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van Wijk's icosahedral foldout
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README.md
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d3-geo-projection.js
// https://d3js.org/d3-geo-projection/ Version 2.2.0. Copyright 2017 Mike Bostock.
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports, require('d3-geo'), require('d3-array')) :
typeof define === 'function' && define.amd ? define(['exports', 'd3-geo', 'd3-array'], factory) :
(factory((global.d3 = global.d3 || {}),global.d3,global.d3));
}(this, (function (exports,d3Geo,d3Array) { 'use strict';
var abs = Math.abs;
var atan = Math.atan;
var atan2 = Math.atan2;
var cos = Math.cos;
var exp = Math.exp;
var floor = Math.floor;
var log = Math.log;
var max = Math.max;
var min = Math.min;
var pow = Math.pow;
var round = Math.round;
var sign = Math.sign || function(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; };
var sin = Math.sin;
var tan = Math.tan;
var epsilon = 1e-6;
var epsilon2 = 1e-12;
var pi = Math.PI;
var halfPi = pi / 2;
var quarterPi = pi / 4;
var sqrt1_2 = Math.SQRT1_2;
var sqrt2 = sqrt(2);
var sqrtPi = sqrt(pi);
var tau = pi * 2;
var degrees = 180 / pi;
var radians = pi / 180;
function sinci(x) {
return x ? x / Math.sin(x) : 1;
}
function asin(x) {
return x > 1 ? halfPi : x < -1 ? -halfPi : Math.asin(x);
}
function acos(x) {
return x > 1 ? 0 : x < -1 ? pi : Math.acos(x);
}
function sqrt(x) {
return x > 0 ? Math.sqrt(x) : 0;
}
function tanh(x) {
x = exp(2 * x);
return (x - 1) / (x + 1);
}
function sinh(x) {
return (exp(x) - exp(-x)) / 2;
}
function cosh(x) {
return (exp(x) + exp(-x)) / 2;
}
function arsinh(x) {
return log(x + sqrt(x * x + 1));
}
function arcosh(x) {
return log(x + sqrt(x * x - 1));
}
function airyRaw(beta) {
var tanBeta_2 = tan(beta / 2),
b = 2 * log(cos(beta / 2)) / (tanBeta_2 * tanBeta_2);
function forward(x, y) {
var cosx = cos(x),
cosy = cos(y),
siny = sin(y),
cosz = cosy * cosx,
k = -((1 - cosz ? log((1 + cosz) / 2) / (1 - cosz) : -0.5) + b / (1 + cosz));
return [k * cosy * sin(x), k * siny];
}
forward.invert = function(x, y) {
var r = sqrt(x * x + y * y),
z = -beta / 2,
i = 50, delta;
if (!r) return [0, 0];
do {
var z_2 = z / 2,
cosz_2 = cos(z_2),
sinz_2 = sin(z_2),
tanz_2 = tan(z_2),
lnsecz_2 = log(1 / cosz_2);
z -= delta = (2 / tanz_2 * lnsecz_2 - b * tanz_2 - r) / (-lnsecz_2 / (sinz_2 * sinz_2) + 1 - b / (2 * cosz_2 * cosz_2));
} while (abs(delta) > epsilon && --i > 0);
var sinz = sin(z);
return [atan2(x * sinz, r * cos(z)), asin(y * sinz / r)];
};
return forward;
}
var airy = function() {
var beta = halfPi,
m = d3Geo.geoProjectionMutator(airyRaw),
p = m(beta);
p.radius = function(_) {
return arguments.length ? m(beta = _ * radians) : beta * degrees;
};
return p
.scale(179.976)
.clipAngle(147);
};
function aitoffRaw(x, y) {
var cosy = cos(y), sincia = sinci(acos(cosy * cos(x /= 2)));
return [2 * cosy * sin(x) * sincia, sin(y) * sincia];
}
// Abort if [x, y] is not within an ellipse centered at [0, 0] with
// semi-major axis pi and semi-minor axis pi/2.
aitoffRaw.invert = function(x, y) {
if (x * x + 4 * y * y > pi * pi + epsilon) return;
var x1 = x, y1 = y, i = 25;
do {
var sinx = sin(x1),
sinx_2 = sin(x1 / 2),
cosx_2 = cos(x1 / 2),
siny = sin(y1),
cosy = cos(y1),
sin_2y = sin(2 * y1),
sin2y = siny * siny,
cos2y = cosy * cosy,
sin2x_2 = sinx_2 * sinx_2,
c = 1 - cos2y * cosx_2 * cosx_2,
e = c ? acos(cosy * cosx_2) * sqrt(f = 1 / c) : f = 0,
f,
fx = 2 * e * cosy * sinx_2 - x,
fy = e * siny - y,
dxdx = f * (cos2y * sin2x_2 + e * cosy * cosx_2 * sin2y),
dxdy = f * (0.5 * sinx * sin_2y - e * 2 * siny * sinx_2),
dydx = f * 0.25 * (sin_2y * sinx_2 - e * siny * cos2y * sinx),
dydy = f * (sin2y * cosx_2 + e * sin2x_2 * cosy),
z = dxdy * dydx - dydy * dxdx;
if (!z) break;
var dx = (fy * dxdy - fx * dydy) / z,
dy = (fx * dydx - fy * dxdx) / z;
x1 -= dx, y1 -= dy;
} while ((abs(dx) > epsilon || abs(dy) > epsilon) && --i > 0);
return [x1, y1];
};
var aitoff = function() {
return d3Geo.geoProjection(aitoffRaw)
.scale(152.63);
};
function armadilloRaw(phi0) {
var sinPhi0 = sin(phi0),
cosPhi0 = cos(phi0),
sPhi0 = phi0 >= 0 ? 1 : -1,
tanPhi0 = tan(sPhi0 * phi0),
k = (1 + sinPhi0 - cosPhi0) / 2;
function forward(lambda, phi) {
var cosPhi = cos(phi),
cosLambda = cos(lambda /= 2);
return [
(1 + cosPhi) * sin(lambda),
(sPhi0 * phi > -atan2(cosLambda, tanPhi0) - 1e-3 ? 0 : -sPhi0 * 10) + k + sin(phi) * cosPhi0 - (1 + cosPhi) * sinPhi0 * cosLambda // TODO D3 core should allow null or [NaN, NaN] to be returned.
];
}
forward.invert = function(x, y) {
var lambda = 0,
phi = 0,
i = 50;
do {
var cosLambda = cos(lambda),
sinLambda = sin(lambda),
cosPhi = cos(phi),
sinPhi = sin(phi),
A = 1 + cosPhi,
fx = A * sinLambda - x,
fy = k + sinPhi * cosPhi0 - A * sinPhi0 * cosLambda - y,
dxdLambda = A * cosLambda / 2,
dxdPhi = -sinLambda * sinPhi,
dydLambda = sinPhi0 * A * sinLambda / 2,
dydPhi = cosPhi0 * cosPhi + sinPhi0 * cosLambda * sinPhi,
denominator = dxdPhi * dydLambda - dydPhi * dxdLambda,
dLambda = (fy * dxdPhi - fx * dydPhi) / denominator / 2,
dPhi = (fx * dydLambda - fy * dxdLambda) / denominator;
lambda -= dLambda, phi -= dPhi;
} while ((abs(dLambda) > epsilon || abs(dPhi) > epsilon) && --i > 0);
return sPhi0 * phi > -atan2(cos(lambda), tanPhi0) - 1e-3 ? [lambda * 2, phi] : null;
};
return forward;
}
var armadillo = function() {
var phi0 = 20 * radians,
sPhi0 = phi0 >= 0 ? 1 : -1,
tanPhi0 = tan(sPhi0 * phi0),
m = d3Geo.geoProjectionMutator(armadilloRaw),
p = m(phi0),
stream_ = p.stream;
p.parallel = function(_) {
if (!arguments.length) return phi0 * degrees;
tanPhi0 = tan((sPhi0 = (phi0 = _ * radians) >= 0 ? 1 : -1) * phi0);
return m(phi0);
};
p.stream = function(stream) {
var rotate = p.rotate(),
rotateStream = stream_(stream),
sphereStream = (p.rotate([0, 0]), stream_(stream));
p.rotate(rotate);
rotateStream.sphere = function() {
sphereStream.polygonStart(), sphereStream.lineStart();
for (var lambda = sPhi0 * -180; sPhi0 * lambda < 180; lambda += sPhi0 * 90) sphereStream.point(lambda, sPhi0 * 90);
while (sPhi0 * (lambda -= phi0) >= -180) { // TODO precision?
sphereStream.point(lambda, sPhi0 * -atan2(cos(lambda * radians / 2), tanPhi0) * degrees);
}
sphereStream.lineEnd(), sphereStream.polygonEnd();
};
return rotateStream;
};
return p
.scale(218.695)
.center([0, 28.0974]);
};
function augustRaw(lambda, phi) {
var tanPhi = tan(phi / 2),
k = sqrt(1 - tanPhi * tanPhi),
c = 1 + k * cos(lambda /= 2),
x = sin(lambda) * k / c,
y = tanPhi / c,
x2 = x * x,
y2 = y * y;
return [
4 / 3 * x * (3 + x2 - 3 * y2),
4 / 3 * y * (3 + 3 * x2 - y2)
];
}
augustRaw.invert = function(x, y) {
x *= 3 / 8, y *= 3 / 8;
if (!x && abs(y) > 1) return null;
var x2 = x * x,
y2 = y * y,
s = 1 + x2 + y2,
sin3Eta = sqrt((s - sqrt(s * s - 4 * y * y)) / 2),
eta = asin(sin3Eta) / 3,
xi = sin3Eta ? arcosh(abs(y / sin3Eta)) / 3 : arsinh(abs(x)) / 3,
cosEta = cos(eta),
coshXi = cosh(xi),
d = coshXi * coshXi - cosEta * cosEta;
return [
sign(x) * 2 * atan2(sinh(xi) * cosEta, 0.25 - d),
sign(y) * 2 * atan2(coshXi * sin(eta), 0.25 + d)
];
};
var august = function() {
return d3Geo.geoProjection(augustRaw)
.scale(66.1603);
};
var sqrt8 = sqrt(8);
var phi0 = log(1 + sqrt2);
function bakerRaw(lambda, phi) {
var phi0 = abs(phi);
return phi0 < quarterPi
? [lambda, log(tan(quarterPi + phi / 2))]
: [lambda * cos(phi0) * (2 * sqrt2 - 1 / sin(phi0)), sign(phi) * (2 * sqrt2 * (phi0 - quarterPi) - log(tan(phi0 / 2)))];
}
bakerRaw.invert = function(x, y) {
if ((y0 = abs(y)) < phi0) return [x, 2 * atan(exp(y)) - halfPi];
var phi = quarterPi, i = 25, delta, y0;
do {
var cosPhi_2 = cos(phi / 2), tanPhi_2 = tan(phi / 2);
phi -= delta = (sqrt8 * (phi - quarterPi) - log(tanPhi_2) - y0) / (sqrt8 - cosPhi_2 * cosPhi_2 / (2 * tanPhi_2));
} while (abs(delta) > epsilon2 && --i > 0);
return [x / (cos(phi) * (sqrt8 - 1 / sin(phi))), sign(y) * phi];
};
var baker = function() {
return d3Geo.geoProjection(bakerRaw)
.scale(112.314);
};
function berghausRaw(lobes) {
var k = 2 * pi / lobes;
function forward(lambda, phi) {
var p = d3Geo.geoAzimuthalEquidistantRaw(lambda, phi);
if (abs(lambda) > halfPi) { // back hemisphere
var theta = atan2(p[1], p[0]),
r = sqrt(p[0] * p[0] + p[1] * p[1]),
theta0 = k * round((theta - halfPi) / k) + halfPi,
alpha = atan2(sin(theta -= theta0), 2 - cos(theta)); // angle relative to lobe end
theta = theta0 + asin(pi / r * sin(alpha)) - alpha;
p[0] = r * cos(theta);
p[1] = r * sin(theta);
}
return p;
}
forward.invert = function(x, y) {
var r = sqrt(x * x + y * y);
if (r > halfPi) {
var theta = atan2(y, x),
theta0 = k * round((theta - halfPi) / k) + halfPi,
s = theta > theta0 ? -1 : 1,
A = r * cos(theta0 - theta),
cotAlpha = 1 / tan(s * acos((A - pi) / sqrt(pi * (pi - 2 * A) + r * r)));
theta = theta0 + 2 * atan((cotAlpha + s * sqrt(cotAlpha * cotAlpha - 3)) / 3);
x = r * cos(theta), y = r * sin(theta);
}
return d3Geo.geoAzimuthalEquidistantRaw.invert(x, y);
};
return forward;
}
var berghaus = function() {
var lobes = 5,
m = d3Geo.geoProjectionMutator(berghausRaw),
p = m(lobes),
projectionStream = p.stream,
epsilon$$1 = 1e-2,
cr = -cos(epsilon$$1 * radians),
sr = sin(epsilon$$1 * radians);
p.lobes = function(_) {
return arguments.length ? m(lobes = +_) : lobes;
};
p.stream = function(stream) {
var rotate = p.rotate(),
rotateStream = projectionStream(stream),
sphereStream = (p.rotate([0, 0]), projectionStream(stream));
p.rotate(rotate);
rotateStream.sphere = function() {
sphereStream.polygonStart(), sphereStream.lineStart();
for (var i = 0, delta = 360 / lobes, delta0 = 2 * pi / lobes, phi = 90 - 180 / lobes, phi0 = halfPi; i < lobes; ++i, phi -= delta, phi0 -= delta0) {
sphereStream.point(atan2(sr * cos(phi0), cr) * degrees, asin(sr * sin(phi0)) * degrees);
if (phi < -90) {
sphereStream.point(-90, -180 - phi - epsilon$$1);
sphereStream.point(-90, -180 - phi + epsilon$$1);
} else {
sphereStream.point(90, phi + epsilon$$1);
sphereStream.point(90, phi - epsilon$$1);
}
}
sphereStream.lineEnd(), sphereStream.polygonEnd();
};
return rotateStream;
};
return p
.scale(87.8076)
.center([0, 17.1875])
.clipAngle(180 - 1e-3);
};
function mollweideBromleyTheta(cp, phi) {
var cpsinPhi = cp * sin(phi), i = 30, delta;
do phi -= delta = (phi + sin(phi) - cpsinPhi) / (1 + cos(phi));
while (abs(delta) > epsilon && --i > 0);
return phi / 2;
}
function mollweideBromleyRaw(cx, cy, cp) {
function forward(lambda, phi) {
return [cx * lambda * cos(phi = mollweideBromleyTheta(cp, phi)), cy * sin(phi)];
}
forward.invert = function(x, y) {
return y = asin(y / cy), [x / (cx * cos(y)), asin((2 * y + sin(2 * y)) / cp)];
};
return forward;
}
var mollweideRaw = mollweideBromleyRaw(sqrt2 / halfPi, sqrt2, pi);
var mollweide = function() {
return d3Geo.geoProjection(mollweideRaw)
.scale(169.529);
};
var k = 2.00276;
var w = 1.11072;
function boggsRaw(lambda, phi) {
var theta = mollweideBromleyTheta(pi, phi);
return [k * lambda / (1 / cos(phi) + w / cos(theta)), (phi + sqrt2 * sin(theta)) / k];
}
boggsRaw.invert = function(x, y) {
var ky = k * y, theta = y < 0 ? -quarterPi : quarterPi, i = 25, delta, phi;
do {
phi = ky - sqrt2 * sin(theta);
theta -= delta = (sin(2 * theta) + 2 * theta - pi * sin(phi)) / (2 * cos(2 * theta) + 2 + pi * cos(phi) * sqrt2 * cos(theta));
} while (abs(delta) > epsilon && --i > 0);
phi = ky - sqrt2 * sin(theta);
return [x * (1 / cos(phi) + w / cos(theta)) / k, phi];
};
var boggs = function() {
return d3Geo.geoProjection(boggsRaw)
.scale(160.857);
};
var parallel1 = function(projectAt) {
var phi0 = 0,
m = d3Geo.geoProjectionMutator(projectAt),
p = m(phi0);
p.parallel = function(_) {
return arguments.length ? m(phi0 = _ * radians) : phi0 * degrees;
};
return p;
};
function sinusoidalRaw(lambda, phi) {
return [lambda * cos(phi), phi];
}
sinusoidalRaw.invert = function(x, y) {
return [x / cos(y), y];
};
var sinusoidal = function() {
return d3Geo.geoProjection(sinusoidalRaw)
.scale(152.63);
};
function bonneRaw(phi0) {
if (!phi0) return sinusoidalRaw;
var cotPhi0 = 1 / tan(phi0);
function forward(lambda, phi) {
var rho = cotPhi0 + phi0 - phi,
e = rho ? lambda * cos(phi) / rho : rho;
return [rho * sin(e), cotPhi0 - rho * cos(e)];
}
forward.invert = function(x, y) {
var rho = sqrt(x * x + (y = cotPhi0 - y) * y),
phi = cotPhi0 + phi0 - rho;
return [rho / cos(phi) * atan2(x, y), phi];
};
return forward;
}
var bonne = function() {
return parallel1(bonneRaw)
.scale(123.082)
.center([0, 26.1441])
.parallel(45);
};
function bottomleyRaw(sinPsi) {
function forward(lambda, phi) {
var rho = halfPi - phi,
eta = rho ? lambda * sinPsi * sin(rho) / rho : rho;
return [rho * sin(eta) / sinPsi, halfPi - rho * cos(eta)];
}
forward.invert = function(x, y) {
var x1 = x * sinPsi,
y1 = halfPi - y,
rho = sqrt(x1 * x1 + y1 * y1),
eta = atan2(x1, y1);
return [(rho ? rho / sin(rho) : 1) * eta / sinPsi, halfPi - rho];
};
return forward;
}
var bottomley = function() {
var sinPsi = 0.5,
m = d3Geo.geoProjectionMutator(bottomleyRaw),
p = m(sinPsi);
p.fraction = function(_) {
return arguments.length ? m(sinPsi = +_) : sinPsi;
};
return p
.scale(158.837);
};
var bromleyRaw = mollweideBromleyRaw(1, 4 / pi, pi);
var bromley = function() {
return d3Geo.geoProjection(bromleyRaw)
.scale(152.63);
};
// Azimuthal distance.
