length;
	    while (++i < n) streamGeometry(geometries[i], stream);
	  }
	};

	function streamLine(coordinates, stream, closed) {
	  var i = -1, n = coordinates.length - closed, coordinate;
	  stream.lineStart();
	  while (++i < n) coordinate = coordinates[i], stream.point(coordinate[0], coordinate[1], coordinate[2]);
	  stream.lineEnd();
	}

	function streamPolygon(coordinates, stream) {
	  var i = -1, n = coordinates.length;
	  stream.polygonStart();
	  while (++i < n) streamLine(coordinates[i], stream, 1);
	  stream.polygonEnd();
	}

	function geoStream(object, stream) {
	  if (object && streamObjectType.hasOwnProperty(object.type)) {
	    streamObjectType[object.type](object, stream);
	  } else {
	    streamGeometry(object, stream);
	  }
	}

	var areaRingSum = adder();

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

	function spherical(cartesian) {
	  return [atan2(cartesian[1], cartesian[0]), asin(cartesian[2])];
	}

	function cartesian(spherical) {
	  var lambda = spherical[0], phi = spherical[1], cosPhi = cos(phi);
	  return [cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi)];
	}

	function cartesianDot(a, b) {
	  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
	}

	function cartesianCross(a, b) {
	  return [a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]];
	}

	// TODO return a
	function cartesianAddInPlace(a, b) {
	  a[0] += b[0], a[1] += b[1], a[2] += b[2];
	}

	function cartesianScale(vector, k) {
	  return [vector[0] * k, vector[1] * k, vector[2] * k];
	}

	// TODO return d
	function cartesianNormalizeInPlace(d) {
	  var l = sqrt(d[0] * d[0] + d[1] * d[1] + d[2] * d[2]);
	  d[0] /= l, d[1] /= l, d[2] /= l;
	}

	var lambda0$1;
	var phi0;
	var lambda1;
	var phi1;
	var lambda2;
	var lambda00$1;
	var phi00$1;
	var p0;
	var deltaSum = adder();
	var ranges;
	var range$1;
	var boundsStream = {
	  point: boundsPoint,
	  lineStart: boundsLineStart,
	  lineEnd: boundsLineEnd,
	  polygonStart: function() {
	    boundsStream.point = boundsRingPoint;
	    boundsStream.lineStart = boundsRingStart;
	    boundsStream.lineEnd = boundsRingEnd;
	    deltaSum.reset();
	    areaStream.polygonStart();
	  },
	  polygonEnd: function() {
	    areaStream.polygonEnd();
	    boundsStream.point = boundsPoint;
	    boundsStream.lineStart = boundsLineStart;
	    boundsStream.lineEnd = boundsLineEnd;
	    if (areaRingSum < 0) lambda0$1 = -(lambda1 = 180), phi0 = -(phi1 = 90);
	    else if (deltaSum > epsilon) phi1 = 90;
	    else if (deltaSum < -epsilon) phi0 = -90;
	    range$1[0] = lambda0$1, range$1[1] = lambda1;
	  }
	};

	function boundsPoint(lambda, phi) {
	  ranges.push(range$1 = [lambda0$1 = lambda, lambda1 = lambda]);
	  if (phi < phi0) phi0 = phi;
	  if (phi > phi1) phi1 = phi;
	}

	function linePoint(lambda, phi) {
	  var p = cartesian([lambda * radians, phi * radians]);
	  if (p0) {
	    var normal = cartesianCross(p0, p),
	        equatorial = [normal[1], -normal[0], 0],
	        inflection = cartesianCross(equatorial, normal);
	    cartesianNormalizeInPlace(inflection);
	    inflection = spherical(inflection);
	    var delta = lambda - lambda2,
	        sign = delta > 0 ? 1 : -1,
	        lambdai = inflection[0] * degrees * sign,
	        phii,
	        antimeridian = abs(delta) > 180;
	    if (antimeridian ^ (sign * lambda2 < lambdai && lambdai < sign * lambda)) {
	      phii = inflection[1] * degrees;
	      if (phii > phi1) phi1 = phii;
	    } else if (lambdai = (lambdai + 360) % 360 - 180, antimeridian ^ (sign * lambda2 < lambdai && lambdai < sign * lambda)) {
	      phii = -inflection[1] * degrees;
	      if (phii < phi0) phi0 = phii;
	    } else {
	      if (phi < phi0) phi0 = phi;
	      if (phi > phi1) phi1 = phi;
	    }
	    if (antimeridian) {
	      if (lambda < lambda2) {
	        if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda;
	      } else {
	        if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda;
	      }
	    } else {
	      if (lambda1 >= lambda0$1) {
	        if (lambda < lambda0$1) lambda0$1 = lambda;
	        if (lambda > lambda1) lambda1 = lambda;
	      } else {
	        if (lambda > lambda2) {
	          if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda;
	        } else {
	          if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda;
	        }
	      }
	    }
	  } else {
	    ranges.push(range$1 = [lambda0$1 = lambda, lambda1 = lambda]);
	  }
	  if (phi < phi0) phi0 = phi;
	  if (phi > phi1) phi1 = phi;
	  p0 = p, lambda2 = lambda;
	}

	function boundsLineStart() {
	  boundsStream.point = linePoint;
	}

	function boundsLineEnd() {
	  range$1[0] = lambda0$1, range$1[1] = lambda1;
	  boundsStream.point = boundsPoint;
	  p0 = null;
	}

	function boundsRingPoint(lambda, phi) {
	  if (p0) {
	    var delta = lambda - lambda2;
	    deltaSum.add(abs(delta) > 180 ? delta + (delta > 0 ? 360 : -360) : delta);
	  } else {
	    lambda00$1 = lambda, phi00$1 = phi;
	  }
	  areaStream.point(lambda, phi);
	  linePoint(lambda, phi);
	}

	function boundsRingStart() {
	  areaStream.lineStart();
	}

	function boundsRingEnd() {
	  boundsRingPoint(lambda00$1, phi00$1);
	  areaStream.lineEnd();
	  if (abs(deltaSum) > epsilon) lambda0$1 = -(lambda1 = 180);
	  range$1[0] = lambda0$1, range$1[1] = lambda1;
	  p0 = null;
	}