function distance(dPhi, c1, s1, c2, s2, dLambda) {
var cosdLambda = cos(dLambda), r;
if (abs(dPhi) > 1 || abs(dLambda) > 1) {
r = acos(s1 * s2 + c1 * c2 * cosdLambda);
} else {
var sindPhi = sin(dPhi / 2), sindLambda = sin(dLambda / 2);
r = 2 * asin(sqrt(sindPhi * sindPhi + c1 * c2 * sindLambda * sindLambda));
}
return abs(r) > epsilon ? [r, atan2(c2 * sin(dLambda), c1 * s2 - s1 * c2 * cosdLambda)] : [0, 0];
}
// Angle opposite a, and contained between sides of lengths b and c.
function angle(b, c, a) {
return acos((b * b + c * c - a * a) / (2 * b * c));
}
// Normalize longitude.
function longitude(lambda) {
return lambda - 2 * pi * floor((lambda + pi) / (2 * pi));
}
function chamberlinRaw(p0, p1, p2) {
var points = [
[p0[0], p0[1], sin(p0[1]), cos(p0[1])],
[p1[0], p1[1], sin(p1[1]), cos(p1[1])],
[p2[0], p2[1], sin(p2[1]), cos(p2[1])]
];
for (var a = points[2], b, i = 0; i < 3; ++i, a = b) {
b = points[i];
a.v = distance(b[1] - a[1], a[3], a[2], b[3], b[2], b[0] - a[0]);
a.point = [0, 0];
}
var beta0 = angle(points[0].v[0], points[2].v[0], points[1].v[0]),
beta1 = angle(points[0].v[0], points[1].v[0], points[2].v[0]),
beta2 = pi - beta0;
points[2].point[1] = 0;
points[0].point[0] = -(points[1].point[0] = points[0].v[0] / 2);
var mean = [
points[2].point[0] = points[0].point[0] + points[2].v[0] * cos(beta0),
2 * (points[0].point[1] = points[1].point[1] = points[2].v[0] * sin(beta0))
];
function forward(lambda, phi) {
var sinPhi = sin(phi),
cosPhi = cos(phi),
v = new Array(3), i;
// Compute distance and azimuth from control points.
for (i = 0; i < 3; ++i) {
var p = points[i];
v[i] = distance(phi - p[1], p[3], p[2], cosPhi, sinPhi, lambda - p[0]);
if (!v[i][0]) return p.point;
v[i][1] = longitude(v[i][1] - p.v[1]);
}
// Arithmetic mean of interception points.
var point = mean.slice();
for (i = 0; i < 3; ++i) {
var j = i == 2 ? 0 : i + 1;
var a = angle(points[i].v[0], v[i][0], v[j][0]);
if (v[i][1] < 0) a = -a;
if (!i) {
point[0] += v[i][0] * cos(a);
point[1] -= v[i][0] * sin(a);
} else if (i == 1) {
a = beta1 - a;
point[0] -= v[i][0] * cos(a);
point[1] -= v[i][0] * sin(a);
} else {
a = beta2 - a;
point[0] += v[i][0] * cos(a);
point[1] += v[i][0] * sin(a);
}
}
point[0] /= 3, point[1] /= 3;
return point;
}
return forward;
}
function pointRadians(p) {
return p[0] *= radians, p[1] *= radians, p;
}
function chamberlinAfrica() {
return chamberlin([0, 22], [45, 22], [22.5, -22])
.scale(380)
.center([22.5, 2]);
}
function chamberlin(p0, p1, p2) { // TODO order matters!
var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: [p0, p1, p2]}),
R = [-c[0], -c[1]],
r = d3Geo.geoRotation(R),
p = d3Geo.geoProjection(chamberlinRaw(pointRadians(r(p0)), pointRadians(r(p1)), pointRadians(r(p2)))).rotate(R),
center = p.center;
delete p.rotate;
p.center = function(_) {
return arguments.length ? center(r(_)) : r.invert(center());
};
return p
.clipAngle(90);
}
function collignonRaw(lambda, phi) {
var alpha = sqrt(1 - sin(phi));
return [(2 / sqrtPi) * lambda * alpha, sqrtPi * (1 - alpha)];
}
collignonRaw.invert = function(x, y) {
var lambda = (lambda = y / sqrtPi - 1) * lambda;
return [lambda > 0 ? x * sqrt(pi / lambda) / 2 : 0, asin(1 - lambda)];
};
var collignon = function() {
return d3Geo.geoProjection(collignonRaw)
.scale(95.6464)
.center([0, 30]);
};
function craigRaw(phi0) {
var tanPhi0 = tan(phi0);
function forward(lambda, phi) {
return [lambda, (lambda ? lambda / sin(lambda) : 1) * (sin(phi) * cos(lambda) - tanPhi0 * cos(phi))];
}
forward.invert = tanPhi0 ? function(x, y) {
if (x) y *= sin(x) / x;
var cosLambda = cos(x);
return [x, 2 * atan2(sqrt(cosLambda * cosLambda + tanPhi0 * tanPhi0 - y * y) - cosLambda, tanPhi0 - y)];
} : function(x, y) {
return [x, asin(x ? y * tan(x) / x : y)];
};
return forward;
}
var craig = function() {
return parallel1(craigRaw)
.scale(249.828)
.clipAngle(90);
};
var sqrt3 = sqrt(3);
function crasterRaw(lambda, phi) {
return [sqrt3 * lambda * (2 * cos(2 * phi / 3) - 1) / sqrtPi, sqrt3 * sqrtPi * sin(phi / 3)];
}
crasterRaw.invert = function(x, y) {
var phi = 3 * asin(y / (sqrt3 * sqrtPi));
return [sqrtPi * x / (sqrt3 * (2 * cos(2 * phi / 3) - 1)), phi];
};
var craster = function() {
return d3Geo.geoProjection(crasterRaw)
.scale(156.19);
};
function cylindricalEqualAreaRaw(phi0) {
var cosPhi0 = cos(phi0);
function forward(lambda, phi) {
return [lambda * cosPhi0, sin(phi) / cosPhi0];
}
forward.invert = function(x, y) {
return [x / cosPhi0, asin(y * cosPhi0)];
};
return forward;
}
var cylindricalEqualArea = function() {
return parallel1(cylindricalEqualAreaRaw)
.parallel(38.58) // acos(sqrt(width / height / pi)) * radians
.scale(195.044); // width / (sqrt(width / height / pi) * 2 * pi)
};
function cylindricalStereographicRaw(phi0) {
var cosPhi0 = cos(phi0);
function forward(lambda, phi) {
return [lambda * cosPhi0, (1 + cosPhi0) * tan(phi / 2)];
}
forward.invert = function(x, y) {
return [x / cosPhi0, atan(y / (1 + cosPhi0)) * 2];
};
return forward;
}
var cylindricalStereographic = function() {
return parallel1(cylindricalStereographicRaw)
.scale(124.75);
};
function eckert1Raw(lambda, phi) {
var alpha = sqrt(8 / (3 * pi));
return [
alpha * lambda * (1 - abs(phi) / pi),
alpha * phi
];
}
eckert1Raw.invert = function(x, y) {
var alpha = sqrt(8 / (3 * pi)),
phi = y / alpha;
return [
x / (alpha * (1 - abs(phi) / pi)),
phi
];
};
var eckert1 = function() {
return d3Geo.geoProjection(eckert1Raw)
.scale(165.664);
};
function eckert2Raw(lambda, phi) {
var alpha = sqrt(4 - 3 * sin(abs(phi)));
return [
2 / sqrt(6 * pi) * lambda * alpha,
sign(phi) * sqrt(2 * pi / 3) * (2 - alpha)
];
}
eckert2Raw.invert = function(x, y) {
var alpha = 2 - abs(y) / sqrt(2 * pi / 3);
return [
x * sqrt(6 * pi) / (2 * alpha),
sign(y) * asin((4 - alpha * alpha) / 3)
];
};
var eckert2 = function() {
return d3Geo.geoProjection(eckert2Raw)
.scale(165.664);
};
function eckert3Raw(lambda, phi) {
var k = sqrt(pi * (4 + pi));
return [
2 / k * lambda * (1 + sqrt(1 - 4 * phi * phi / (pi * pi))),
4 / k * phi
];
}
eckert3Raw.invert = function(x, y) {
var k = sqrt(pi * (4 + pi)) / 2;
return [
x * k / (1 + sqrt(1 - y * y * (4 + pi) / (4 * pi))),
y * k / 2
];
};
var eckert3 = function() {
return d3Geo.geoProjection(eckert3Raw)
.scale(180.739);
};
function eckert4Raw(lambda, phi) {
var k = (2 + halfPi) * sin(phi);
phi /= 2;
for (var i = 0, delta = Infinity; i < 10 && abs(delta) > epsilon; i++) {
var cosPhi = cos(phi);
phi -= delta = (phi + sin(phi) * (cosPhi + 2) - k) / (2 * cosPhi * (1 + cosPhi));
}
return [
2 / sqrt(pi * (4 + pi)) * lambda * (1 + cos(phi)),
2 * sqrt(pi / (4 + pi)) * sin(phi)
];
}
eckert4Raw.invert = function(x, y) {
var A = y * sqrt((4 + pi) / pi) / 2,
k = asin(A),
c = cos(k);
return [
x / (2 / sqrt(pi * (4 + pi)) * (1 + c)),
asin((k + A * (c + 2)) / (2 + halfPi))
];
};
var eckert4 = function() {
return d3Geo.geoProjection(eckert4Raw)
.scale(180.739);
};
function eckert5Raw(lambda, phi) {
return [
lambda * (1 + cos(phi)) / sqrt(2 + pi),
2 * phi / sqrt(2 + pi)
];
}
eckert5Raw.invert = function(x, y) {
var k = sqrt(2 + pi),
phi = y * k / 2;
return [
k * x / (1 + cos(phi)),
phi
];
};
var eckert5 = function() {
return d3Geo.geoProjection(eckert5Raw)
.scale(173.044);
};
function eckert6Raw(lambda, phi) {
var k = (1 + halfPi) * sin(phi);
for (var i = 0, delta = Infinity; i < 10 && abs(delta) > epsilon; i++) {
phi -= delta = (phi + sin(phi) - k) / (1 + cos(phi));
}
k = sqrt(2 + pi);
return [
lambda * (1 + cos(phi)) / k,
2 * phi / k
];
}
eckert6Raw.invert = function(x, y) {
var j = 1 + halfPi,
k = sqrt(j / 2);
return [
x * 2 * k / (1 + cos(y *= k)),
asin((y + sin(y)) / j)
];
};
var eckert6 = function() {
return d3Geo.geoProjection(eckert6Raw)
.scale(173.044);
};
var eisenlohrK = 3 + 2 * sqrt2;
function eisenlohrRaw(lambda, phi) {
var s0 = sin(lambda /= 2),
c0 = cos(lambda),
k = sqrt(cos(phi)),
c1 = cos(phi /= 2),
t = sin(phi) / (c1 + sqrt2 * c0 * k),
c = sqrt(2 / (1 + t * t)),
v = sqrt((sqrt2 * c1 + (c0 + s0) * k) / (sqrt2 * c1 + (c0 - s0) * k));
return [
eisenlohrK * (c * (v - 1 / v) - 2 * log(v)),
eisenlohrK * (c * t * (v + 1 / v) - 2 * atan(t))
];
}
eisenlohrRaw.invert = function(x, y) {
if (!(p = augustRaw.invert(x / 1.2, y * 1.065))) return null;
var lambda = p[0], phi = p[1], i = 20, p;
x /= eisenlohrK, y /= eisenlohrK;
do {
var _0 = lambda / 2,
_1 = phi / 2,
s0 = sin(_0),
c0 = cos(_0),
s1 = sin(_1),
c1 = cos(_1),
cos1 = cos(phi),
k = sqrt(cos1),
t = s1 / (c1 + sqrt2 * c0 * k),
t2 = t * t,
c = sqrt(2 / (1 + t2)),
v0 = (sqrt2 * c1 + (c0 + s0) * k),
v1 = (sqrt2 * c1 + (c0 - s0) * k),
v2 = v0 / v1,
v = sqrt(v2),
vm1v = v - 1 / v,
vp1v = v + 1 / v,
fx = c * vm1v - 2 * log(v) - x,
fy = c * t * vp1v - 2 * atan(t) - y,
deltatDeltaLambda = s1 && sqrt1_2 * k * s0 * t2 / s1,
deltatDeltaPhi = (sqrt2 * c0 * c1 + k) / (2 * (c1 + sqrt2 * c0 * k) * (c1 + sqrt2 * c0 * k) * k),
deltacDeltat = -0.5 * t * c * c * c,
deltacDeltaLambda = deltacDeltat * deltatDeltaLambda,
deltacDeltaPhi = deltacDeltat * deltatDeltaPhi,
A = (A = 2 * c1 + sqrt2 * k * (c0 - s0)) * A * v,
deltavDeltaLambda = (sqrt2 * c0 * c1 * k + cos1) / A,
deltavDeltaPhi = -(sqrt2 * s0 * s1) / (k * A),
deltaxDeltaLambda = vm1v * deltacDeltaLambda - 2 * deltavDeltaLambda / v + c * (deltavDeltaLambda + deltavDeltaLambda / v2),
deltaxDeltaPhi = vm1v * deltacDeltaPhi - 2 * deltavDeltaPhi / v + c * (deltavDeltaPhi + deltavDeltaPhi / v2),
deltayDeltaLambda = t * vp1v * deltacDeltaLambda - 2 * deltatDeltaLambda / (1 + t2) + c * vp1v * deltatDeltaLambda + c * t * (deltavDeltaLambda - deltavDeltaLambda / v2),
deltayDeltaPhi = t * vp1v * deltacDeltaPhi - 2 * deltatDeltaPhi / (1 + t2) + c * vp1v * deltatDeltaPhi + c * t * (deltavDeltaPhi - deltavDeltaPhi / v2),
denominator = deltaxDeltaPhi * deltayDeltaLambda - deltayDeltaPhi * deltaxDeltaLambda;
if (!denominator) break;
var deltaLambda = (fy * deltaxDeltaPhi - fx * deltayDeltaPhi) / denominator,
deltaPhi = (fx * deltayDeltaLambda - fy * deltaxDeltaLambda) / denominator;
lambda -= deltaLambda;
phi = max(-halfPi, min(halfPi, phi - deltaPhi));
} while ((abs(deltaLambda) > epsilon || abs(deltaPhi) > epsilon) && --i > 0);
return abs(abs(phi) - halfPi) < epsilon ? [0, phi] : i && [lambda, phi];
};
var eisenlohr = function() {
return d3Geo.geoProjection(eisenlohrRaw)
.scale(62.5271);
};
var faheyK = cos(35 * radians);
function faheyRaw(lambda, phi) {
var t = tan(phi / 2);
return [lambda * faheyK * sqrt(1 - t * t), (1 + faheyK) * t];
}
faheyRaw.invert = function(x, y) {
var t = y / (1 + faheyK);
return [x && x / (faheyK * sqrt(1 - t * t)), 2 * atan(t)];
};
var fahey = function() {
return d3Geo.geoProjection(faheyRaw)
.scale(137.152);
};
function foucautRaw(lambda, phi) {
var k = phi / 2, cosk = cos(k);
return [ 2 * lambda / sqrtPi * cos(phi) * cosk * cosk, sqrtPi * tan(k)];
}
foucautRaw.invert = function(x, y) {
var k = atan(y / sqrtPi), cosk = cos(k), phi = 2 * k;
return [x * sqrtPi / 2 / (cos(phi) * cosk * cosk), phi];