	// Finds the left-right distance between two longitudes.
	// This is almost the same as (lambda1 - lambda0 + 360°) % 360°, except that we want
	// the distance between ±180° to be 360°.
	function angle(lambda0, lambda1) {
	  return (lambda1 -= lambda0) < 0 ? lambda1 + 360 : lambda1;
	}

	var W0;
	var W1;
	var X0;
	var Y0;
	var Z0;
	var X1;
	var Y1;
	var Z1;
	var X2;
	var Y2;
	var Z2;
	var lambda00$2;
	var phi00$2;
	var x0;
	var y0;
	var z0;
	// previous point

	var centroidStream = {
	  sphere: noop,
	  point: centroidPoint,
	  lineStart: centroidLineStart,
	  lineEnd: centroidLineEnd,
	  polygonStart: function() {
	    centroidStream.lineStart = centroidRingStart;
	    centroidStream.lineEnd = centroidRingEnd;
	  },
	  polygonEnd: function() {
	    centroidStream.lineStart = centroidLineStart;
	    centroidStream.lineEnd = centroidLineEnd;
	  }
	};

	// Arithmetic mean of Cartesian vectors.
	function centroidPoint(lambda, phi) {
	  lambda *= radians, phi *= radians;
	  var cosPhi = cos(phi);
	  centroidPointCartesian(cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi));
	}

	function centroidPointCartesian(x, y, z) {
	  ++W0;
	  X0 += (x - X0) / W0;
	  Y0 += (y - Y0) / W0;
	  Z0 += (z - Z0) / W0;
	}

	function centroidLineStart() {
	  centroidStream.point = centroidLinePointFirst;
	}

	function centroidLinePointFirst(lambda, phi) {
	  lambda *= radians, phi *= radians;
	  var cosPhi = cos(phi);
	  x0 = cosPhi * cos(lambda);
	  y0 = cosPhi * sin(lambda);
	  z0 = sin(phi);
	  centroidStream.point = centroidLinePoint;
	  centroidPointCartesian(x0, y0, z0);
	}

	function centroidLinePoint(lambda, phi) {
	  lambda *= radians, phi *= radians;
	  var cosPhi = cos(phi),
	      x = cosPhi * cos(lambda),
	      y = cosPhi * sin(lambda),
	      z = sin(phi),
	      w = atan2(sqrt((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w), x0 * x + y0 * y + z0 * z);
	  W1 += w;
	  X1 += w * (x0 + (x0 = x));
	  Y1 += w * (y0 + (y0 = y));
	  Z1 += w * (z0 + (z0 = z));
	  centroidPointCartesian(x0, y0, z0);
	}

	function centroidLineEnd() {
	  centroidStream.point = centroidPoint;
	}

	// See J. E. Brock, The Inertia Tensor for a Spherical Triangle,
	// J. Applied Mechanics 42, 239 (1975).
	function centroidRingStart() {
	  centroidStream.point = centroidRingPointFirst;
	}

	function centroidRingEnd() {
	  centroidRingPoint(lambda00$2, phi00$2);
	  centroidStream.point = centroidPoint;
	}

	function centroidRingPointFirst(lambda, phi) {
	  lambda00$2 = lambda, phi00$2 = phi;
	  lambda *= radians, phi *= radians;
	  centroidStream.point = centroidRingPoint;
	  var cosPhi = cos(phi);
	  x0 = cosPhi * cos(lambda);
	  y0 = cosPhi * sin(lambda);
	  z0 = sin(phi);
	  centroidPointCartesian(x0, y0, z0);
	}

	function centroidRingPoint(lambda, phi) {
	  lambda *= radians, phi *= radians;
	  var cosPhi = cos(phi),
	      x = cosPhi * cos(lambda),
	      y = cosPhi * sin(lambda),
	      z = sin(phi),
	      cx = y0 * z - z0 * y,
	      cy = z0 * x - x0 * z,
	      cz = x0 * y - y0 * x,
	      m = sqrt(cx * cx + cy * cy + cz * cz),
	      w = asin(m), // line weight = angle
	      v = m && -w / m; // area weight multiplier
	  X2 += v * cx;
	  Y2 += v * cy;
	  Z2 += v * cz;
	  W1 += w;
	  X1 += w * (x0 + (x0 = x));
	  Y1 += w * (y0 + (y0 = y));
	  Z1 += w * (z0 + (z0 = z));
	  centroidPointCartesian(x0, y0, z0);
	}

	function compose(a, b) {

	  function compose(x, y) {
	    return x = a(x, y), b(x[0], x[1]);
	  }

	  if (a.invert && b.invert) compose.invert = function(x, y) {
	    return x = b.invert(x, y), x && a.invert(x[0], x[1]);
	  };

	  return compose;
	}

	function rotationIdentity(lambda, phi) {
	  return [lambda > pi ? lambda - tau : lambda < -pi ? lambda + tau : lambda, phi];
	}

	rotationIdentity.invert = rotationIdentity;

	function rotateRadians(deltaLambda, deltaPhi, deltaGamma) {
	  return (deltaLambda %= tau) ? (deltaPhi || deltaGamma ? compose(rotationLambda(deltaLambda), rotationPhiGamma(deltaPhi, deltaGamma))
	    : rotationLambda(deltaLambda))
	    : (deltaPhi || deltaGamma ? rotationPhiGamma(deltaPhi, deltaGamma)
	    : rotationIdentity);
	}

	function forwardRotationLambda(deltaLambda) {
	  return function(lambda, phi) {
	    return lambda += deltaLambda, [lambda > pi ? lambda - tau : lambda < -pi ? lambda + tau : lambda, phi];
	  };
	}

	function rotationLambda(deltaLambda) {
	  var rotation = forwardRotationLambda(deltaLambda);
	  rotation.invert = forwardRotationLambda(-deltaLambda);
	  return rotation;
	}

	function rotationPhiGamma(deltaPhi, deltaGamma) {
	  var cosDeltaPhi = cos(deltaPhi),
	      sinDeltaPhi = sin(deltaPhi),
	      cosDeltaGamma = cos(deltaGamma),
	      sinDeltaGamma = sin(deltaGamma);

	  function rotation(lambda, phi) {
	    var cosPhi = cos(phi),
	        x = cos(lambda) * cosPhi,
	        y = sin(lambda) * cosPhi,
	        z = sin(phi),
	        k = z * cosDeltaPhi + x * sinDeltaPhi;
	    return [
	      atan2(y * cosDeltaGamma - k * sinDeltaGamma, x * cosDeltaPhi - z * sinDeltaPhi),
	      asin(k * cosDeltaGamma + y * sinDeltaGamma)
	    ];
	  }

	  rotation.invert = function(lambda, phi) {
	    var cosPhi = cos(phi),
	        x = cos(lambda) * cosPhi,
	        y = sin(lambda) * cosPhi,
	        z = sin(phi),
	        k = z * cosDeltaGamma - y * sinDeltaGamma;
	    return [
	      atan2(y * cosDeltaGamma + z * sinDeltaGamma, x * cosDeltaPhi + k * sinDeltaPhi),
	      asin(k * cosDeltaPhi - x * sinDeltaPhi)
	    ];
	  };

	  return rotation;
	}

	// Generates a circle centered at [0°, 0°], with a given radius and precision.
	function circleStream(stream, radius, delta, direction, t0, t1) {
	  if (!delta) return;
	  var cosRadius = cos(radius),
	      sinRadius = sin(radius),
	      step = direction * delta;
	  if (t0 == null) {
	    t0 = radius + direction * tau;
	    t1 = radius - step / 2;
	  } else {
	    t0 = circleRadius(cosRadius, t0);
	    t1 = circleRadius(cosRadius, t1);
	    if (direction > 0 ? t0 < t1 : t0 > t1) t0 += direction * tau;
	  }
	  for (var point, t = t0; direction > 0 ? t > t1 : t < t1; t -= step) {
	    point = spherical([cosRadius, -sinRadius * cos(t), -sinRadius * sin(t)]);
	    stream.point(point[0], point[1]);
	  }
	}

	// Returns the signed angle of a cartesian point relative to [cosRadius, 0, 0].
	function circleRadius(cosRadius, point) {
	  point = cartesian(point), point[0] -= cosRadius;
	  cartesianNormalizeInPlace(point);
	  var radius = acos(-point[1]);
	  return ((-point[2] < 0 ? -radius : radius) + tau - epsilon) % tau;
	}

	function clipBuffer() {
	  var lines = [],
	      line;
	  return {
	    point: function(x, y) {
	      line.push([x, y]);
	    },
	    lineStart: function() {
	      lines.push(line = []);
	    },
	    lineEnd: noop,
	    rejoin: function() {
	      if (lines.length > 1) lines.push(lines.pop().concat(lines.shift()));
	    },
	    result: function() {
	      var result = lines;
	      lines = [];
	      line = null;
	      return result;
	    }
	  };
	}

	function clipLine(a, b, x0, y0, x1, y1) {
	  var ax = a[0],
	      ay = a[1],
	      bx = b[0],
	      by = b[1],
	      t0 = 0,
	      t1 = 1,
	      dx = bx - ax,
	      dy = by - ay,
	      r;

	  r = x0 - ax;
	  if (!dx && r > 0) return;
	  r /= dx;
	  if (dx < 0) {
	    if (r < t0) return;
	    if (r < t1) t1 = r;
	  } else if (dx > 0) {
	    if (r > t1) return;
	    if (r > t0) t0 = r;
	  }

	  r = x1 - ax;
	  if (!dx && r < 0) return;
	  r /= dx;
	  if (dx < 0) {
	    if (r > t1) return;
	    if (r > t0) t0 = r;
	  } else if (dx > 0) {
	    if (r < t0) return;
	    if (r < t1) t1 = r;
	  }

	  r = y0 - ay;
	  if (!dy && r > 0) return;
	  r /= dy;
	  if (dy < 0) {
	    if (r < t0) return;
	    if (r < t1) t1 = r;
	  } else if (dy > 0) {
	    if (r > t1) return;
	    if (r > t0) t0 = r;
	  }

	  r = y1 - ay;
	  if (!dy && r < 0) return;
	  r /= dy;
	  if (dy < 0) {
	    if (r > t1) return;
	    if (r > t0) t0 = r;
	  } else if (dy > 0) {
	    if (r < t0) return;
	    if (r < t1) t1 = r;
	  }

	  if (t0 > 0) a[0] = ax + t0 * dx, a[1] = ay + t0 * dy;
	  if (t1 < 1) b[0] = ax + t1 * dx, b[1] = ay + t1 * dy;
	  return true;
	}

	function pointEqual(a, b) {
	  return abs(a[0] - b[0]) < epsilon && abs(a[1] - b[1]) < epsilon;
	}

	function Intersection(point, points, other, entry) {
	  this.x = point;
	  this.z = points;
	  this.o = other; // another intersection
	  this.e = entry; // is an entry?
	  this.v = false; // visited
	  this.n = this.p = null; // next & previous
	}

	// A generalized polygon clipping algorithm: given a polygon that has been cut
	// into its visible line segments, and rejoins the segments by interpolating
	// along the clip edge.
	function clipPolygon(segments, compareIntersection, startInside, interpolate, stream) {
	  var subject = [],
	      clip = [],
	      i,
	      n;

	  segments.forEach(function(segment) {
	    if ((n = segment.length - 1) <= 0) return;
	    var n, p0 = segment[0], p1 = segment[n], x;

	    // If the first and last points of a segment are coincident, then treat as a
	    // closed ring. TODO if all rings are closed, then the winding order of the
	    // exterior ring should be checked.
	    if (pointEqual(p0, p1)) {
	      stream.lineStart();
	      for (i = 0; i < n; ++i) stream.point((p0 = segment[i])[0], p0[1]);
	      stream.lineEnd();
	      return;
	    }

	    subject.push(x = new Intersection(p0, segment, null, true));
	    clip.push(x.o = new Intersection(p0, null, x, false));
	    subject.push(x = new Intersection(p1, segment, null, false));
	    clip.push(x.o = new Intersection(p1, null, x, true));
	  });

	  if (!subject.length) return;

	  clip.sort(compareIntersection);
	  link(subject);
	  link(clip);

	  for (i = 0, n = clip.length; i < n; ++i) {
	    clip[i].e = startInside = !startInside;
	  }

	  var start = subject[0],
	      points,
	      point;

	  while (1) {
	    // Find first unvisited intersection.
	    var current = start,
	        isSubject = true;
	    while (current.v) if ((current = current.n) === start) return;
	    points = current.z;
	    stream.lineStart();
	    do {
	      current.v = current.o.v = true;
	      if (current.e) {
	        if (isSubject) {
	          for (i = 0, n = points.length; i < n; ++i) stream.point((point = points[i])[0], point[1]);
	        } else {
	          interpolate(current.x, current.n.x, 1, stream);
	        }
	        current = current.n;
	      } else {
	        if (isSubject) {
	          points = current.p.z;
	          for (i = points.length - 1; i >= 0; --i) stream.point((point = points[i])[0], point[1]);
	        } else {
	          interpolate(current.x, current.p.x, -1, stream);
	        }
	        current = current.p;
	      }
	      current = current.o;
	      points = current.z;
	      isSubject = !isSubject;
	    } while (!current.v);
	    stream.lineEnd();
	  }
	}

	function link(array) {
	  if (!(n = array.length)) return;
	  var n,
	      i = 0,
	      a = array[0],
	      b;
	  while (++i < n) {
	    a.n = b = array[i];
	    b.p = a;
	    a = b;
	  }
	  a.n = b = array[0];
	  b.p = a;
	}

	var clipMax = 1e9;
	var clipMin = -clipMax;
	// TODO Use d3-polygon’s polygonContains here for the ring check?
	// TODO Eliminate duplicate buffering in clipBuffer and polygon.push?