};
var foucaut = function() {
return d3Geo.geoProjection(foucautRaw)
.scale(135.264);
};
function gilbertForward(point) {
return [point[0] / 2, asin(tan(point[1] / 2 * radians)) * degrees];
}
function gilbertInvert(point) {
return [point[0] * 2, 2 * atan(sin(point[1] * radians)) * degrees];
}
var gilbert = function(projectionType) {
if (projectionType == null) projectionType = d3Geo.geoOrthographic;
var projection = projectionType(),
equirectangular = d3Geo.geoEquirectangular().scale(degrees).precision(0).clipAngle(null).translate([0, 0]); // antimeridian cutting
function gilbert(point) {
return projection(gilbertForward(point));
}
if (projection.invert) gilbert.invert = function(point) {
return gilbertInvert(projection.invert(point));
};
gilbert.stream = function(stream) {
var s1 = projection.stream(stream), s0 = equirectangular.stream({
point: function(lambda, phi) { s1.point(lambda / 2, asin(tan(-phi / 2 * radians)) * degrees); },
lineStart: function() { s1.lineStart(); },
lineEnd: function() { s1.lineEnd(); },
polygonStart: function() { s1.polygonStart(); },
polygonEnd: function() { s1.polygonEnd(); }
});
s0.sphere = s1.sphere;
return s0;
};
function property(name) {
gilbert[name] = function(_) {
return arguments.length ? (projection[name](_), gilbert) : projection[name]();
};
}
gilbert.rotate = function(_) {
return arguments.length ? (equirectangular.rotate(_), gilbert) : equirectangular.rotate();
};
gilbert.center = function(_) {
return arguments.length ? (projection.center(gilbertForward(_)), gilbert) : gilbertInvert(projection.center());
};
property("clipAngle");
property("clipExtent");
property("scale");
property("translate");
property("precision");
return gilbert
.scale(249.5);
};
function gingeryRaw(rho, n) {
var k = 2 * pi / n,
rho2 = rho * rho;
function forward(lambda, phi) {
var p = d3Geo.geoAzimuthalEquidistantRaw(lambda, phi),
x = p[0],
y = p[1],
r2 = x * x + y * y;
if (r2 > rho2) {
var r = sqrt(r2),
theta = atan2(y, x),
theta0 = k * round(theta / k),
alpha = theta - theta0,
rhoCosAlpha = rho * cos(alpha),
k_ = (rho * sin(alpha) - alpha * sin(rhoCosAlpha)) / (halfPi - rhoCosAlpha),
s_ = gingeryLength(alpha, k_),
e = (pi - rho) / gingeryIntegrate(s_, rhoCosAlpha, pi);
x = r;
var i = 50, delta;
do {
x -= delta = (rho + gingeryIntegrate(s_, rhoCosAlpha, x) * e - r) / (s_(x) * e);
} while (abs(delta) > epsilon && --i > 0);
y = alpha * sin(x);
if (x < halfPi) y -= k_ * (x - halfPi);
var s = sin(theta0),
c = cos(theta0);
p[0] = x * c - y * s;
p[1] = x * s + y * c;
}
return p;
}
forward.invert = function(x, y) {
var r2 = x * x + y * y;
if (r2 > rho2) {
var r = sqrt(r2),
theta = atan2(y, x),
theta0 = k * round(theta / k),
dTheta = theta - theta0;
x = r * cos(dTheta);
y = r * sin(dTheta);
var x_halfPi = x - halfPi,
sinx = sin(x),
alpha = y / sinx,
delta = x < halfPi ? Infinity : 0,
i = 10;
while (true) {
var rhosinAlpha = rho * sin(alpha),
rhoCosAlpha = rho * cos(alpha),
sinRhoCosAlpha = sin(rhoCosAlpha),
halfPi_RhoCosAlpha = halfPi - rhoCosAlpha,
k_ = (rhosinAlpha - alpha * sinRhoCosAlpha) / halfPi_RhoCosAlpha,
s_ = gingeryLength(alpha, k_);
if (abs(delta) < epsilon2 || !--i) break;
alpha -= delta = (alpha * sinx - k_ * x_halfPi - y) / (
sinx - x_halfPi * 2 * (
halfPi_RhoCosAlpha * (rhoCosAlpha + alpha * rhosinAlpha * cos(rhoCosAlpha) - sinRhoCosAlpha) -
rhosinAlpha * (rhosinAlpha - alpha * sinRhoCosAlpha)
) / (halfPi_RhoCosAlpha * halfPi_RhoCosAlpha));
}
r = rho + gingeryIntegrate(s_, rhoCosAlpha, x) * (pi - rho) / gingeryIntegrate(s_, rhoCosAlpha, pi);
theta = theta0 + alpha;
x = r * cos(theta);
y = r * sin(theta);
}
return d3Geo.geoAzimuthalEquidistantRaw.invert(x, y);
};
return forward;
}
function gingeryLength(alpha, k) {
return function(x) {
var y_ = alpha * cos(x);
if (x < halfPi) y_ -= k;
return sqrt(1 + y_ * y_);
};
}
// Numerical integration: trapezoidal rule.
function gingeryIntegrate(f, a, b) {
var n = 50,
h = (b - a) / n,
s = f(a) + f(b);
for (var i = 1, x = a; i < n; ++i) s += 2 * f(x += h);
return s * 0.5 * h;
}
var gingery = function() {
var n = 6,
rho = 30 * radians,
cRho = cos(rho),
sRho = sin(rho),
m = d3Geo.geoProjectionMutator(gingeryRaw),
p = m(rho, n),
stream_ = p.stream,
epsilon$$1 = 1e-2,
cr = -cos(epsilon$$1 * radians),
sr = sin(epsilon$$1 * radians);
p.radius = function(_) {
if (!arguments.length) return rho * degrees;
cRho = cos(rho = _ * radians);
sRho = sin(rho);
return m(rho, n);
};
p.lobes = function(_) {
if (!arguments.length) return n;
return m(rho, n = +_);
};
p.stream = function(stream) {
var rotate = p.rotate(),
rotateStream = stream_(stream),
sphereStream = (p.rotate([0, 0]), stream_(stream));
p.rotate(rotate);
rotateStream.sphere = function() {
sphereStream.polygonStart(), sphereStream.lineStart();
for (var i = 0, delta = 2 * pi / n, phi = 0; i < n; ++i, phi -= delta) {
sphereStream.point(atan2(sr * cos(phi), cr) * degrees, asin(sr * sin(phi)) * degrees);
sphereStream.point(atan2(sRho * cos(phi - delta / 2), cRho) * degrees, asin(sRho * sin(phi - delta / 2)) * degrees);
}
sphereStream.lineEnd(), sphereStream.polygonEnd();
};
return rotateStream;
};
return p
.rotate([90, -40])
.scale(91.7095)
.clipAngle(180 - 1e-3);
};
var ginzburgPolyconicRaw = function(a, b, c, d, e, f, g, h) {
if (arguments.length < 8) h = 0;
function forward(lambda, phi) {
if (!phi) return [a * lambda / pi, 0];
var phi2 = phi * phi,
xB = a + phi2 * (b + phi2 * (c + phi2 * d)),
yB = phi * (e - 1 + phi2 * (f - h + phi2 * g)),
m = (xB * xB + yB * yB) / (2 * yB),
alpha = lambda * asin(xB / m) / pi;
return [m * sin(alpha), phi * (1 + phi2 * h) + m * (1 - cos(alpha))];
}
forward.invert = function(x, y) {
var lambda = pi * x / a,
phi = y,
deltaLambda, deltaPhi, i = 50;
do {
var phi2 = phi * phi,
xB = a + phi2 * (b + phi2 * (c + phi2 * d)),
yB = phi * (e - 1 + phi2 * (f - h + phi2 * g)),
p = xB * xB + yB * yB,
q = 2 * yB,
m = p / q,
m2 = m * m,
dAlphadLambda = asin(xB / m) / pi,
alpha = lambda * dAlphadLambda,
xB2 = xB * xB,
dxBdPhi = (2 * b + phi2 * (4 * c + phi2 * 6 * d)) * phi,
dyBdPhi = e + phi2 * (3 * f + phi2 * 5 * g),
dpdPhi = 2 * (xB * dxBdPhi + yB * (dyBdPhi - 1)),
dqdPhi = 2 * (dyBdPhi - 1),
dmdPhi = (dpdPhi * q - p * dqdPhi) / (q * q),
cosAlpha = cos(alpha),
sinAlpha = sin(alpha),
mcosAlpha = m * cosAlpha,
msinAlpha = m * sinAlpha,
dAlphadPhi = ((lambda / pi) * (1 / sqrt(1 - xB2 / m2)) * (dxBdPhi * m - xB * dmdPhi)) / m2,
fx = msinAlpha - x,
fy = phi * (1 + phi2 * h) + m - mcosAlpha - y,
deltaxDeltaPhi = dmdPhi * sinAlpha + mcosAlpha * dAlphadPhi,
deltaxDeltaLambda = mcosAlpha * dAlphadLambda,
deltayDeltaPhi = 1 + dmdPhi - (dmdPhi * cosAlpha - msinAlpha * dAlphadPhi),
deltayDeltaLambda = msinAlpha * dAlphadLambda,
denominator = deltaxDeltaPhi * deltayDeltaLambda - deltayDeltaPhi * deltaxDeltaLambda;
if (!denominator) break;
lambda -= deltaLambda = (fy * deltaxDeltaPhi - fx * deltayDeltaPhi) / denominator;
phi -= deltaPhi = (fx * deltayDeltaLambda - fy * deltaxDeltaLambda) / denominator;
} while ((abs(deltaLambda) > epsilon || abs(deltaPhi) > epsilon) && --i > 0);
return [lambda, phi];
};
return forward;
};
var ginzburg4Raw = ginzburgPolyconicRaw(2.8284, -1.6988, 0.75432, -0.18071, 1.76003, -0.38914, 0.042555);
var ginzburg4 = function() {
return d3Geo.geoProjection(ginzburg4Raw)
.scale(149.995);
};
var ginzburg5Raw = ginzburgPolyconicRaw(2.583819, -0.835827, 0.170354, -0.038094, 1.543313, -0.411435,0.082742);
var ginzburg5 = function() {
return d3Geo.geoProjection(ginzburg5Raw)
.scale(153.93);
};
var ginzburg6Raw = ginzburgPolyconicRaw(5 / 6 * pi, -0.62636, -0.0344, 0, 1.3493, -0.05524, 0, 0.045);
var ginzburg6 = function() {
return d3Geo.geoProjection(ginzburg6Raw)
.scale(130.945);
};
function ginzburg8Raw(lambda, phi) {
var lambda2 = lambda * lambda,
phi2 = phi * phi;
return [
lambda * (1 - 0.162388 * phi2) * (0.87 - 0.000952426 * lambda2 * lambda2),
phi * (1 + phi2 / 12)
];
}
ginzburg8Raw.invert = function(x, y) {
var lambda = x,
phi = y,
i = 50, delta;
do {
var phi2 = phi * phi;
phi -= delta = (phi * (1 + phi2 / 12) - y) / (1 + phi2 / 4);
} while (abs(delta) > epsilon && --i > 0);
i = 50;
x /= 1 -0.162388 * phi2;
do {
var lambda4 = (lambda4 = lambda * lambda) * lambda4;
lambda -= delta = (lambda * (0.87 - 0.000952426 * lambda4) - x) / (0.87 - 0.00476213 * lambda4);
} while (abs(delta) > epsilon && --i > 0);
return [lambda, phi];
};
var ginzburg8 = function() {
return d3Geo.geoProjection(ginzburg8Raw)
.scale(131.747);
};
var ginzburg9Raw = ginzburgPolyconicRaw(2.6516, -0.76534, 0.19123, -0.047094, 1.36289, -0.13965,0.031762);
var ginzburg9 = function() {
return d3Geo.geoProjection(ginzburg9Raw)
.scale(131.087);
};
var squareRaw = function(project) {
var dx = project(halfPi, 0)[0] - project(-halfPi, 0)[0];
function projectSquare(lambda, phi) {
var s = lambda > 0 ? -0.5 : 0.5,
point = project(lambda + s * pi, phi);
point[0] -= s * dx;
return point;
}
if (project.invert) projectSquare.invert = function(x, y) {
var s = x > 0 ? -0.5 : 0.5,
location = project.invert(x + s * dx, y),
lambda = location[0] - s * pi;
if (lambda < -pi) lambda += 2 * pi;
else if (lambda > pi) lambda -= 2 * pi;
location[0] = lambda;
return location;
};
return projectSquare;
};
function gringortenRaw(lambda, phi) {
var sLambda = sign(lambda),
sPhi = sign(phi),
cosPhi = cos(phi),
x = cos(lambda) * cosPhi,
y = sin(lambda) * cosPhi,
z = sin(sPhi * phi);
lambda = abs(atan2(y, z));
phi = asin(x);
if (abs(lambda - halfPi) > epsilon) lambda %= halfPi;
var point = gringortenHexadecant(lambda > pi / 4 ? halfPi - lambda : lambda, phi);
if (lambda > pi / 4) z = point[0], point[0] = -point[1], point[1] = -z;
return (point[0] *= sLambda, point[1] *= -sPhi, point);
}
gringortenRaw.invert = function(x, y) {
if (abs(x) > 1) x = sign(x) * 2 - x;
if (abs(y) > 1) y = sign(y) * 2 - y;
var sx = sign(x),
sy = sign(y),
x0 = -sx * x,
y0 = -sy * y,
t = y0 / x0 < 1,
p = gringortenHexadecantInvert(t ? y0 : x0, t ? x0 : y0),
lambda = p[0],
phi = p[1],
cosPhi = cos(phi);
if (t) lambda = -halfPi - lambda;
return [sx * (atan2(sin(lambda) * cosPhi, -sin(phi)) + pi), sy * asin(cos(lambda) * cosPhi)];
};
function gringortenHexadecant(lambda, phi) {
if (phi === halfPi) return [0, 0];
var sinPhi = sin(phi),
r = sinPhi * sinPhi,
r2 = r * r,
j = 1 + r2,
k = 1 + 3 * r2,
q = 1 - r2,
z = asin(1 / sqrt(j)),
v = q + r * j * z,
p2 = (1 - sinPhi) / v,
p = sqrt(p2),
a2 = p2 * j,
a = sqrt(a2),
h = p * q,
x,
i;
if (lambda === 0) return [0, -(h + r * a)];
var cosPhi = cos(phi),
secPhi = 1 / cosPhi,
drdPhi = 2 * sinPhi * cosPhi,
dvdPhi = (-3 * r + z * k) * drdPhi,
dp2dPhi = (-v * cosPhi - (1 - sinPhi) * dvdPhi) / (v * v),
dpdPhi = (0.5 * dp2dPhi) / p,
dhdPhi = q * dpdPhi - 2 * r * p * drdPhi,
dra2dPhi = r * j * dp2dPhi + p2 * k * drdPhi,
mu = -secPhi * drdPhi,
nu = -secPhi * dra2dPhi,
zeta = -2 * secPhi * dhdPhi,
lambda1 = 4 * lambda / pi,
delta;
// Slower but accurate bisection method.
if (lambda > 0.222 * pi || phi < pi / 4 && lambda > 0.175 * pi) {
x = (h + r * sqrt(a2 * (1 + r2) - h * h)) / (1 + r2);
if (lambda > pi / 4) return [x, x];
var x1 = x, x0 = 0.5 * x;
x = 0.5 * (x0 + x1), i = 50;
do {
var g = sqrt(a2 - x * x),
f = (x * (zeta + mu * g) + nu * asin(x / a)) - lambda1;
if (!f) break;
if (f < 0) x0 = x;
else x1 = x;
x = 0.5 * (x0 + x1);
} while (abs(x1 - x0) > epsilon && --i > 0);
}
// Newton-Raphson.
else {
x = epsilon, i = 25;
do {
var x2 = x * x,
g2 = sqrt(a2 - x2),
zetaMug = zeta + mu * g2,
f2 = x * zetaMug + nu * asin(x / a) - lambda1,
df = zetaMug + (nu - mu * x2) / g2;
x -= delta = g2 ? f2 / df : 0;
} while (abs(delta) > epsilon && --i > 0);
}
return [x, -h - r * sqrt(a2 - x * x)];
}
function gringortenHexadecantInvert(x, y) {
var x0 = 0,
x1 = 1,
r = 0.5,
i = 50;
while (true) {
var r2 = r * r,
sinPhi = sqrt(r),
z = asin(1 / sqrt(1 + r2)),
v = (1 - r2) + r * (1 + r2) * z,
p2 = (1 - sinPhi) / v,
p = sqrt(p2),
a2 = p2 * (1 + r2),
h = p * (1 - r2),
g2 = a2 - x * x,
g = sqrt(g2),
y0 = y + h + r * g;
if (abs(x1 - x0) < epsilon2 || --i === 0 || y0 === 0) break;
if (y0 > 0) x0 = r;
else x1 = r;
r = 0.5 * (x0 + x1);
}
if (!i) return null;
var phi = asin(sinPhi),
cosPhi = cos(phi),
secPhi = 1 / cosPhi,
drdPhi = 2 * sinPhi * cosPhi,
dvdPhi = (-3 * r + z * (1 + 3 * r2)) * drdPhi,
dp2dPhi = (-v * cosPhi - (1 - sinPhi) * dvdPhi) / (v * v),
dpdPhi = 0.5 * dp2dPhi / p,
dhdPhi = (1 - r2) * dpdPhi - 2 * r * p * drdPhi,
zeta = -2 * secPhi * dhdPhi,
mu = -secPhi * drdPhi,
nu = -secPhi * (r * (1 + r2) * dp2dPhi + p2 * (1 + 3 * r2) * drdPhi);
return [pi / 4 * (x * (zeta + mu * g) + nu * asin(x / sqrt(a2))), phi];
}
var gringorten = function() {
return d3Geo.geoProjection(squareRaw(gringortenRaw))
.scale(239.75);
};
// Returns [sn, cn, dn](u + iv|m).
function ellipticJi(u, v, m) {
var a, b, c;
if (!u) {
b = ellipticJ(v, 1 - m);
return [
[0, b[0] / b[1]],
[1 / b[1], 0],
[b[2] / b[1], 0]
];
}
a = ellipticJ(u, m);
if (!v) return [[a[0], 0], [a[1], 0], [a[2], 0]];
b = ellipticJ(v, 1 - m);
c = b[1] * b[1] + m * a[0] * a[0] * b[0] * b[0];
return [
[a[0] * b[2] / c, a[1] * a[2] * b[0] * b[1] / c],
[a[1] * b[1] / c, -a[0] * a[2] * b[0] * b[2] / c],
[a[2] * b[1] * b[2] / c, -m * a[0] * a[1] * b[0] / c]
];
}
// Returns [sn, cn, dn, ph](u|m).
function ellipticJ(u, m) {
var ai, b, phi, t, twon;
if (m < epsilon) {
t = sin(u);
b = cos(u);
ai = m * (u - t * b) / 4;
return [
t - ai * b,
b + ai * t,
1 - m * t * t / 2,
u - ai
];
}
if (m >= 1 - epsilon) {
ai = (1 - m) / 4;
b = cosh(u);
t = tanh(u);
phi = 1 / b;
twon = b * sinh(u);
return [
t + ai * (twon - u) / (b * b),
phi - ai * t * phi * (twon - u),
phi + ai * t * phi * (twon + u),
2 * atan(exp(u)) - halfPi + ai * (twon - u) / b
];
}
var a = [1, 0, 0, 0, 0, 0, 0, 0, 0],
c = [sqrt(m), 0, 0, 0, 0, 0, 0, 0, 0],
i = 0;
b = sqrt(1 - m);
twon = 1;
while (abs(c[i] / a[i]) > epsilon && i < 8) {
ai = a[i++];
c[i] = (ai - b) / 2;
a[i] = (ai + b) / 2;
b = sqrt(ai * b);
twon *= 2;
}
phi = twon * a[i] * u;
do {
t = c[i] * sin(b = phi) / a[i];
phi = (asin(t) + phi) / 2;
} while (--i);
return [sin(phi), t = cos(phi), t / cos(phi - b), phi];
}
// Calculate F(phi+iPsi|m).
// See Abramowitz and Stegun, 17.4.11.
function ellipticFi(phi, psi, m) {
var r = abs(phi),
i = abs(psi),
sinhPsi = sinh(i);
if (r) {
var cscPhi = 1 / sin(r),
cotPhi2 = 1 / (tan(r) * tan(r)),
b = -(cotPhi2 + m * (sinhPsi * sinhPsi * cscPhi * cscPhi) - 1 + m),
c = (m - 1) * cotPhi2,
cotLambda2 = (-b + sqrt(b * b - 4 * c)) / 2;
return [
ellipticF(atan(1 / sqrt(cotLambda2)), m) * sign(phi),
ellipticF(atan(sqrt((cotLambda2 / cotPhi2 - 1) / m)), 1 - m) * sign(psi)
];
}
return [
0,
ellipticF(atan(sinhPsi), 1 - m) * sign(psi)
];
}
// Calculate F(phi|m) where m = k² = sin²α.
// See Abramowitz and Stegun, 17.6.7.
function ellipticF(phi, m) {
if (!m) return phi;
if (m === 1) return log(tan(phi / 2 + quarterPi));
var a = 1,
b = sqrt(1 - m),
c = sqrt(m);
for (var i = 0; abs(c) > epsilon; i++) {
if (phi % pi) {
var dPhi = atan(b * tan(phi) / a);
if (dPhi < 0) dPhi += pi;
phi += dPhi + ~~(phi / pi) * pi;
} else phi += phi;
c = (a + b) / 2;
b = sqrt(a * b);
c = ((a = c) - b) / 2;
}
return phi / (pow(2, i) * a);
}
function guyouRaw(lambda, phi) {
var k_ = (sqrt2 - 1) / (sqrt2 + 1),
k = sqrt(1 - k_ * k_),
K = ellipticF(halfPi, k * k),
f = -1,
psi = log(tan(pi / 4 + abs(phi) / 2)),
r = exp(f * psi) / sqrt(k_),
at = guyouComplexAtan(r * cos(f * lambda), r * sin(f * lambda)),
t = ellipticFi(at[0], at[1], k * k);
return [-t[1], (phi >= 0 ? 1 : -1) * (0.5 * K - t[0])];
}
function guyouComplexAtan(x, y) {
var x2 = x * x,
y_1 = y + 1,
t = 1 - x2 - y * y;
return [
0.5 * ((x >= 0 ? halfPi : -halfPi) - atan2(t, 2 * x)),
-0.25 * log(t * t + 4 * x2) +0.5 * log(y_1 * y_1 + x2)
];
}
function guyouComplexDivide(a, b) {
var denominator = b[0] * b[0] + b[1] * b[1];
return [
(a[0] * b[0] + a[1] * b[1]) / denominator,
(a[1] * b[0] - a[0] * b[1]) / denominator
];
}
guyouRaw.invert = function(x, y) {
var k_ = (sqrt2 - 1) / (sqrt2 + 1),
k = sqrt(1 - k_ * k_),
K = ellipticF(halfPi, k * k),
f = -1,
j = ellipticJi(0.5 * K - y, -x, k * k),
tn = guyouComplexDivide(j[0], j[1]),
lambda = atan2(tn[1], tn[0]) / f;
return [
lambda,
2 * atan(exp(0.5 / f * log(k_ * tn[0] * tn[0] + k_ * tn[1] * tn[1]))) - halfPi
];
};
var guyou = function() {
return d3Geo.geoProjection(squareRaw(guyouRaw))
.scale(151.496);
};
function hammerRaw(A, B) {
if (arguments.length < 2) B = A;
if (B === 1) return d3Geo.geoAzimuthalEqualAreaRaw;
if (B === Infinity) return hammerQuarticAuthalicRaw;
function forward(lambda, phi) {
var coordinates = d3Geo.geoAzimuthalEqualAreaRaw(lambda / B, phi);
coordinates[0] *= A;
return coordinates;
}
forward.invert = function(x, y) {
var coordinates = d3Geo.geoAzimuthalEqualAreaRaw.invert(x / A, y);
coordinates[0] *= B;
return coordinates;
};
return forward;
}
function hammerQuarticAuthalicRaw(lambda, phi) {
return [
lambda * cos(phi) / cos(phi /= 2),
2 * sin(phi)
];
}
hammerQuarticAuthalicRaw.invert = function(x, y) {
var phi = 2 * asin(y / 2);
return [
x * cos(phi / 2) / cos(phi),
phi
];
};
var hammer = function() {
var B = 2,
m = d3Geo.geoProjectionMutator(hammerRaw),
p = m(B);
p.coefficient = function(_) {
if (!arguments.length) return B;
return m(B = +_);
};
return p
.scale(169.529);
};
function hammerRetroazimuthalRaw(phi0) {
var sinPhi0 = sin(phi0),
cosPhi0 = cos(phi0),
rotate = hammerRetroazimuthalRotation(phi0);
rotate.invert = hammerRetroazimuthalRotation(-phi0);
function forward(lambda, phi) {
var p = rotate(lambda, phi);
lambda = p[0], phi = p[1];
var sinPhi = sin(phi),
cosPhi = cos(phi),
cosLambda = cos(lambda),
z = acos(sinPhi0 * sinPhi + cosPhi0 * cosPhi * cosLambda),
sinz = sin(z),
K = abs(sinz) > epsilon ? z / sinz : 1;
return [
K * cosPhi0 * sin(lambda),
(abs(lambda) > halfPi ? K : -K) // rotate for back hemisphere
* (sinPhi0 * cosPhi - cosPhi0 * sinPhi * cosLambda)
];
}
forward.invert = function(x, y) {
var rho = sqrt(x * x + y * y),
sinz = -sin(rho),
cosz = cos(rho),
a = rho * cosz,
b = -y * sinz,
c = rho * sinPhi0,
d = sqrt(a * a + b * b - c * c),
phi = atan2(a * c + b * d, b * c - a * d),
lambda = (rho > halfPi ? -1 : 1) * atan2(x * sinz, rho * cos(phi) * cosz + y * sin(phi) * sinz);
return rotate.invert(lambda, phi);
};
return forward;
}
// Latitudinal rotation by phi0.
// Temporary hack until D3 supports arbitrary small-circle clipping origins.
function hammerRetroazimuthalRotation(phi0) {
var sinPhi0 = sin(phi0),
cosPhi0 = cos(phi0);
return function(lambda, phi) {
var cosPhi = cos(phi),
x = cos(lambda) * cosPhi,
y = sin(lambda) * cosPhi,
z = sin(phi);
return [
atan2(y, x * cosPhi0 - z * sinPhi0),
asin(z * cosPhi0 + x * sinPhi0)
];
};
}
var hammerRetroazimuthal = function() {
var phi0 = 0,
m = d3Geo.geoProjectionMutator(hammerRetroazimuthalRaw),
p = m(phi0),
rotate_ = p.rotate,
stream_ = p.stream,
circle = d3Geo.geoCircle();
p.parallel = function(_) {
if (!arguments.length) return phi0 * degrees;
var r = p.rotate();
return m(phi0 = _ * radians).rotate(r);
};
// Temporary hack; see hammerRetroazimuthalRotation.