	function clipExtent(x0, y0, x1, y1) {

	  function visible(x, y) {
	    return x0 <= x && x <= x1 && y0 <= y && y <= y1;
	  }

	  function interpolate(from, to, direction, stream) {
	    var a = 0, a1 = 0;
	    if (from == null
	        || (a = corner(from, direction)) !== (a1 = corner(to, direction))
	        || comparePoint(from, to) < 0 ^ direction > 0) {
	      do stream.point(a === 0 || a === 3 ? x0 : x1, a > 1 ? y1 : y0);
	      while ((a = (a + direction + 4) % 4) !== a1);
	    } else {
	      stream.point(to[0], to[1]);
	    }
	  }

	  function corner(p, direction) {
	    return abs(p[0] - x0) < epsilon ? direction > 0 ? 0 : 3
	        : abs(p[0] - x1) < epsilon ? direction > 0 ? 2 : 1
	        : abs(p[1] - y0) < epsilon ? direction > 0 ? 1 : 0
	        : direction > 0 ? 3 : 2; // abs(p[1] - y1) < epsilon
	  }

	  function compareIntersection(a, b) {
	    return comparePoint(a.x, b.x);
	  }

	  function comparePoint(a, b) {
	    var ca = corner(a, 1),
	        cb = corner(b, 1);
	    return ca !== cb ? ca - cb
	        : ca === 0 ? b[1] - a[1]
	        : ca === 1 ? a[0] - b[0]
	        : ca === 2 ? a[1] - b[1]
	        : b[0] - a[0];
	  }

	  return function(stream) {
	    var activeStream = stream,
	        bufferStream = clipBuffer(),
	        segments,
	        polygon,
	        ring,
	        x__, y__, v__, // first point
	        x_, y_, v_, // previous point
	        first,
	        clean;

	    var clipStream = {
	      point: point,
	      lineStart: lineStart,
	      lineEnd: lineEnd,
	      polygonStart: polygonStart,
	      polygonEnd: polygonEnd
	    };

	    function point(x, y) {
	      if (visible(x, y)) activeStream.point(x, y);
	    }

	    function polygonInside() {
	      var winding = 0;

	      for (var i = 0, n = polygon.length; i < n; ++i) {
	        for (var ring = polygon[i], j = 1, m = ring.length, point = ring[0], a0, a1, b0 = point[0], b1 = point[1]; j < m; ++j) {
	          a0 = b0, a1 = b1, point = ring[j], b0 = point[0], b1 = point[1];
	          if (a1 <= y1) { if (b1 > y1 && (b0 - a0) * (y1 - a1) > (b1 - a1) * (x0 - a0)) ++winding; }
	          else { if (b1 <= y1 && (b0 - a0) * (y1 - a1) < (b1 - a1) * (x0 - a0)) --winding; }
	        }
	      }

	      return winding;
	    }

	    // Buffer geometry within a polygon and then clip it en masse.
	    function polygonStart() {
	      activeStream = bufferStream, segments = [], polygon = [], clean = true;
	    }

	    function polygonEnd() {
	      var startInside = polygonInside(),
	          cleanInside = clean && startInside,
	          visible = (segments = merge(segments)).length;
	      if (cleanInside || visible) {
	        stream.polygonStart();
	        if (cleanInside) {
	          stream.lineStart();
	          interpolate(null, null, 1, stream);
	          stream.lineEnd();
	        }
	        if (visible) {
	          clipPolygon(segments, compareIntersection, startInside, interpolate, stream);
	        }
	        stream.polygonEnd();
	      }
	      activeStream = stream, segments = polygon = ring = null;
	    }

	    function lineStart() {
	      clipStream.point = linePoint;
	      if (polygon) polygon.push(ring = []);
	      first = true;
	      v_ = false;
	      x_ = y_ = NaN;
	    }

	    // TODO rather than special-case polygons, simply handle them separately.
	    // Ideally, coincident intersection points should be jittered to avoid
	    // clipping issues.
	    function lineEnd() {
	      if (segments) {
	        linePoint(x__, y__);
	        if (v__ && v_) bufferStream.rejoin();
	        segments.push(bufferStream.result());
	      }
	      clipStream.point = point;
	      if (v_) activeStream.lineEnd();
	    }

	    function linePoint(x, y) {
	      var v = visible(x, y);
	      if (polygon) ring.push([x, y]);
	      if (first) {
	        x__ = x, y__ = y, v__ = v;
	        first = false;
	        if (v) {
	          activeStream.lineStart();
	          activeStream.point(x, y);
	        }
	      } else {
	        if (v && v_) activeStream.point(x, y);
	        else {
	          var a = [x_ = Math.max(clipMin, Math.min(clipMax, x_)), y_ = Math.max(clipMin, Math.min(clipMax, y_))],
	              b = [x = Math.max(clipMin, Math.min(clipMax, x)), y = Math.max(clipMin, Math.min(clipMax, y))];
	          if (clipLine(a, b, x0, y0, x1, y1)) {
	            if (!v_) {
	              activeStream.lineStart();
	              activeStream.point(a[0], a[1]);
	            }
	            activeStream.point(b[0], b[1]);
	            if (!v) activeStream.lineEnd();
	            clean = false;
	          } else if (v) {
	            activeStream.lineStart();
	            activeStream.point(x, y);
	            clean = false;
	          }
	        }
	      }
	      x_ = x, y_ = y, v_ = v;
	    }

	    return clipStream;
	  };
	}

	var sum$1 = adder();