p.rotate = function(_) {
if (!arguments.length) return (_ = rotate_.call(p), _[1] += phi0 * degrees, _);
rotate_.call(p, [_[0], _[1] - phi0 * degrees]);
circle.center([-_[0], -_[1]]);
return p;
};
p.stream = function(stream) {
stream = stream_(stream);
stream.sphere = function() {
stream.polygonStart();
var epsilon$$1 = 1e-2,
ring = circle.radius(90 - epsilon$$1)().coordinates[0],
n = ring.length - 1,
i = -1,
p;
stream.lineStart();
while (++i < n) stream.point((p = ring[i])[0], p[1]);
stream.lineEnd();
ring = circle.radius(90 + epsilon$$1)().coordinates[0];
n = ring.length - 1;
stream.lineStart();
while (--i >= 0) stream.point((p = ring[i])[0], p[1]);
stream.lineEnd();
stream.polygonEnd();
};
return stream;
};
return p
.scale(79.4187)
.parallel(45)
.clipAngle(180 - 1e-3);
};
var healpixParallel = 41 + 48 / 36 + 37 / 3600;
var healpixLambert = cylindricalEqualAreaRaw(0);
function healpixRaw(H) {
var phi0 = healpixParallel * radians,
dx = collignonRaw(pi, phi0)[0] - collignonRaw(-pi, phi0)[0],
y0 = healpixLambert(0, phi0)[1],
y1 = collignonRaw(0, phi0)[1],
dy1 = sqrtPi - y1,
k = tau / H,
w = 4 / tau,
h = y0 + (dy1 * dy1 * 4) / tau;
function forward(lambda, phi) {
var point,
phi2 = abs(phi);
if (phi2 > phi0) {
var i = min(H - 1, max(0, floor((lambda + pi) / k)));
lambda += pi * (H - 1) / H - i * k;
point = collignonRaw(lambda, phi2);
point[0] = point[0] * tau / dx - tau * (H - 1) / (2 * H) + i * tau / H;
point[1] = y0 + (point[1] - y1) * 4 * dy1 / tau;
if (phi < 0) point[1] = -point[1];
} else {
point = healpixLambert(lambda, phi);
}
point[0] *= w, point[1] /= h;
return point;
}
forward.invert = function(x, y) {
x /= w, y *= h;
var y2 = abs(y);
if (y2 > y0) {
var i = min(H - 1, max(0, floor((x + pi) / k)));
x = (x + pi * (H - 1) / H - i * k) * dx / tau;
var point = collignonRaw.invert(x, 0.25 * (y2 - y0) * tau / dy1 + y1);
point[0] -= pi * (H - 1) / H - i * k;
if (y < 0) point[1] = -point[1];
return point;
}
return healpixLambert.invert(x, y);
};
return forward;
}
function sphere(step) {
return {
type: "Polygon",
coordinates: [
d3Array.range(-180, 180 + step / 2, step).map(function(x, i) { return [x, i & 1 ? 90 - 1e-6 : healpixParallel]; })
.concat(d3Array.range(180, -180 - step / 2, -step).map(function(x, i) { return [x, i & 1 ? -90 + 1e-6 : -healpixParallel]; }))
]
};
}
var healpix = function() {
var H = 4,
m = d3Geo.geoProjectionMutator(healpixRaw),
p = m(H),
stream_ = p.stream;
p.lobes = function(_) {
return arguments.length ? m(H = +_) : H;
};
p.stream = function(stream) {
var rotate = p.rotate(),
rotateStream = stream_(stream),
sphereStream = (p.rotate([0, 0]), stream_(stream));
p.rotate(rotate);
rotateStream.sphere = function() { d3Geo.geoStream(sphere(180 / H), sphereStream); };
return rotateStream;
};
return p
.scale(239.75);
};
function hillRaw(K) {
var L = 1 + K,
sinBt = sin(1 / L),
Bt = asin(sinBt),
A = 2 * sqrt(pi / (B = pi + 4 * Bt * L)),
B,
rho0 = 0.5 * A * (L + sqrt(K * (2 + K))),
K2 = K * K,
L2 = L * L;
function forward(lambda, phi) {
var t = 1 - sin(phi),
rho,
omega;
if (t && t < 2) {
var theta = halfPi - phi, i = 25, delta;
do {
var sinTheta = sin(theta),
cosTheta = cos(theta),
Bt_Bt1 = Bt + atan2(sinTheta, L - cosTheta),
C = 1 + L2 - 2 * L * cosTheta;
theta -= delta = (theta - K2 * Bt - L * sinTheta + C * Bt_Bt1 -0.5 * t * B) / (2 * L * sinTheta * Bt_Bt1);
} while (abs(delta) > epsilon2 && --i > 0);
rho = A * sqrt(C);
omega = lambda * Bt_Bt1 / pi;
} else {
rho = A * (K + t);
omega = lambda * Bt / pi;
}
return [
rho * sin(omega),
rho0 - rho * cos(omega)
];
}
forward.invert = function(x, y) {
var rho2 = x * x + (y -= rho0) * y,
cosTheta = (1 + L2 - rho2 / (A * A)) / (2 * L),
theta = acos(cosTheta),
sinTheta = sin(theta),
Bt_Bt1 = Bt + atan2(sinTheta, L - cosTheta);
return [
asin(x / sqrt(rho2)) * pi / Bt_Bt1,
asin(1 - 2 * (theta - K2 * Bt - L * sinTheta + (1 + L2 - 2 * L * cosTheta) * Bt_Bt1) / B)
];
};
return forward;
}
var hill = function() {
var K = 1,
m = d3Geo.geoProjectionMutator(hillRaw),
p = m(K);
p.ratio = function(_) {
return arguments.length ? m(K = +_) : K;
};
return p
.scale(167.774)
.center([0, 18.67]);
};
var sinuMollweidePhi = 0.7109889596207567;
var sinuMollweideY = 0.0528035274542;
function sinuMollweideRaw(lambda, phi) {
return phi > -sinuMollweidePhi
? (lambda = mollweideRaw(lambda, phi), lambda[1] += sinuMollweideY, lambda)
: sinusoidalRaw(lambda, phi);
}
sinuMollweideRaw.invert = function(x, y) {
return y > -sinuMollweidePhi
? mollweideRaw.invert(x, y - sinuMollweideY)
: sinusoidalRaw.invert(x, y);
};
var sinuMollweide = function() {
return d3Geo.geoProjection(sinuMollweideRaw)
.rotate([-20, -55])
.scale(164.263)
.center([0, -5.4036]);
};
function homolosineRaw(lambda, phi) {
return abs(phi) > sinuMollweidePhi
? (lambda = mollweideRaw(lambda, phi), lambda[1] -= phi > 0 ? sinuMollweideY : -sinuMollweideY, lambda)
: sinusoidalRaw(lambda, phi);
}
homolosineRaw.invert = function(x, y) {
return abs(y) > sinuMollweidePhi
? mollweideRaw.invert(x, y + (y > 0 ? sinuMollweideY : -sinuMollweideY))
: sinusoidalRaw.invert(x, y);
};
var homolosine = function() {
return d3Geo.geoProjection(homolosineRaw)
.scale(152.63);
};
function pointEqual(a, b) {
return abs(a[0] - b[0]) < epsilon && abs(a[1] - b[1]) < epsilon;
}
function interpolateLine(coordinates, m) {
var i = -1,
n = coordinates.length,
p0 = coordinates[0],
p1,
dx,
dy,
resampled = [];
while (++i < n) {
p1 = coordinates[i];
dx = (p1[0] - p0[0]) / m;
dy = (p1[1] - p0[1]) / m;
for (var j = 0; j < m; ++j) resampled.push([p0[0] + j * dx, p0[1] + j * dy]);
p0 = p1;
}
resampled.push(p1);
return resampled;
}
function interpolateSphere(lobes) {
var coordinates = [],
lobe,
lambda0, phi0, phi1,
lambda2, phi2,
i, n = lobes[0].length;
// Northern Hemisphere
for (i = 0; i < n; ++i) {
lobe = lobes[0][i];
lambda0 = lobe[0][0], phi0 = lobe[0][1], phi1 = lobe[1][1];
lambda2 = lobe[2][0], phi2 = lobe[2][1];
coordinates.push(interpolateLine([
[lambda0 + epsilon, phi0 + epsilon],
[lambda0 + epsilon, phi1 - epsilon],
[lambda2 - epsilon, phi1 - epsilon],
[lambda2 - epsilon, phi2 + epsilon]
], 30));
}
// Southern Hemisphere
for (i = lobes[1].length - 1; i >= 0; --i) {
lobe = lobes[1][i];
lambda0 = lobe[0][0], phi0 = lobe[0][1], phi1 = lobe[1][1];
lambda2 = lobe[2][0], phi2 = lobe[2][1];
coordinates.push(interpolateLine([
[lambda2 - epsilon, phi2 - epsilon],
[lambda2 - epsilon, phi1 + epsilon],
[lambda0 + epsilon, phi1 + epsilon],
[lambda0 + epsilon, phi0 - epsilon]
], 30));
}
return {
type: "Polygon",
coordinates: [d3Array.merge(coordinates)]
};
}
var interrupt = function(project, lobes) {
var sphere, bounds;
function forward(lambda, phi) {
var sign$$1 = phi < 0 ? -1 : +1, lobe = lobes[+(phi < 0)];
for (var i = 0, n = lobe.length - 1; i < n && lambda > lobe[i][2][0]; ++i);
var p = project(lambda - lobe[i][1][0], phi);
p[0] += project(lobe[i][1][0], sign$$1 * phi > sign$$1 * lobe[i][0][1] ? lobe[i][0][1] : phi)[0];
return p;
}
// Assumes mutually exclusive bounding boxes for lobes.
if (project.invert) forward.invert = function(x, y) {
var bound = bounds[+(y < 0)], lobe = lobes[+(y < 0)];
for (var i = 0, n = bound.length; i < n; ++i) {
var b = bound[i];
if (b[0][0] <= x && x < b[1][0] && b[0][1] <= y && y < b[1][1]) {
var p = project.invert(x - project(lobe[i][1][0], 0)[0], y);
p[0] += lobe[i][1][0];
return pointEqual(forward(p[0], p[1]), [x, y]) ? p : null;
}
}
};
var p = d3Geo.geoProjection(forward),
stream_ = p.stream;
p.stream = function(stream) {
var rotate = p.rotate(),
rotateStream = stream_(stream),
sphereStream = (p.rotate([0, 0]), stream_(stream));
p.rotate(rotate);
rotateStream.sphere = function() { d3Geo.geoStream(sphere, sphereStream); };
return rotateStream;
};
p.lobes = function(_) {
if (!arguments.length) return lobes.map(function(lobe) {
return lobe.map(function(l) {
return [
[l[0][0] * degrees, l[0][1] * degrees],
[l[1][0] * degrees, l[1][1] * degrees],
[l[2][0] * degrees, l[2][1] * degrees]
];
});
});
sphere = interpolateSphere(_);
lobes = _.map(function(lobe) {
return lobe.map(function(l) {
return [
[l[0][0] * radians, l[0][1] * radians],
[l[1][0] * radians, l[1][1] * radians],
[l[2][0] * radians, l[2][1] * radians]
];
});
});
bounds = lobes.map(function(lobe) {
return lobe.map(function(l) {
var x0 = project(l[0][0], l[0][1])[0],
x1 = project(l[2][0], l[2][1])[0],
y0 = project(l[1][0], l[0][1])[1],
y1 = project(l[1][0], l[1][1])[1],
t;
if (y0 > y1) t = y0, y0 = y1, y1 = t;
return [[x0, y0], [x1, y1]];
});
});
return p;
};
if (lobes != null) p.lobes(lobes);
return p;
};
var lobes = [[ // northern hemisphere
[[-180, 0], [-100, 90], [ -40, 0]],
[[ -40, 0], [ 30, 90], [ 180, 0]]
], [ // southern hemisphere
[[-180, 0], [-160, -90], [-100, 0]],
[[-100, 0], [ -60, -90], [ -20, 0]],
[[ -20, 0], [ 20, -90], [ 80, 0]],
[[ 80, 0], [ 140, -90], [ 180, 0]]
]];
var boggs$1 = function() {
return interrupt(boggsRaw, lobes)
.scale(160.857);
};
var lobes$1 = [[ // northern hemisphere
[[-180, 0], [-100, 90], [ -40, 0]],
[[ -40, 0], [ 30, 90], [ 180, 0]]
], [ // southern hemisphere
[[-180, 0], [-160, -90], [-100, 0]],
[[-100, 0], [ -60, -90], [ -20, 0]],
[[ -20, 0], [ 20, -90], [ 80, 0]],
[[ 80, 0], [ 140, -90], [ 180, 0]]
]];
var homolosine$1 = function() {
return interrupt(homolosineRaw, lobes$1)
.scale(152.63);
};
var lobes$2 = [[ // northern hemisphere
[[-180, 0], [-100, 90], [ -40, 0]],
[[ -40, 0], [ 30, 90], [ 180, 0]]
], [ // southern hemisphere
[[-180, 0], [-160, -90], [-100, 0]],
[[-100, 0], [ -60, -90], [ -20, 0]],
[[ -20, 0], [ 20, -90], [ 80, 0]],
[[ 80, 0], [ 140, -90], [ 180, 0]]
]];
var mollweide$1 = function() {
return interrupt(mollweideRaw, lobes$2)
.scale(169.529);
};
var lobes$3 = [[ // northern hemisphere
[[-180, 0], [ -90, 90], [ 0, 0]],
[[ 0, 0], [ 90, 90], [ 180, 0]]
], [ // southern hemisphere
[[-180, 0], [ -90, -90], [ 0, 0]],
[[ 0, 0], [ 90, -90], [ 180, 0]]
]];
var mollweideHemispheres = function() {
return interrupt(mollweideRaw, lobes$3)
.scale(169.529)
.rotate([20, 0]);
};
var lobes$4 = [[ // northern hemisphere
[[-180, 35], [ -30, 90], [ 0, 35]],
[[ 0, 35], [ 30, 90], [ 180, 35]]
], [ // southern hemisphere
[[-180, -10], [-102, -90], [ -65, -10]],
[[ -65, -10], [ 5, -90], [ 77, -10]],
[[ 77, -10], [ 103, -90], [ 180, -10]]
]];
var sinuMollweide$1 = function() {
return interrupt(sinuMollweideRaw, lobes$4)
.rotate([-20, -55])
.scale(164.263)
.center([0, -5.4036]);
};
var lobes$5 = [[ // northern hemisphere
[[-180, 0], [-110, 90], [ -40, 0]],
[[ -40, 0], [ 0, 90], [ 40, 0]],
[[ 40, 0], [ 110, 90], [ 180, 0]]
], [ // southern hemisphere
[[-180, 0], [-110, -90], [ -40, 0]],
[[ -40, 0], [ 0, -90], [ 40, 0]],
[[ 40, 0], [ 110, -90], [ 180, 0]]
]];
var sinusoidal$1 = function() {
return interrupt(sinusoidalRaw, lobes$5)
.scale(152.63)
.rotate([-20, 0]);
};
function kavrayskiy7Raw(lambda, phi) {
return [3 / tau * lambda * sqrt(pi * pi / 3 - phi * phi), phi];
}
kavrayskiy7Raw.invert = function(x, y) {
return [tau / 3 * x / sqrt(pi * pi / 3 - y * y), y];
};
var kavrayskiy7 = function() {
return d3Geo.geoProjection(kavrayskiy7Raw)
.scale(158.837);
};
function lagrangeRaw(n) {
function forward(lambda, phi) {
if (abs(abs(phi) - halfPi) < epsilon) return [0, phi < 0 ? -2 : 2];
var sinPhi = sin(phi),
v = pow((1 + sinPhi) / (1 - sinPhi), n / 2),
c = 0.5 * (v + 1 / v) + cos(lambda *= n);
return [
2 * sin(lambda) / c,
(v - 1 / v) / c
];
}
forward.invert = function(x, y) {
var y0 = abs(y);
if (abs(y0 - 2) < epsilon) return x ? null : [0, sign(y) * halfPi];
if (y0 > 2) return null;
x /= 2, y /= 2;
var x2 = x * x,
y2 = y * y,
t = 2 * y / (1 + x2 + y2); // tanh(nPhi)
t = pow((1 + t) / (1 - t), 1 / n);
return [
atan2(2 * x, 1 - x2 - y2) / n,
asin((t - 1) / (t + 1))
];
};
return forward;
}
var lagrange = function() {
var n = 0.5,
m = d3Geo.geoProjectionMutator(lagrangeRaw),
p = m(n);
p.spacing = function(_) {
return arguments.length ? m(n = +_) : n;
};
return p
.scale(124.75);
};
var pi_sqrt2 = pi / sqrt2;
function larriveeRaw(lambda, phi) {
return [
lambda * (1 + sqrt(cos(phi))) / 2,
phi / (cos(phi / 2) * cos(lambda / 6))
];
}
larriveeRaw.invert = function(x, y) {
var x0 = abs(x),
y0 = abs(y),
lambda = epsilon,
phi = halfPi;
if (y0 < pi_sqrt2) phi *= y0 / pi_sqrt2;
else lambda += 6 * acos(pi_sqrt2 / y0);
for (var i = 0; i < 25; i++) {
var sinPhi = sin(phi),
sqrtcosPhi = sqrt(cos(phi)),
sinPhi_2 = sin(phi / 2),
cosPhi_2 = cos(phi / 2),
sinLambda_6 = sin(lambda / 6),
cosLambda_6 = cos(lambda / 6),
f0 = 0.5 * lambda * (1 + sqrtcosPhi) - x0,
f1 = phi / (cosPhi_2 * cosLambda_6) - y0,
df0dPhi = sqrtcosPhi ? -0.25 * lambda * sinPhi / sqrtcosPhi : 0,
df0dLambda = 0.5 * (1 + sqrtcosPhi),
df1dPhi = (1 +0.5 * phi * sinPhi_2 / cosPhi_2) / (cosPhi_2 * cosLambda_6),
df1dLambda = (phi / cosPhi_2) * (sinLambda_6 / 6) / (cosLambda_6 * cosLambda_6),
denom = df0dPhi * df1dLambda - df1dPhi * df0dLambda,
dPhi = (f0 * df1dLambda - f1 * df0dLambda) / denom,
dLambda = (f1 * df0dPhi - f0 * df1dPhi) / denom;
phi -= dPhi;
lambda -= dLambda;
if (abs(dPhi) < epsilon && abs(dLambda) < epsilon) break;
}
return [x < 0 ? -lambda : lambda, y < 0 ? -phi : phi];
};
var larrivee = function() {
return d3Geo.geoProjection(larriveeRaw)
.scale(97.2672);
};
function laskowskiRaw(lambda, phi) {
var lambda2 = lambda * lambda, phi2 = phi * phi;
return [
lambda * (0.975534 + phi2 * (-0.119161 + lambda2 * -0.0143059 + phi2 * -0.0547009)),
phi * (1.00384 + lambda2 * (0.0802894 + phi2 * -0.02855 + lambda2 * 0.000199025) + phi2 * (0.0998909 + phi2 * -0.0491032))
];
}
laskowskiRaw.invert = function(x, y) {
var lambda = sign(x) * pi,
phi = y / 2,
i = 50;
do {
var lambda2 = lambda * lambda,
phi2 = phi * phi,
lambdaPhi = lambda * phi,
fx = lambda * (0.975534 + phi2 * (-0.119161 + lambda2 * -0.0143059 + phi2 * -0.0547009)) - x,
fy = phi * (1.00384 + lambda2 * (0.0802894 + phi2 * -0.02855 + lambda2 * 0.000199025) + phi2 * (0.0998909 + phi2 * -0.0491032)) - y,
deltaxDeltaLambda = 0.975534 - phi2 * (0.119161 + 3 * lambda2 * 0.0143059 + phi2 * 0.0547009),
deltaxDeltaPhi = -lambdaPhi * (2 * 0.119161 + 4 * 0.0547009 * phi2 + 2 * 0.0143059 * lambda2),
deltayDeltaLambda = lambdaPhi * (2 * 0.0802894 + 4 * 0.000199025 * lambda2 + 2 * -0.02855 * phi2),
deltayDeltaPhi = 1.00384 + lambda2 * (0.0802894 + 0.000199025 * lambda2) + phi2 * (3 * (0.0998909 - 0.02855 * lambda2) - 5 * 0.0491032 * phi2),
denominator = deltaxDeltaPhi * deltayDeltaLambda - deltayDeltaPhi * deltaxDeltaLambda,
deltaLambda = (fy * deltaxDeltaPhi - fx * deltayDeltaPhi) / denominator,
deltaPhi = (fx * deltayDeltaLambda - fy * deltaxDeltaLambda) / denominator;
lambda -= deltaLambda, phi -= deltaPhi;
} while ((abs(deltaLambda) > epsilon || abs(deltaPhi) > epsilon) && --i > 0);
return i && [lambda, phi];
};
var laskowski = function() {
return d3Geo.geoProjection(laskowskiRaw)
.scale(139.98);
};
function littrowRaw(lambda, phi) {
return [
sin(lambda) / cos(phi),
tan(phi) * cos(lambda)
];
}
littrowRaw.invert = function(x, y) {
var x2 = x * x,
y2 = y * y,
y2_1 = y2 + 1,
cosPhi = x
? sqrt1_2 * sqrt((y2_1 - sqrt(x2 * x2 + 2 * x2 * (y2 - 1) + y2_1 * y2_1)) / x2 + 1)
: 1 / sqrt(y2_1);
return [
asin(x * cosPhi),
sign(y) * acos(cosPhi)
];
};
var littrow = function() {
return d3Geo.geoProjection(littrowRaw)
.scale(144.049)
.clipAngle(90 - 1e-3);
};
function loximuthalRaw(phi0) {
var cosPhi0 = cos(phi0),
tanPhi0 = tan(quarterPi + phi0 / 2);
function forward(lambda, phi) {
var y = phi - phi0,
x = abs(y) < epsilon ? lambda * cosPhi0
: abs(x = quarterPi + phi / 2) < epsilon || abs(abs(x) - halfPi) < epsilon
? 0 : lambda * y / log(tan(x) / tanPhi0);
return [x, y];
}
forward.invert = function(x, y) {
var lambda,
phi = y + phi0;
return [
abs(y) < epsilon ? x / cosPhi0
: (abs(lambda = quarterPi + phi / 2) < epsilon || abs(abs(lambda) - halfPi) < epsilon) ? 0
: x * log(tan(lambda) / tanPhi0) / y,
phi
];
};
return forward;
}
var loximuthal = function() {
return parallel1(loximuthalRaw)
.parallel(40)
.scale(158.837);
};
function millerRaw(lambda, phi) {
return [lambda, 1.25 * log(tan(quarterPi + 0.4 * phi))];
}
millerRaw.invert = function(x, y) {
return [x, 2.5 * atan(exp(0.8 * y)) - 0.625 * pi];
};
var miller = function() {
return d3Geo.geoProjection(millerRaw)
.scale(108.318);
};
function modifiedStereographicRaw(C) {
var m = C.length - 1;
function forward(lambda, phi) {
var cosPhi = cos(phi),
k = 2 / (1 + cosPhi * cos(lambda)),
zr = k * cosPhi * sin(lambda),
zi = k * sin(phi),
i = m,
w = C[i],
ar = w[0],
ai = w[1],
t;
while (--i >= 0) {
w = C[i];
ar = w[0] + zr * (t = ar) - zi * ai;
ai = w[1] + zr * ai + zi * t;
}
ar = zr * (t = ar) - zi * ai;
ai = zr * ai + zi * t;
return [ar, ai];
}
forward.invert = function(x, y) {
var i = 20,
zr = x,
zi = y;
do {
var j = m,
w = C[j],
ar = w[0],
ai = w[1],
br = 0,
bi = 0,
t;
while (--j >= 0) {
w = C[j];
br = ar + zr * (t = br) - zi * bi;
bi = ai + zr * bi + zi * t;
ar = w[0] + zr * (t = ar) - zi * ai;
ai = w[1] + zr * ai + zi * t;
}
br = ar + zr * (t = br) - zi * bi;
bi = ai + zr * bi + zi * t;
ar = zr * (t = ar) - zi * ai - x;
ai = zr * ai + zi * t - y;
var denominator = br * br + bi * bi, deltar, deltai;
zr -= deltar = (ar * br + ai * bi) / denominator;
zi -= deltai = (ai * br - ar * bi) / denominator;
} while (abs(deltar) + abs(deltai) > epsilon * epsilon && --i > 0);
if (i) {
var rho = sqrt(zr * zr + zi * zi),
c = 2 * atan(rho * 0.5),
sinc = sin(c);
return [atan2(zr * sinc, rho * cos(c)), rho ? asin(zi * sinc / rho) : 0];
}
};
return forward;
}
var alaska = [[0.9972523, 0], [0.0052513, -0.0041175], [0.0074606, 0.0048125], [-0.0153783, -0.1968253], [0.0636871, -0.1408027], [0.3660976, -0.2937382]];
var gs48 = [[0.98879, 0], [0, 0], [-0.050909, 0], [0, 0], [0.075528, 0]];
var gs50 = [[0.9842990, 0], [0.0211642, 0.0037608], [-0.1036018, -0.0575102], [-0.0329095, -0.0320119], [0.0499471, 0.1223335], [0.0260460, 0.0899805], [0.0007388, -0.1435792], [0.0075848, -0.1334108], [-0.0216473, 0.0776645], [-0.0225161, 0.0853673]];
var miller$1 = [[0.9245, 0], [0, 0], [0.01943, 0]];
var lee = [[0.721316, 0], [0, 0], [-0.00881625, -0.00617325]];
function modifiedStereographicAlaska() {
return modifiedStereographic(alaska, [152, -64])
.scale(1500)
.center([-160.908, 62.4864])
.clipAngle(25);
}
function modifiedStereographicGs48() {
return modifiedStereographic(gs48, [95, -38])
.scale(1000)
.clipAngle(55)
.center([-96.5563, 38.8675]);
}
function modifiedStereographicGs50() {
return modifiedStereographic(gs50, [120, -45])
.scale(359.513)
.clipAngle(55)
.center([-117.474, 53.0628]);
}
function modifiedStereographicMiller() {
return modifiedStereographic(miller$1, [-20, -18])
.scale(209.091)
.center([20, 16.7214])
.clipAngle(82);
}
function modifiedStereographicLee() {
return modifiedStereographic(lee, [165, 10])
.scale(250)
.clipAngle(130)
.center([-165, -10]);
}
function modifiedStereographic(coefficients, rotate) {
var p = d3Geo.geoProjection(modifiedStereographicRaw(coefficients)).rotate(rotate).clipAngle(90),
r = d3Geo.geoRotation(rotate),
center = p.center;
delete p.rotate;
p.center = function(_) {
return arguments.length ? center(r(_)) : r.invert(center());
};
return p;
}
var sqrt6 = sqrt(6);
var sqrt7 = sqrt(7);
function mtFlatPolarParabolicRaw(lambda, phi) {
var theta = asin(7 * sin(phi) / (3 * sqrt6));
return [
sqrt6 * lambda * (2 * cos(2 * theta / 3) - 1) / sqrt7,
9 * sin(theta / 3) / sqrt7
];
}
mtFlatPolarParabolicRaw.invert = function(x, y) {
var theta = 3 * asin(y * sqrt7 / 9);
return [
x * sqrt7 / (sqrt6 * (2 * cos(2 * theta / 3) - 1)),
asin(sin(theta) * 3 * sqrt6 / 7)
];
};
var mtFlatPolarParabolic = function() {
return d3Geo.geoProjection(mtFlatPolarParabolicRaw)
.scale(164.859);
};
function mtFlatPolarQuarticRaw(lambda, phi) {
var k = (1 + sqrt1_2) * sin(phi),
theta = phi;
for (var i = 0, delta; i < 25; i++) {
theta -= delta = (sin(theta / 2) + sin(theta) - k) / (0.5 * cos(theta / 2) + cos(theta));
if (abs(delta) < epsilon) break;
}
return [
lambda * (1 + 2 * cos(theta) / cos(theta / 2)) / (3 * sqrt2),
2 * sqrt(3) * sin(theta / 2) / sqrt(2 + sqrt2)
];
}
mtFlatPolarQuarticRaw.invert = function(x, y) {
var sinTheta_2 = y * sqrt(2 + sqrt2) / (2 * sqrt(3)),
theta = 2 * asin(sinTheta_2);
return [
3 * sqrt2 * x / (1 + 2 * cos(theta) / cos(theta / 2)),
asin((sinTheta_2 + sin(theta)) / (1 + sqrt1_2))
];
};
var mtFlatPolarQuartic = function() {
return d3Geo.geoProjection(mtFlatPolarQuarticRaw)
.scale(188.209);
};
function mtFlatPolarSinusoidalRaw(lambda, phi) {
var A = sqrt(6 / (4 + pi)),
k = (1 + pi / 4) * sin(phi),
theta = phi / 2;
for (var i = 0, delta; i < 25; i++) {
theta -= delta = (theta / 2 + sin(theta) - k) / (0.5 + cos(theta));
if (abs(delta) < epsilon) break;
}
return [
A * (0.5 + cos(theta)) * lambda / 1.5,
A * theta
];
}
mtFlatPolarSinusoidalRaw.invert = function(x, y) {
var A = sqrt(6 / (4 + pi)),
theta = y / A;
if (abs(abs(theta) - halfPi) < epsilon) theta = theta < 0 ? -halfPi : halfPi;
return [
1.5 * x / (A * (0.5 + cos(theta))),
asin((theta / 2 + sin(theta)) / (1 + pi / 4))
];
};
var mtFlatPolarSinusoidal = function() {
return d3Geo.geoProjection(mtFlatPolarSinusoidalRaw)
.scale(166.518);
};
function naturalEarthRaw(lambda, phi) {
var phi2 = phi * phi, phi4 = phi2 * phi2;
return [
lambda * (0.8707 - 0.131979 * phi2 + phi4 * (-0.013791 + phi4 * (0.003971 * phi2 - 0.001529 * phi4))),
phi * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4)))
];
}
naturalEarthRaw.invert = function(x, y) {
var phi = y, i = 25, delta;
do {
var phi2 = phi * phi, phi4 = phi2 * phi2;
phi -= delta = (phi * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4))) - y) /
(1.007226 + phi2 * (0.015085 * 3 + phi4 * (-0.044475 * 7 + 0.028874 * 9 * phi2 - 0.005916 * 11 * phi4)));
} while (abs(delta) > epsilon && --i > 0);
return [
x / (0.8707 + (phi2 = phi * phi) * (-0.131979 + phi2 * (-0.013791 + phi2 * phi2 * phi2 * (0.003971 - 0.001529 * phi2)))),
phi
];
};
var naturalEarth = function() {
return d3Geo.geoProjection(naturalEarthRaw)
.scale(175.295);
};
function naturalEarth2Raw(lambda, phi) {
var phi2 = phi * phi, phi4 = phi2 * phi2, phi6 = phi2 * phi4;
return [
lambda * (0.84719 - 0.13063 * phi2 + phi6 * phi6 * (-0.04515 + 0.05494 * phi2 - 0.02326 * phi4 + 0.00331 * phi6)),
phi * (1.01183 + phi4 * phi4 * (-0.02625 + 0.01926 * phi2 - 0.00396 * phi4))
];
}
naturalEarth2Raw.invert = function(x, y) {
var phi = y, i = 25, delta, phi2, phi4, phi6;
do {
phi2 = phi * phi; phi4 = phi2 * phi2;
phi -= delta = ((phi * (1.01183 + phi4 * phi4 * (-0.02625 + 0.01926 * phi2 - 0.00396 * phi4))) - y) /
(1.01183 + phi4 * phi4 * ((9 * -0.02625) + (11 * 0.01926) * phi2 + (13 * -0.00396) * phi4));
} while (abs(delta) > epsilon2 && --i > 0);
phi2 = phi * phi; phi4 = phi2 * phi2; phi6 = phi2 * phi4;
return [
x / (0.84719 - 0.13063 * phi2 + phi6 * phi6 * (-0.04515 + 0.05494 * phi2 - 0.02326 * phi4 + 0.00331 * phi6)),
phi
];
};
var naturalEarth2 = function() {
return d3Geo.geoProjection(naturalEarth2Raw)
.scale(175.295);
};
function nellHammerRaw(lambda, phi) {
return [
lambda * (1 + cos(phi)) / 2,
2 * (phi - tan(phi / 2))
];
}
nellHammerRaw.invert = function(x, y) {
var p = y / 2;
for (var i = 0, delta = Infinity; i < 10 && abs(delta) > epsilon; ++i) {
var c = cos(y / 2);
y -= delta = (y - tan(y / 2) - p) / (1 - 0.5 / (c * c));
}
return [
2 * x / (1 + cos(y)),
y
];
};
var nellHammer = function() {
return d3Geo.geoProjection(nellHammerRaw)
.scale(152.63);
};
// Based on Java implementation by Bojan Savric.
// https://github.com/OSUCartography/JMapProjLib/blob/master/src/com/jhlabs/map/proj/PattersonProjection.java
var pattersonK1 = 1.0148;
var pattersonK2 = 0.23185;
var pattersonK3 = -0.14499;
var pattersonK4 = 0.02406;
var pattersonC1 = pattersonK1;
var pattersonC2 = 5 * pattersonK2;
var pattersonC3 = 7 * pattersonK3;
var pattersonC4 = 9 * pattersonK4;
var pattersonYmax = 1.790857183;
function pattersonRaw(lambda, phi) {
var phi2 = phi * phi;
return [
lambda,
phi * (pattersonK1 + phi2 * phi2 * (pattersonK2 + phi2 * (pattersonK3 + pattersonK4 * phi2)))
];
}
pattersonRaw.invert = function(x, y) {
if (y > pattersonYmax) y = pattersonYmax;
else if (y < -pattersonYmax) y = -pattersonYmax;
var yc = y, delta;
do { // Newton-Raphson
var y2 = yc * yc;
yc -= delta = ((yc * (pattersonK1 + y2 * y2 * (pattersonK2 + y2 * (pattersonK3 + pattersonK4 * y2)))) - y) / (pattersonC1 + y2 * y2 * (pattersonC2 + y2 * (pattersonC3 + pattersonC4 * y2)));
} while (abs(delta) > epsilon);
return [x, yc];
};
var patterson = function() {
return d3Geo.geoProjection(pattersonRaw)
.scale(139.319);
};
function polyconicRaw(lambda, phi) {
if (abs(phi) < epsilon) return [lambda, 0];
var tanPhi = tan(phi),
k = lambda * sin(phi);
return [
sin(k) / tanPhi,
phi + (1 - cos(k)) / tanPhi
];
}
polyconicRaw.invert = function(x, y) {
if (abs(y) < epsilon) return [x, 0];
var k = x * x + y * y,
phi = y * 0.5,
i = 10, delta;
do {
var tanPhi = tan(phi),
secPhi = 1 / cos(phi),
j = k - 2 * y * phi + phi * phi;
phi -= delta = (tanPhi * j + 2 * (phi - y)) / (2 + j * secPhi * secPhi + 2 * (phi - y) * tanPhi);
} while (abs(delta) > epsilon && --i > 0);
tanPhi = tan(phi);
return [
(abs(y) < abs(phi + 1 / tanPhi) ? asin(x * tanPhi) : sign(x) * (acos(abs(x * tanPhi)) + halfPi)) / sin(phi),
phi
];
};
var polyconic = function() {
return d3Geo.geoProjection(polyconicRaw)
.scale(103.74);
};
// Note: 6-element arrays are used to denote the 3x3 affine transform matrix:
// [a, b, c,
// d, e, f,
// 0, 0, 1] - this redundant row is left out.
// Transform matrix for [a0, a1] -> [b0, b1].
var matrix = function(a, b) {
var u = subtract(a[1], a[0]),
v = subtract(b[1], b[0]),
phi = angle$1(u, v),
s = length(u) / length(v);
return multiply([
1, 0, a[0][0],
0, 1, a[0][1]
], multiply([
s, 0, 0,
0, s, 0
], multiply([
cos(phi), sin(phi), 0,
-sin(phi), cos(phi), 0
], [
1, 0, -b[0][0],
0, 1, -b[0][1]
])));
};
// Inverts a transform matrix.
function inverse(m) {
var k = 1 / (m[0] * m[4] - m[1] * m[3]);
return [
k * m[4], -k * m[1], k * (m[1] * m[5] - m[2] * m[4]),
-k * m[3], k * m[0], k * (m[2] * m[3] - m[0] * m[5])
];
}
// Multiplies two 3x2 matrices.
function multiply(a, b) {
return [
a[0] * b[0] + a[1] * b[3],
a[0] * b[1] + a[1] * b[4],
a[0] * b[2] + a[1] * b[5] + a[2],
a[3] * b[0] + a[4] * b[3],
a[3] * b[1] + a[4] * b[4],
a[3] * b[2] + a[4] * b[5] + a[5]
];
}
// Subtracts 2D vectors.
function subtract(a, b) {
return [a[0] - b[0], a[1] - b[1]];
}
// Magnitude of a 2D vector.
function length(v) {
return sqrt(v[0] * v[0] + v[1] * v[1]);
}
// Angle between two 2D vectors.
function angle$1(a, b) {
return atan2(a[0] * b[1] - a[1] * b[0], a[0] * b[0] + a[1] * b[1]);
}
// Creates a polyhedral projection.