	function polygonContains(polygon, point) {
	  var lambda = point[0],
	      phi = point[1],
	      normal = [sin(lambda), -cos(lambda), 0],
	      angle = 0,
	      winding = 0;

	  sum$1.reset();

	  for (var i = 0, n = polygon.length; i < n; ++i) {
	    if (!(m = (ring = polygon[i]).length)) continue;
	    var ring,
	        m,
	        point0 = ring[m - 1],
	        lambda0 = point0[0],
	        phi0 = point0[1] / 2 + quarterPi,
	        sinPhi0 = sin(phi0),
	        cosPhi0 = cos(phi0);

	    for (var j = 0; j < m; ++j, lambda0 = lambda1, sinPhi0 = sinPhi1, cosPhi0 = cosPhi1, point0 = point1) {
	      var point1 = ring[j],
	          lambda1 = point1[0],
	          phi1 = point1[1] / 2 + quarterPi,
	          sinPhi1 = sin(phi1),
	          cosPhi1 = cos(phi1),
	          delta = lambda1 - lambda0,
	          sign = delta >= 0 ? 1 : -1,
	          absDelta = sign * delta,
	          antimeridian = absDelta > pi,
	          k = sinPhi0 * sinPhi1;

	      sum$1.add(atan2(k * sign * sin(absDelta), cosPhi0 * cosPhi1 + k * cos(absDelta)));
	      angle += antimeridian ? delta + sign * tau : delta;

	      // Are the longitudes either side of the point’s meridian (lambda),
	      // and are the latitudes smaller than the parallel (phi)?
	      if (antimeridian ^ lambda0 >= lambda ^ lambda1 >= lambda) {
	        var arc = cartesianCross(cartesian(point0), cartesian(point1));
	        cartesianNormalizeInPlace(arc);
	        var intersection = cartesianCross(normal, arc);
	        cartesianNormalizeInPlace(intersection);
	        var phiArc = (antimeridian ^ delta >= 0 ? -1 : 1) * asin(intersection[2]);
	        if (phi > phiArc || phi === phiArc && (arc[0] || arc[1])) {
	          winding += antimeridian ^ delta >= 0 ? 1 : -1;
	        }
	      }
	    }
	  }

	  // First, determine whether the South pole is inside or outside:
	  //
	  // It is inside if:
	  // * the polygon winds around it in a clockwise direction.
	  // * the polygon does not (cumulatively) wind around it, but has a negative
	  //   (counter-clockwise) area.
	  //
	  // Second, count the (signed) number of times a segment crosses a lambda
	  // from the point to the South pole.  If it is zero, then the point is the
	  // same side as the South pole.

	  return (angle < -epsilon || angle < epsilon && sum$1 < -epsilon) ^ (winding & 1);
	}

	var lengthSum = adder();
	var lambda0$2;
	var sinPhi0$1;
	var cosPhi0$1;
	var lengthStream = {
	  sphere: noop,
	  point: noop,
	  lineStart: lengthLineStart,
	  lineEnd: noop,
	  polygonStart: noop,
	  polygonEnd: noop
	};

	function lengthLineStart() {
	  lengthStream.point = lengthPointFirst;
	  lengthStream.lineEnd = lengthLineEnd;
	}

	function lengthLineEnd() {
	  lengthStream.point = lengthStream.lineEnd = noop;
	}

	function lengthPointFirst(lambda, phi) {
	  lambda *= radians, phi *= radians;
	  lambda0$2 = lambda, sinPhi0$1 = sin(phi), cosPhi0$1 = cos(phi);
	  lengthStream.point = lengthPoint;
	}

	function lengthPoint(lambda, phi) {
	  lambda *= radians, phi *= radians;
	  var sinPhi = sin(phi),
	      cosPhi = cos(phi),
	      delta = abs(lambda - lambda0$2),
	      cosDelta = cos(delta),
	      sinDelta = sin(delta),
	      x = cosPhi * sinDelta,
	      y = cosPhi0$1 * sinPhi - sinPhi0$1 * cosPhi * cosDelta,
	      z = sinPhi0$1 * sinPhi + cosPhi0$1 * cosPhi * cosDelta;
	  lengthSum.add(atan2(sqrt(x * x + y * y), z));
	  lambda0$2 = lambda, sinPhi0$1 = sinPhi, cosPhi0$1 = cosPhi;
	}

	function identity$1(x) {
	  return x;
	}

	var areaSum$1 = adder();
	var areaRingSum$1 = adder();
	var x00;
	var y00;
	var x0$1;
	var y0$1;
	var areaStream$1 = {
	  point: noop,
	  lineStart: noop,
	  lineEnd: noop,
	  polygonStart: function() {
	    areaStream$1.lineStart = areaRingStart$1;
	    areaStream$1.lineEnd = areaRingEnd$1;
	  },
	  polygonEnd: function() {
	    areaStream$1.lineStart = areaStream$1.lineEnd = areaStream$1.point = noop;
	    areaSum$1.add(abs(areaRingSum$1));
	    areaRingSum$1.reset();
	  },
	  result: function() {
	    var area = areaSum$1 / 2;
	    areaSum$1.reset();
	    return area;
	  }
	};

	function areaRingStart$1() {
	  areaStream$1.point = areaPointFirst$1;
	}

	function areaPointFirst$1(x, y) {
	  areaStream$1.point = areaPoint$1;
	  x00 = x0$1 = x, y00 = y0$1 = y;
	}

	function areaPoint$1(x, y) {
	  areaRingSum$1.add(y0$1 * x - x0$1 * y);
	  x0$1 = x, y0$1 = y;
	}

	function areaRingEnd$1() {
	  areaPoint$1(x00, y00);
	}

	var x0$2 = Infinity;
	var y0$2 = x0$2;
	var x1 = -x0$2;
	var y1 = x1;
	var boundsStream$1 = {
	  point: boundsPoint$1,
	  lineStart: noop,
	  lineEnd: noop,
	  polygonStart: noop,
	  polygonEnd: noop,
	  result: function() {
	    var bounds = [[x0$2, y0$2], [x1, y1]];
	    x1 = y1 = -(y0$2 = x0$2 = Infinity);
	    return bounds;
	  }
	};

	function boundsPoint$1(x, y) {
	  if (x < x0$2) x0$2 = x;
	  if (x > x1) x1 = x;
	  if (y < y0$2) y0$2 = y;
	  if (y > y1) y1 = y;
	}

	var X0$1 = 0;
	var Y0$1 = 0;
	var Z0$1 = 0;
	var X1$1 = 0;
	var Y1$1 = 0;
	var Z1$1 = 0;
	var X2$1 = 0;
	var Y2$1 = 0;
	var Z2$1 = 0;
	var x00$1;
	var y00$1;
	var x0$3;
	var y0$3;
	var centroidStream$1 = {
	  point: centroidPoint$1,
	  lineStart: centroidLineStart$1,
	  lineEnd: centroidLineEnd$1,
	  polygonStart: function() {
	    centroidStream$1.lineStart = centroidRingStart$1;
	    centroidStream$1.lineEnd = centroidRingEnd$1;
	  },
	  polygonEnd: function() {
	    centroidStream$1.point = centroidPoint$1;
	    centroidStream$1.lineStart = centroidLineStart$1;
	    centroidStream$1.lineEnd = centroidLineEnd$1;
	  },
	  result: function() {
	    var centroid = Z2$1 ? [X2$1 / Z2$1, Y2$1 / Z2$1]
	        : Z1$1 ? [X1$1 / Z1$1, Y1$1 / Z1$1]
	        : Z0$1 ? [X0$1 / Z0$1, Y0$1 / Z0$1]
	        : [NaN, NaN];
	    X0$1 = Y0$1 = Z0$1 =
	    X1$1 = Y1$1 = Z1$1 =
	    X2$1 = Y2$1 = Z2$1 = 0;
	    return centroid;
	  }
	};

	function centroidPoint$1(x, y) {
	  X0$1 += x;
	  Y0$1 += y;
	  ++Z0$1;
	}

	function centroidLineStart$1() {
	  centroidStream$1.point = centroidPointFirstLine;
	}

	function centroidPointFirstLine(x, y) {
	  centroidStream$1.point = centroidPointLine;
	  centroidPoint$1(x0$3 = x, y0$3 = y);
	}

	function centroidPointLine(x, y) {
	  var dx = x - x0$3, dy = y - y0$3, z = sqrt(dx * dx + dy * dy);
	  X1$1 += z * (x0$3 + x) / 2;
	  Y1$1 += z * (y0$3 + y) / 2;
	  Z1$1 += z;
	  centroidPoint$1(x0$3 = x, y0$3 = y);
	}

	function centroidLineEnd$1() {
	  centroidStream$1.point = centroidPoint$1;
	}

	function centroidRingStart$1() {
	  centroidStream$1.point = centroidPointFirstRing;
	}

	function centroidRingEnd$1() {
	  centroidPointRing(x00$1, y00$1);
	}

	function centroidPointFirstRing(x, y) {
	  centroidStream$1.point = centroidPointRing;
	  centroidPoint$1(x00$1 = x0$3 = x, y00$1 = y0$3 = y);
	}

	function centroidPointRing(x, y) {
	  var dx = x - x0$3,
	      dy = y - y0$3,
	      z = sqrt(dx * dx + dy * dy);

	  X1$1 += z * (x0$3 + x) / 2;
	  Y1$1 += z * (y0$3 + y) / 2;
	  Z1$1 += z;

	  z = y0$3 * x - x0$3 * y;
	  X2$1 += z * (x0$3 + x);
	  Y2$1 += z * (y0$3 + y);
	  Z2$1 += z * 3;
	  centroidPoint$1(x0$3 = x, y0$3 = y);
	}

	function PathContext(context) {
	  this._context = context;
	}

	PathContext.prototype = {
	  _radius: 4.5,
	  pointRadius: function(_) {
	    return this._radius = _, this;
	  },
	  polygonStart: function() {
	    this._line = 0;
	  },
	  polygonEnd: function() {
	    this._line = NaN;
	  },
	  lineStart: function() {
	    this._point = 0;
	  },
	  lineEnd: function() {
	    if (this._line === 0) this._context.closePath();
	    this._point = NaN;
	  },
	  point: function(x, y) {
	    switch (this._point) {
	      case 0: {
	        this._context.moveTo(x, y);
	        this._point = 1;
	        break;
	      }
	      case 1: {
	        this._context.lineTo(x, y);
	        break;
	      }
	      default: {
	        this._context.moveTo(x + this._radius, y);
	        this._context.arc(x, y, this._radius, 0, tau);
	        break;
	      }
	    }
	  },
	  result: noop
	};

	var lengthSum$1 = adder();
	var lengthRing;
	var x00$2;
	var y00$2;
	var x0$4;
	var y0$4;
	var lengthStream$1 = {
	  point: noop,
	  lineStart: function() {
	    lengthStream$1.point = lengthPointFirst$1;
	  },
	  lineEnd: function() {
	    if (lengthRing) lengthPoint$1(x00$2, y00$2);
	    lengthStream$1.point = noop;
	  },
	  polygonStart: function() {
	    lengthRing = true;
	  },
	  polygonEnd: function() {
	    lengthRing = null;
	  },
	  result: function() {
	    var length = +lengthSum$1;
	    lengthSum$1.reset();
	    return length;
	  }
	};

	function lengthPointFirst$1(x, y) {
	  lengthStream$1.point = lengthPoint$1;
	  x00$2 = x0$4 = x, y00$2 = y0$4 = y;
	}

	function lengthPoint$1(x, y) {
	  x0$4 -= x, y0$4 -= y;
	  lengthSum$1.add(sqrt(x0$4 * x0$4 + y0$4 * y0$4));
	  x0$4 = x, y0$4 = y;
	}

	function PathString() {
	  this._string = [];
	}

	PathString.prototype = {
	  _circle: circle$1(4.5),
	  pointRadius: function(_) {
	    return this._circle = circle$1(_), this;
	  },
	  polygonStart: function() {
	    this._line = 0;
	  },
	  polygonEnd: function() {
	    this._line = NaN;
	  },
	  lineStart: function() {
	    this._point = 0;
	  },
	  lineEnd: function() {
	    if (this._line === 0) this._string.push("Z");
	    this._point = NaN;
	  },
	  point: function(x, y) {
	    switch (this._point) {
	      case 0: {
	        this._string.push("M", x, ",", y);
	        this._point = 1;
	        break;
	      }
	      case 1: {
	        this._string.push("L", x, ",", y);
	        break;
	      }
	      default: {
	        this._string.push("M", x, ",", y, this._circle);
	        break;
	      }
	    }
	  },
	  result: function() {
	    if (this._string.length) {
	      var result = this._string.join("");
	      this._string = [];
	      return result;
	    }
	  }
	};