// * root: a spanning tree of polygon faces. Nodes are automatically
// augmented with a transform matrix.
// * face: a function that returns the appropriate node for a given {lambda, phi}
// point (radians).
// * r: rotation angle for final polyhedral net. Defaults to -pi / 6 (for
// butterflies).
var polyhedral = function(root, face, r) {
r = r == null ? -pi / 6 : r; // TODO automate
recurse(root, {transform: [
cos(r), sin(r), 0,
-sin(r), cos(r), 0
]});
function recurse(node, parent) {
node.edges = faceEdges(node.face);
// Find shared edge.
if (parent.face) {
var shared = node.shared = sharedEdge(node.face, parent.face),
m = matrix(shared.map(parent.project), shared.map(node.project));
node.transform = parent.transform ? multiply(parent.transform, m) : m;
// Replace shared edge in parent edges array.
var edges = parent.edges;
for (var i = 0, n = edges.length; i < n; ++i) {
if (pointEqual$1(shared[0], edges[i][1]) && pointEqual$1(shared[1], edges[i][0])) edges[i] = node;
if (pointEqual$1(shared[0], edges[i][0]) && pointEqual$1(shared[1], edges[i][1])) edges[i] = node;
}
edges = node.edges;
for (i = 0, n = edges.length; i < n; ++i) {
if (pointEqual$1(shared[0], edges[i][0]) && pointEqual$1(shared[1], edges[i][1])) edges[i] = parent;
if (pointEqual$1(shared[0], edges[i][1]) && pointEqual$1(shared[1], edges[i][0])) edges[i] = parent;
}
} else {
node.transform = parent.transform;
}
if (node.children) {
node.children.forEach(function(child) {
recurse(child, node);
});
}
return node;
}
function forward(lambda, phi) {
var node = face(lambda, phi),
point = node.project([lambda * degrees, phi * degrees]),
t;
if (t = node.transform) {
return [
t[0] * point[0] + t[1] * point[1] + t[2],
-(t[3] * point[0] + t[4] * point[1] + t[5])
];
}
point[1] = -point[1];
return point;
}
// Naive inverse! A faster solution would use bounding boxes, or even a
// polygonal quadtree.
if (hasInverse(root)) forward.invert = function(x, y) {
var coordinates = faceInvert(root, [x, -y]);
return coordinates && (coordinates[0] *= radians, coordinates[1] *= radians, coordinates);
};
function faceInvert(node, coordinates) {
var invert = node.project.invert,
t = node.transform,
point = coordinates;
if (t) {
t = inverse(t);
point = [
t[0] * point[0] + t[1] * point[1] + t[2],
(t[3] * point[0] + t[4] * point[1] + t[5])
];
}
if (invert && node === faceDegrees(p = invert(point))) return p;
var p,
children = node.children;
for (var i = 0, n = children && children.length; i < n; ++i) {
if (p = faceInvert(children[i], coordinates)) return p;
}
}
function faceDegrees(coordinates) {
return face(coordinates[0] * radians, coordinates[1] * radians);
}
var proj = d3Geo.geoProjection(forward),
stream_ = proj.stream;
if (proj.clipPolygon) {
// run around the mesh of faces and stream all vertices in order to create the clip polygon
var polygon = [];
outline({point: function(lambda, phi) { polygon.push([lambda, phi]); }}, root);
polygon.push(polygon[0]);
proj.clipPolygon([polygon]);
}
proj.stream = function(stream) {
var rotate = proj.rotate(),
clipPolygon = proj.clipPolygon ? proj.clipPolygon() : null,
angle = proj.clipAngle(),
precision = proj.precision(),
rotateStream = stream_(stream),
sphereStream = (proj.rotate([0, 0]).clipAngle(angle ? 180 : 0).precision(1), stream_(stream));
proj.rotate(rotate).clipAngle(angle).precision(precision);
if (clipPolygon) proj.clipPolygon(clipPolygon);
rotateStream.sphere = function() {
sphereStream.polygonStart();
sphereStream.lineStart();
outline(sphereStream, root);
sphereStream.lineEnd();
sphereStream.polygonEnd();
};
return rotateStream;
};
return proj;
};
function outline(stream, node, parent) {
var point,
edges = node.edges,
n = edges.length,
edge,
multiPoint = {type: "MultiPoint", coordinates: node.face},
notPoles = node.face.filter(function(d) { return abs(d[1]) !== 90; }),
b = d3Geo.geoBounds({type: "MultiPoint", coordinates: notPoles}),
inside = false,
j = -1,
dx = b[1][0] - b[0][0];
// TODO
var c = dx === 180 || dx === 360
? [(b[0][0] + b[1][0]) / 2, (b[0][1] + b[1][1]) / 2]
: d3Geo.geoCentroid(multiPoint);
// First find the shared edge…
if (parent) while (++j < n) {
if (edges[j] === parent) break;
}
++j;
for (var i = 0; i < n; ++i) {
edge = edges[(i + j) % n];
if (Array.isArray(edge)) {
if (!inside) {
stream.point((point = d3Geo.geoInterpolate(edge[0], c)(epsilon))[0], point[1]);
inside = true;
}
stream.point((point = d3Geo.geoInterpolate(edge[1], c)(epsilon))[0], point[1]);
} else {
inside = false;
if (edge !== parent) outline(stream, edge, node);
}
}
}
// Tests equality of two spherical points.
function pointEqual$1(a, b) {
return a && b && a[0] === b[0] && a[1] === b[1];
}
// Finds a shared edge given two clockwise polygons.
function sharedEdge(a, b) {
var x, y, n = a.length, found = null;
for (var i = 0; i < n; ++i) {
x = a[i];
for (var j = b.length; --j >= 0;) {
y = b[j];
if (x[0] === y[0] && x[1] === y[1]) {
if (found) return [found, x];
found = x;
}
}
}
}
// Converts an array of n face vertices to an array of n + 1 edges.
function faceEdges(face) {
var n = face.length,
edges = [];
for (var a = face[n - 1], i = 0; i < n; ++i) edges.push([a, a = face[i]]);
return edges;
}
function hasInverse(node) {
return node.project.invert || node.children && node.children.some(hasInverse);
}
// TODO generate on-the-fly to avoid external modification.
var octahedron = [
[0, 90],
[-90, 0], [0, 0], [90, 0], [180, 0],
[0, -90]
];
var octahedron$1 = [
[0, 2, 1],
[0, 3, 2],
[5, 1, 2],
[5, 2, 3],
[0, 1, 4],
[0, 4, 3],
[5, 4, 1],
[5, 3, 4]
].map(function(face) {
return face.map(function(i) {
return octahedron[i];
});
});
var butterfly = function(faceProjection) {
faceProjection = faceProjection || function(face) {
var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face});
return d3Geo.geoGnomonic().scale(1).translate([0, 0]).rotate([-c[0], -c[1]]);
};
var faces = octahedron$1.map(function(face) {
return {face: face, project: faceProjection(face)};
});
[-1, 0, 0, 1, 0, 1, 4, 5].forEach(function(d, i) {
var node = faces[d];
node && (node.children || (node.children = [])).push(faces[i]);
});
return polyhedral(faces[0], function(lambda, phi) {
return faces[lambda < -pi / 2 ? phi < 0 ? 6 : 4
: lambda < 0 ? phi < 0 ? 2 : 0
: lambda < pi / 2 ? phi < 0 ? 3 : 1
: phi < 0 ? 7 : 5];
})
.clipPolygon([])
.scale(101.858)
.center([0, 45]);
};
var kx = 2 / sqrt(3);
function collignonK(a, b) {
var p = collignonRaw(a, b);
return [p[0] * kx, p[1]];
}
collignonK.invert = function(x,y) {
return collignonRaw.invert(x / kx, y);
};
var collignon$1 = function(faceProjection) {
faceProjection = faceProjection || function(face) {
var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face});
return d3Geo.geoProjection(collignonK).translate([0, 0]).scale(1).rotate(c[1] > 0 ? [-c[0], 0] : [180 - c[0], 180]);
};
var faces = octahedron$1.map(function(face) {
return {face: face, project: faceProjection(face)};
});
[-1, 0, 0, 1, 0, 1, 4, 5].forEach(function(d, i) {
var node = faces[d];
node && (node.children || (node.children = [])).push(faces[i]);
});
return polyhedral(faces[0], function(lambda, phi) {
return faces[lambda < -pi / 2 ? phi < 0 ? 6 : 4
: lambda < 0 ? phi < 0 ? 2 : 0
: lambda < pi / 2 ? phi < 0 ? 3 : 1
: phi < 0 ? 7 : 5];
})
.clipPolygon([])
.scale(121.906)
.center([0, 48.5904]);
};
var waterman = function(faceProjection) {
faceProjection = faceProjection || function(face) {
var c = face.length === 6 ? d3Geo.geoCentroid({type: "MultiPoint", coordinates: face}) : face[0];
return d3Geo.geoGnomonic().scale(1).translate([0, 0]).rotate([-c[0], -c[1]]);
};
var w5 = octahedron$1.map(function(face) {
var xyz = face.map(cartesian),
n = xyz.length,
a = xyz[n - 1],
b,
hexagon = [];
for (var i = 0; i < n; ++i) {
b = xyz[i];
hexagon.push(spherical([
a[0] * 0.9486832980505138 + b[0] * 0.31622776601683794,
a[1] * 0.9486832980505138 + b[1] * 0.31622776601683794,
a[2] * 0.9486832980505138 + b[2] * 0.31622776601683794
]), spherical([
b[0] * 0.9486832980505138 + a[0] * 0.31622776601683794,
b[1] * 0.9486832980505138 + a[1] * 0.31622776601683794,
b[2] * 0.9486832980505138 + a[2] * 0.31622776601683794
]));
a = b;
}
return hexagon;
});
var cornerNormals = [];
var parents = [-1, 0, 0, 1, 0, 1, 4, 5];
w5.forEach(function(hexagon, j) {
var face = octahedron$1[j],
n = face.length,
normals = cornerNormals[j] = [];
for (var i = 0; i < n; ++i) {
w5.push([
face[i],
hexagon[(i * 2 + 2) % (2 * n)],
hexagon[(i * 2 + 1) % (2 * n)]
]);
parents.push(j);
normals.push(cross(
cartesian(hexagon[(i * 2 + 2) % (2 * n)]),
cartesian(hexagon[(i * 2 + 1) % (2 * n)])
));
}
});
var faces = w5.map(function(face) {
return {
project: faceProjection(face),
face: face
};
});
parents.forEach(function(d, i) {
var parent = faces[d];
parent && (parent.children || (parent.children = [])).push(faces[i]);
});
function face(lambda, phi) {
var cosphi = cos(phi),
p = [cosphi * cos(lambda), cosphi * sin(lambda), sin(phi)];
var hexagon = lambda < -pi / 2 ? phi < 0 ? 6 : 4
: lambda < 0 ? phi < 0 ? 2 : 0
: lambda < pi / 2 ? phi < 0 ? 3 : 1
: phi < 0 ? 7 : 5;
var n = cornerNormals[hexagon];
return faces[dot(n[0], p) < 0 ? 8 + 3 * hexagon
: dot(n[1], p) < 0 ? 8 + 3 * hexagon + 1
: dot(n[2], p) < 0 ? 8 + 3 * hexagon + 2
: hexagon];
}
return polyhedral(faces[0], face)
.clipPolygon([])
.scale(110.625)
.center([0,45]);
};
function dot(a, b) {
for (var i = 0, n = a.length, s = 0; i < n; ++i) s += a[i] * b[i];
return s;
}
function cross(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]
];
}
// Converts 3D Cartesian to spherical coordinates (degrees).
function spherical(cartesian) {
return [
atan2(cartesian[1], cartesian[0]) * degrees,
asin(max(-1, min(1, cartesian[2]))) * degrees
];
}
// Converts spherical coordinates (degrees) to 3D Cartesian.
function cartesian(coordinates) {
var lambda = coordinates[0] * radians,
phi = coordinates[1] * radians,
cosphi = cos(phi);
return [
cosphi * cos(lambda),
cosphi * sin(lambda),
sin(phi)
];
}
var noop = function() {};
var clockwise = function(ring) {
if ((n = ring.length) < 4) return false;
var i = 0,
n,
area = ring[n - 1][1] * ring[0][0] - ring[n - 1][0] * ring[0][1];
while (++i < n) area += ring[i - 1][1] * ring[i][0] - ring[i - 1][0] * ring[i][1];
return area <= 0;
};
var contains = function(ring, point) {
var x = point[0],
y = point[1],
contains = false;
for (var i = 0, n = ring.length, j = n - 1; i < n; j = i++) {
var pi = ring[i], xi = pi[0], yi = pi[1],
pj = ring[j], xj = pj[0], yj = pj[1];
if (((yi > y) ^ (yj > y)) && (x < (xj - xi) * (y - yi) / (yj - yi) + xi)) contains = !contains;
}
return contains;
};
var index = function(object, projection) {
var stream = projection.stream, project;
if (!stream) throw new Error("invalid projection");
switch (object && object.type) {
case "Feature": project = projectFeature; break;
case "FeatureCollection": project = projectFeatureCollection; break;
default: project = projectGeometry; break;
}
return project(object, stream);
};
function projectFeatureCollection(o, stream) {
return {
type: "FeatureCollection",
features: o.features.map(function(f) {
return projectFeature(f, stream);
})
};
}
function projectFeature(o, stream) {
return {
type: "Feature",
id: o.id,
properties: o.properties,
geometry: projectGeometry(o.geometry, stream)
};
}
function projectGeometryCollection(o, stream) {
return {
type: "GeometryCollection",
geometries: o.geometries.map(function(o) {
return projectGeometry(o, stream);
})
};
}
function projectGeometry(o, stream) {
if (!o) return null;
if (o.type === "GeometryCollection") return projectGeometryCollection(o, stream);
var sink;
switch (o.type) {
case "Point": sink = sinkPoint; break;
case "MultiPoint": sink = sinkPoint; break;
case "LineString": sink = sinkLine; break;
case "MultiLineString": sink = sinkLine; break;
case "Polygon": sink = sinkPolygon; break;
case "MultiPolygon": sink = sinkPolygon; break;
case "Sphere": sink = sinkPolygon; break;
default: return null;
}
d3Geo.geoStream(o, stream(sink));
return sink.result();
}
var points = [];
var lines = [];
var sinkPoint = {
point: function(x, y) {
points.push([x, y]);
},
result: function() {
var result = !points.length ? null
: points.length < 2 ? {type: "Point", coordinates: points[0]}
: {type: "MultiPoint", coordinates: points};
points = [];
return result;
}
};
var sinkLine = {
lineStart: noop,
point: function(x, y) {
points.push([x, y]);
},
lineEnd: function() {
if (points.length) lines.push(points), points = [];
},
result: function() {
var result = !lines.length ? null
: lines.length < 2 ? {type: "LineString", coordinates: lines[0]}
: {type: "MultiLineString", coordinates: lines};
lines = [];
return result;
}
};
var sinkPolygon = {
polygonStart: noop,
lineStart: noop,
point: function(x, y) {
points.push([x, y]);
},
lineEnd: function() {
var n = points.length;
if (n) {
do points.push(points[0].slice()); while (++n < 4);
lines.push(points), points = [];
}
},
polygonEnd: noop,
result: function() {
if (!lines.length) return null;
var polygons = [],
holes = [];
// https://github.com/d3/d3/issues/1558
lines.forEach(function(ring) {
if (clockwise(ring)) polygons.push([ring]);
else holes.push(ring);
});
holes.forEach(function(hole) {
var point = hole[0];
polygons.some(function(polygon) {
if (contains(polygon[0], point)) {
polygon.push(hole);
return true;
}
}) || polygons.push([hole]);
});
lines = [];
return !polygons.length ? null
: polygons.length > 1 ? {type: "MultiPolygon", coordinates: polygons}
: {type: "Polygon", coordinates: polygons[0]};
}
};
var quincuncial = function(project) {
var dx = project(halfPi, 0)[0] - project(-halfPi, 0)[0];
function projectQuincuncial(lambda, phi) {
var t = abs(lambda) < halfPi,
p = project(t ? lambda : lambda > 0 ? lambda - pi : lambda + pi, phi),
x = (p[0] - p[1]) * sqrt1_2,
y = (p[0] + p[1]) * sqrt1_2;
if (t) return [x, y];
var d = dx * sqrt1_2,
s = x > 0 ^ y > 0 ? -1 : 1;
return [s * x - sign(y) * d, s * y - sign(x) * d];
}
if (project.invert) projectQuincuncial.invert = function(x0, y0) {
var x = (x0 + y0) * sqrt1_2,
y = (y0 - x0) * sqrt1_2,
t = abs(x) < 0.5 * dx && abs(y) < 0.5 * dx;
if (!t) {
var d = dx * sqrt1_2,
s = x > 0 ^ y > 0 ? -1 : 1,
x1 = -s * x0 + (y > 0 ? 1 : -1) * d,
y1 = -s * y0 + (x > 0 ? 1 : -1) * d;
x = (-x1 - y1) * sqrt1_2;
y = (x1 - y1) * sqrt1_2;
}
var p = project.invert(x, y);
if (!t) p[0] += x > 0 ? pi : -pi;
return p;
};
return d3Geo.geoProjection(projectQuincuncial)
.rotate([-90, -90, 45])
.clipAngle(180 - 1e-3);
};
var gringorten$1 = function() {
return quincuncial(gringortenRaw)
.scale(176.423);
};
var peirce = function() {
return quincuncial(guyouRaw)
.scale(111.48);
};
var quantize = function(input, digits) {
if (!(0 <= (digits = +digits) && digits <= 20)) throw new Error("invalid digits");
function quantizePoint(input) {
var n = input.length, i = 2, output = new Array(n);
output[0] = +input[0].toFixed(digits);
output[1] = +input[1].toFixed(digits);
while (i < n) output[i] = input[i], ++i;
return output;
}
function quantizePoints(input) {
return input.map(quantizePoint);
}
function quantizePolygon(input) {
return input.map(quantizePoints);
}
function quantizeGeometry(input) {
if (input == null) return input;
var output;
switch (input.type) {
case "GeometryCollection": output = {type: "GeometryCollection", geometries: input.geometries.map(quantizeGeometry)}; break;
case "Point": output = {type: "Point", coordinates: quantizePoint(input.coordinates)}; break;
case "MultiPoint": case "LineString": output = {type: input.type, coordinates: quantizePoints(input.coordinates)}; break;
case "MultiLineString": case "Polygon": output = {type: input.type, coordinates: quantizePolygon(input.coordinates)}; break;
case "MultiPolygon": output = {type: "MultiPolygon", coordinates: input.coordinates.map(quantizePolygon)}; break;
default: return input;
}
if (input.bbox != null) output.bbox = input.bbox;
return output;
}
function quantizeFeature(input) {
var output = {type: "Feature", properties: input.properties, geometry: quantizeGeometry(input.geometry)};
if (input.id != null) output.id = input.id;
if (input.bbox != null) output.bbox = input.bbox;
return output;
}
if (input != null) switch (input.type) {
case "Feature": return quantizeFeature(input);
case "FeatureCollection": {
var output = {type: "FeatureCollection", features: input.features.map(quantizeFeature)};
if (input.bbox != null) output.bbox = input.bbox;
return output;
}
default: return quantizeGeometry(input);
}
return input;
};
function rectangularPolyconicRaw(phi0) {
var sinPhi0 = sin(phi0);
function forward(lambda, phi) {
var A = sinPhi0 ? tan(lambda * sinPhi0 / 2) / sinPhi0 : lambda / 2;
if (!phi) return [2 * A, -phi0];
var E = 2 * atan(A * sin(phi)),
cotPhi = 1 / tan(phi);
return [
sin(E) * cotPhi,
phi + (1 - cos(E)) * cotPhi - phi0
];
}
// TODO return null for points outside outline.