	function circle$1(radius) {
	  return "m0," + radius
	      + "a" + radius + "," + radius + " 0 1,1 0," + -2 * radius
	      + "a" + radius + "," + radius + " 0 1,1 0," + 2 * radius
	      + "z";
	}

	function geoPath(projection, context) {
	  var pointRadius = 4.5,
	      projectionStream,
	      contextStream;

	  function path(object) {
	    if (object) {
	      if (typeof pointRadius === "function") contextStream.pointRadius(+pointRadius.apply(this, arguments));
	      geoStream(object, projectionStream(contextStream));
	    }
	    return contextStream.result();
	  }

	  path.area = function(object) {
	    geoStream(object, projectionStream(areaStream$1));
	    return areaStream$1.result();
	  };

	  path.measure = function(object) {
	    geoStream(object, projectionStream(lengthStream$1));
	    return lengthStream$1.result();
	  };

	  path.bounds = function(object) {
	    geoStream(object, projectionStream(boundsStream$1));
	    return boundsStream$1.result();
	  };

	  path.centroid = function(object) {
	    geoStream(object, projectionStream(centroidStream$1));
	    return centroidStream$1.result();
	  };

	  path.projection = function(_) {
	    return arguments.length ? (projectionStream = _ == null ? (projection = null, identity$1) : (projection = _).stream, path) : projection;
	  };

	  path.context = function(_) {
	    if (!arguments.length) return context;
	    contextStream = _ == null ? (context = null, new PathString) : new PathContext(context = _);
	    if (typeof pointRadius !== "function") contextStream.pointRadius(pointRadius);
	    return path;
	  };

	  path.pointRadius = function(_) {
	    if (!arguments.length) return pointRadius;
	    pointRadius = typeof _ === "function" ? _ : (contextStream.pointRadius(+_), +_);
	    return path;
	  };

	  return path.projection(projection).context(context);
	}

	function clip(pointVisible, clipLine, interpolate, start) {
	  return function(rotate, sink) {
	    var line = clipLine(sink),
	        rotatedStart = rotate.invert(start[0], start[1]),
	        ringBuffer = clipBuffer(),
	        ringSink = clipLine(ringBuffer),
	        polygonStarted = false,
	        polygon,
	        segments,
	        ring;

	    var clip = {
	      point: point,
	      lineStart: lineStart,
	      lineEnd: lineEnd,
	      polygonStart: function() {
	        clip.point = pointRing;
	        clip.lineStart = ringStart;
	        clip.lineEnd = ringEnd;
	        segments = [];
	        polygon = [];
	      },
	      polygonEnd: function() {
	        clip.point = point;
	        clip.lineStart = lineStart;
	        clip.lineEnd = lineEnd;
	        segments = merge(segments);
	        var startInside = polygonContains(polygon, rotatedStart);
	        if (segments.length) {
	          if (!polygonStarted) sink.polygonStart(), polygonStarted = true;
	          clipPolygon(segments, compareIntersection, startInside, interpolate, sink);
	        } else if (startInside) {
	          if (!polygonStarted) sink.polygonStart(), polygonStarted = true;
	          sink.lineStart();
	          interpolate(null, null, 1, sink);
	          sink.lineEnd();
	        }
	        if (polygonStarted) sink.polygonEnd(), polygonStarted = false;
	        segments = polygon = null;
	      },
	      sphere: function() {
	        sink.polygonStart();
	        sink.lineStart();
	        interpolate(null, null, 1, sink);
	        sink.lineEnd();
	        sink.polygonEnd();
	      }
	    };

	    function point(lambda, phi) {
	      var point = rotate(lambda, phi);
	      if (pointVisible(lambda = point[0], phi = point[1])) sink.point(lambda, phi);
	    }

	    function pointLine(lambda, phi) {
	      var point = rotate(lambda, phi);
	      line.point(point[0], point[1]);
	    }

	    function lineStart() {
	      clip.point = pointLine;
	      line.lineStart();
	    }

	    function lineEnd() {
	      clip.point = point;
	      line.lineEnd();
	    }

	    function pointRing(lambda, phi) {
	      ring.push([lambda, phi]);
	      var point = rotate(lambda, phi);
	      ringSink.point(point[0], point[1]);
	    }

	    function ringStart() {
	      ringSink.lineStart();
	      ring = [];
	    }

	    function ringEnd() {
	      pointRing(ring[0][0], ring[0][1]);
	      ringSink.lineEnd();

	      var clean = ringSink.clean(),
	          ringSegments = ringBuffer.result(),
	          i, n = ringSegments.length, m,
	          segment,
	          point;

	      ring.pop();
	      polygon.push(ring);
	      ring = null;

	      if (!n) return;

	      // No intersections.
	      if (clean & 1) {
	        segment = ringSegments[0];
	        if ((m = segment.length - 1) > 0) {
	          if (!polygonStarted) sink.polygonStart(), polygonStarted = true;
	          sink.lineStart();
	          for (i = 0; i < m; ++i) sink.point((point = segment[i])[0], point[1]);
	          sink.lineEnd();
	        }
	        return;
	      }

	      // Rejoin connected segments.
	      // TODO reuse ringBuffer.rejoin()?
	      if (n > 1 && clean & 2) ringSegments.push(ringSegments.pop().concat(ringSegments.shift()));

	      segments.push(ringSegments.filter(validSegment));
	    }

	    return clip;
	  };
	}

	function validSegment(segment) {
	  return segment.length > 1;
	}

	// Intersections are sorted along the clip edge. For both antimeridian cutting
	// and circle clipping, the same comparison is used.
	function compareIntersection(a, b) {
	  return ((a = a.x)[0] < 0 ? a[1] - halfPi - epsilon : halfPi - a[1])
	       - ((b = b.x)[0] < 0 ? b[1] - halfPi - epsilon : halfPi - b[1]);
	}

	var clipAntimeridian = clip(
	  function() { return true; },
	  clipAntimeridianLine,
	  clipAntimeridianInterpolate,
	  [-pi, -halfPi]
	);

	// Takes a line and cuts into visible segments. Return values: 0 - there were
	// intersections or the line was empty; 1 - no intersections; 2 - there were
	// intersections, and the first and last segments should be rejoined.
	function clipAntimeridianLine(stream) {
	  var lambda0 = NaN,
	      phi0 = NaN,
	      sign0 = NaN,
	      clean; // no intersections

	  return {
	    lineStart: function() {
	      stream.lineStart();
	      clean = 1;
	    },
	    point: function(lambda1, phi1) {
	      var sign1 = lambda1 > 0 ? pi : -pi,
	          delta = abs(lambda1 - lambda0);
	      if (abs(delta - pi) < epsilon) { // line crosses a pole
	        stream.point(lambda0, phi0 = (phi0 + phi1) / 2 > 0 ? halfPi : -halfPi);
	        stream.point(sign0, phi0);
	        stream.lineEnd();
	        stream.lineStart();
	        stream.point(sign1, phi0);
	        stream.point(lambda1, phi0);
	        clean = 0;
	      } else if (sign0 !== sign1 && delta >= pi) { // line crosses antimeridian
	        if (abs(lambda0 - sign0) < epsilon) lambda0 -= sign0 * epsilon; // handle degeneracies
	        if (abs(lambda1 - sign1) < epsilon) lambda1 -= sign1 * epsilon;
	        phi0 = clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1);
	        stream.point(sign0, phi0);
	        stream.lineEnd();
	        stream.lineStart();
	        stream.point(sign1, phi0);
	        clean = 0;
	      }
	      stream.point(lambda0 = lambda1, phi0 = phi1);
	      sign0 = sign1;
	    },
	    lineEnd: function() {
	      stream.lineEnd();
	      lambda0 = phi0 = NaN;
	    },
	    clean: function() {
	      return 2 - clean; // if intersections, rejoin first and last segments
	    }
	  };
	}

	function clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1) {
	  var cosPhi0,
	      cosPhi1,
	      sinLambda0Lambda1 = sin(lambda0 - lambda1);
	  return abs(sinLambda0Lambda1) > epsilon
	      ? atan((sin(phi0) * (cosPhi1 = cos(phi1)) * sin(lambda1)
	          - sin(phi1) * (cosPhi0 = cos(phi0)) * sin(lambda0))
	          / (cosPhi0 * cosPhi1 * sinLambda0Lambda1))
	      : (phi0 + phi1) / 2;
	}

	function clipAntimeridianInterpolate(from, to, direction, stream) {
	  var phi;
	  if (from == null) {
	    phi = direction * halfPi;
	    stream.point(-pi, phi);
	    stream.point(0, phi);
	    stream.point(pi, phi);
	    stream.point(pi, 0);
	    stream.point(pi, -phi);
	    stream.point(0, -phi);
	    stream.point(-pi, -phi);
	    stream.point(-pi, 0);
	    stream.point(-pi, phi);
	  } else if (abs(from[0] - to[0]) > epsilon) {
	    var lambda = from[0] < to[0] ? pi : -pi;
	    phi = direction * lambda / 2;
	    stream.point(-lambda, phi);
	    stream.point(0, phi);
	    stream.point(lambda, phi);
	  } else {
	    stream.point(to[0], to[1]);
	  }
	}

	function clipCircle(radius, delta) {
	  var cr = cos(radius),
	      smallRadius = cr > 0,
	      notHemisphere = abs(cr) > epsilon; // TODO optimise for this common case

	  function interpolate(from, to, direction, stream) {
	    circleStream(stream, radius, delta, direction, from, to);
	  }

	  function visible(lambda, phi) {
	    return cos(lambda) * cos(phi) > cr;
	  }

	  // Takes a line and cuts into visible segments. Return values used for polygon
	  // clipping: 0 - there were intersections or the line was empty; 1 - no
	  // intersections 2 - there were intersections, and the first and last segments
	  // should be rejoined.
	  function clipLine(stream) {
	    var point0, // previous point
	        c0, // code for previous point
	        v0, // visibility of previous point
	        v00, // visibility of first point
	        clean; // no intersections
	    return {
	      lineStart: function() {
	        v00 = v0 = false;
	        clean = 1;
	      },
	      point: function(lambda, phi) {
	        var point1 = [lambda, phi],
	            point2,
	            v = visible(lambda, phi),
	            c = smallRadius
	              ? v ? 0 : code(lambda, phi)
	              : v ? code(lambda + (lambda < 0 ? pi : -pi), phi) : 0;
	        if (!point0 && (v00 = v0 = v)) stream.lineStart();
	        // Handle degeneracies.
	        // TODO ignore if not clipping polygons.
	        if (v !== v0) {
	          point2 = intersect(point0, point1);
	          if (pointEqual(point0, point2) || pointEqual(point1, point2)) {
	            point1[0] += epsilon;
	            point1[1] += epsilon;
	            v = visible(point1[0], point1[1]);
	          }
	        }
	        if (v !== v0) {
	          clean = 0;
	          if (v) {
	            // outside going in
	            stream.lineStart();
	            point2 = intersect(point1, point0);
	            stream.point(point2[0], point2[1]);
	          } else {
	            // inside going out
	            point2 = intersect(point0, point1);
	            stream.point(point2[0], point2[1]);
	            stream.lineEnd();
	          }
	          point0 = point2;
	        } else if (notHemisphere && point0 && smallRadius ^ v) {
	          var t;
	          // If the codes for two points are different, or are both zero,
	          // and there this segment intersects with the small circle.
	          if (!(c & c0) && (t = intersect(point1, point0, true))) {
	            clean = 0;
	            if (smallRadius) {
	              stream.lineStart();
	              stream.point(t[0][0], t[0][1]);
	              stream.point(t[1][0], t[1][1]);
	              stream.lineEnd();
	            } else {
	              stream.point(t[1][0], t[1][1]);
	              stream.lineEnd();
	              stream.lineStart();
	              stream.point(t[0][0], t[0][1]);
	            }
	          }
	        }
	        if (v && (!point0 || !pointEqual(point0, point1))) {
	          stream.point(point1[0], point1[1]);
	        }
	        point0 = point1, v0 = v, c0 = c;
	      },
	      lineEnd: function() {
	        if (v0) stream.lineEnd();
	        point0 = null;
	      },
	      // Rejoin first and last segments if there were intersections and the first
	      // and last points were visible.
	      clean: function() {
	        return clean | ((v00 && v0) << 1);
	      }
	    };
	  }

	  // Intersects the great circle between a and b with the clip circle.
	  function intersect(a, b, two) {
	    var pa = cartesian(a),
	        pb = cartesian(b);

	    // We have two planes, n1.p = d1 and n2.p = d2.
	    // Find intersection line p(t) = c1 n1 + c2 n2 + t (n1 ⨯ n2).
	    var n1 = [1, 0, 0], // normal