forward.invert = function(x, y) {
if (abs(y += phi0) < epsilon) return [sinPhi0 ? 2 * atan(sinPhi0 * x / 2) / sinPhi0 : x, 0];
var k = x * x + y * y,
phi = 0,
i = 10, delta;
do {
var tanPhi = tan(phi),
secPhi = 1 / cos(phi),
j = k - 2 * y * phi + phi * phi;
phi -= delta = (tanPhi * j + 2 * (phi - y)) / (2 + j * secPhi * secPhi + 2 * (phi - y) * tanPhi);
} while (abs(delta) > epsilon && --i > 0);
var E = x * (tanPhi = tan(phi)),
A = tan(abs(y) < abs(phi + 1 / tanPhi) ? asin(E) * 0.5 : acos(E) * 0.5 + pi / 4) / sin(phi);
return [
sinPhi0 ? 2 * atan(sinPhi0 * A) / sinPhi0 : 2 * A,
phi
];
};
return forward;
}
var rectangularPolyconic = function() {
return parallel1(rectangularPolyconicRaw)
.scale(131.215);
};
var K = [
[0.9986, -0.062],
[1.0000, 0.0000],
[0.9986, 0.0620],
[0.9954, 0.1240],
[0.9900, 0.1860],
[0.9822, 0.2480],
[0.9730, 0.3100],
[0.9600, 0.3720],
[0.9427, 0.4340],
[0.9216, 0.4958],
[0.8962, 0.5571],
[0.8679, 0.6176],
[0.8350, 0.6769],
[0.7986, 0.7346],
[0.7597, 0.7903],
[0.7186, 0.8435],
[0.6732, 0.8936],
[0.6213, 0.9394],
[0.5722, 0.9761],
[0.5322, 1.0000]
];
K.forEach(function(d) {
d[1] *= 1.0144;
});
function robinsonRaw(lambda, phi) {
var i = min(18, abs(phi) * 36 / pi),
i0 = floor(i),
di = i - i0,
ax = (k = K[i0])[0],
ay = k[1],
bx = (k = K[++i0])[0],
by = k[1],
cx = (k = K[min(19, ++i0)])[0],
cy = k[1],
k;
return [
lambda * (bx + di * (cx - ax) / 2 + di * di * (cx - 2 * bx + ax) / 2),
(phi > 0 ? halfPi : -halfPi) * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2)
];
}
robinsonRaw.invert = function(x, y) {
var yy = y / halfPi,
phi = yy * 90,
i = min(18, abs(phi / 5)),
i0 = max(0, floor(i));
do {
var ay = K[i0][1],
by = K[i0 + 1][1],
cy = K[min(19, i0 + 2)][1],
u = cy - ay,
v = cy - 2 * by + ay,
t = 2 * (abs(yy) - by) / u,
c = v / u,
di = t * (1 - c * t * (1 - 2 * c * t));
if (di >= 0 || i0 === 1) {
phi = (y >= 0 ? 5 : -5) * (di + i);
var j = 50, delta;
do {
i = min(18, abs(phi) / 5);
i0 = floor(i);
di = i - i0;
ay = K[i0][1];
by = K[i0 + 1][1];
cy = K[min(19, i0 + 2)][1];
phi -= (delta = (y >= 0 ? halfPi : -halfPi) * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2) - y) * degrees;
} while (abs(delta) > epsilon2 && --j > 0);
break;
}
} while (--i0 >= 0);
var ax = K[i0][0],
bx = K[i0 + 1][0],
cx = K[min(19, i0 + 2)][0];
return [
x / (bx + di * (cx - ax) / 2 + di * di * (cx - 2 * bx + ax) / 2),
phi * radians
];
};
var robinson = function() {
return d3Geo.geoProjection(robinsonRaw)
.scale(152.63);
};
function satelliteVerticalRaw(P) {
function forward(lambda, phi) {
var cosPhi = cos(phi),
k = (P - 1) / (P - cosPhi * cos(lambda));
return [
k * cosPhi * sin(lambda),
k * sin(phi)
];
}
forward.invert = function(x, y) {
var rho2 = x * x + y * y,
rho = sqrt(rho2),
sinc = (P - sqrt(1 - rho2 * (P + 1) / (P - 1))) / ((P - 1) / rho + rho / (P - 1));
return [
atan2(x * sinc, rho * sqrt(1 - sinc * sinc)),
rho ? asin(y * sinc / rho) : 0
];
};
return forward;
}
function satelliteRaw(P, omega) {
var vertical = satelliteVerticalRaw(P);
if (!omega) return vertical;
var cosOmega = cos(omega),
sinOmega = sin(omega);
function forward(lambda, phi) {
var coordinates = vertical(lambda, phi),
y = coordinates[1],
A = y * sinOmega / (P - 1) + cosOmega;
return [
coordinates[0] * cosOmega / A,
y / A
];
}
forward.invert = function(x, y) {
var k = (P - 1) / (P - 1 - y * sinOmega);
return vertical.invert(k * x, k * y * cosOmega);
};
return forward;
}
var satellite = function() {
var distance = 2,
omega = 0,
m = d3Geo.geoProjectionMutator(satelliteRaw),
p = m(distance, omega);
// As a multiple of radius.
p.distance = function(_) {
if (!arguments.length) return distance;
return m(distance = +_, omega);
};
p.tilt = function(_) {
if (!arguments.length) return omega * degrees;
return m(distance, omega = _ * radians);
};
return p
.scale(432.147)
.clipAngle(acos(1 / distance) * degrees - 1e-6);
};
var epsilon$1 = 1e-4;
var epsilonInverse = 1e4;
var x0 = -180;
var x0e = x0 + epsilon$1;
var x1 = 180;
var x1e = x1 - epsilon$1;
var y0 = -90;
var y0e = y0 + epsilon$1;
var y1 = 90;
var y1e = y1 - epsilon$1;
function nonempty(coordinates) {
return coordinates.length > 0;
}
function quantize$1(x) {
return Math.floor(x * epsilonInverse) / epsilonInverse;
}
function normalizePoint(y) {
return y === y0 || y === y1 ? [0, y] : [x0, quantize$1(y)]; // pole or antimeridian?
}
function clampPoint(p) {
var x = p[0], y = p[1], clamped = false;
if (x <= x0e) x = x0, clamped = true;
else if (x >= x1e) x = x1, clamped = true;
if (y <= y0e) y = y0, clamped = true;
else if (y >= y1e) y = y1, clamped = true;
return clamped ? [x, y] : p;
}
function clampPoints(points) {
return points.map(clampPoint);
}
// For each ring, detect where it crosses the antimeridian or pole.
function extractFragments(rings, polygon, fragments) {
for (var j = 0, m = rings.length; j < m; ++j) {
var ring = rings[j].slice();
// By default, assume that this ring doesn’t need any stitching.
fragments.push({index: -1, polygon: polygon, ring: ring});
for (var i = 0, n = ring.length; i < n; ++i) {
var point = ring[i],
x = point[0],
y = point[1];
// If this is an antimeridian or polar point…
if (x <= x0e || x >= x1e || y <= y0e || y >= y1e) {
ring[i] = clampPoint(point);
// Advance through any antimeridian or polar points…
for (var k = i + 1; k < n; ++k) {
var pointk = ring[k],
xk = pointk[0],
yk = pointk[1];
if (xk > x0e && xk < x1e && yk > y0e && yk < y1e) break;
}
// If this was just a single antimeridian or polar point,
// we don’t need to cut this ring into a fragment;
// we can just leave it as-is.
if (k === i + 1) continue;
// Otherwise, if this is not the first point in the ring,
// cut the current fragment so that it ends at the current point.
// The current point is also normalized for later joining.
if (i) {
var fragmentBefore = {index: -1, polygon: polygon, ring: ring.slice(0, i + 1)};
fragmentBefore.ring[fragmentBefore.ring.length - 1] = normalizePoint(y);
fragments[fragments.length - 1] = fragmentBefore;
}
// If the ring started with an antimeridian fragment,
// we can ignore that fragment entirely.
else fragments.pop();
// If the remainder of the ring is an antimeridian fragment,
// move on to the next ring.
if (k >= n) break;
// Otherwise, add the remaining ring fragment and continue.
fragments.push({index: -1, polygon: polygon, ring: ring = ring.slice(k - 1)});
ring[0] = normalizePoint(ring[0][1]);
i = -1;
n = ring.length;
}
}
}
}
// Now stitch the fragments back together into rings.
function stitchFragments(fragments) {
var i, n = fragments.length;
// To connect the fragments start-to-end, create a simple index by end.
var fragmentByStart = {},
fragmentByEnd = {},
fragment,
start,
startFragment,
end,
endFragment;
// For each fragment…
for (i = 0; i < n; ++i) {
fragment = fragments[i];
start = fragment.ring[0];
end = fragment.ring[fragment.ring.length - 1];
// If this fragment is closed, add it as a standalone ring.
if (start[0] === end[0] && start[1] === end[1]) {
fragment.polygon.push(fragment.ring);
fragments[i] = null;
continue;
}
fragment.index = i;
fragmentByStart[start] = fragmentByEnd[end] = fragment;
}
// For each open fragment…
for (i = 0; i < n; ++i) {
fragment = fragments[i];
if (fragment) {
start = fragment.ring[0];
end = fragment.ring[fragment.ring.length - 1];
startFragment = fragmentByEnd[start];
endFragment = fragmentByStart[end];
delete fragmentByStart[start];
delete fragmentByEnd[end];
// If this fragment is closed, add it as a standalone ring.
if (start[0] === end[0] && start[1] === end[1]) {
fragment.polygon.push(fragment.ring);
continue;
}
if (startFragment) {
delete fragmentByEnd[start];
delete fragmentByStart[startFragment.ring[0]];
startFragment.ring.pop(); // drop the shared coordinate
fragments[startFragment.index] = null;
fragment = {index: -1, polygon: startFragment.polygon, ring: startFragment.ring.concat(fragment.ring)};
if (startFragment === endFragment) {
// Connect both ends to this single fragment to create a ring.
fragment.polygon.push(fragment.ring);
} else {
fragment.index = n++;
fragments.push(fragmentByStart[fragment.ring[0]] = fragmentByEnd[fragment.ring[fragment.ring.length - 1]] = fragment);
}
} else if (endFragment) {
delete fragmentByStart[end];
delete fragmentByEnd[endFragment.ring[endFragment.ring.length - 1]];
fragment.ring.pop(); // drop the shared coordinate
fragment = {index: n++, polygon: endFragment.polygon, ring: fragment.ring.concat(endFragment.ring)};
fragments[endFragment.index] = null;
fragments.push(fragmentByStart[fragment.ring[0]] = fragmentByEnd[fragment.ring[fragment.ring.length - 1]] = fragment);
} else {
fragment.ring.push(fragment.ring[0]); // close ring
fragment.polygon.push(fragment.ring);
}
}
}
}
function stitchFeature(input) {
var output = {type: "Feature", geometry: stitchGeometry(input.geometry)};
if (input.id != null) output.id = input.id;
if (input.bbox != null) output.bbox = input.bbox;
if (input.properties != null) output.properties = input.properties;
return output;
}
function stitchGeometry(input) {
if (input == null) return input;
var output, fragments, i, n;
switch (input.type) {
case "GeometryCollection": output = {type: "GeometryCollection", geometries: input.geometries.map(stitchGeometry)}; break;
case "Point": output = {type: "Point", coordinates: clampPoint(input.coordinates)}; break;
case "MultiPoint": case "LineString": output = {type: input.type, coordinates: clampPoints(input.coordinates)}; break;
case "MultiLineString": output = {type: "MultiLineString", coordinates: input.coordinates.map(clampPoints)}; break;
case "Polygon": {
var polygon = [];
extractFragments(input.coordinates, polygon, fragments = []);
stitchFragments(fragments);
output = {type: "Polygon", coordinates: polygon};
break;
}
case "MultiPolygon": {
fragments = [], i = -1, n = input.coordinates.length;
var polygons = new Array(n);
while (++i < n) extractFragments(input.coordinates[i], polygons[i] = [], fragments);
stitchFragments(fragments);
output = {type: "MultiPolygon", coordinates: polygons.filter(nonempty)};
break;
}
default: return input;
}
if (input.bbox != null) output.bbox = input.bbox;
return output;
}
var stitch = function(input) {
if (input == null) return input;
switch (input.type) {
case "Feature": return stitchFeature(input);
case "FeatureCollection": {
var output = {type: "FeatureCollection", features: input.features.map(stitchFeature)};
if (input.bbox != null) output.bbox = input.bbox;
return output;
}
default: return stitchGeometry(input);
}
};
function timesRaw(lambda, phi) {
var t = tan(phi / 2),
s = sin(quarterPi * t);
return [
lambda * (0.74482 - 0.34588 * s * s),
1.70711 * t
];
}
timesRaw.invert = function(x, y) {
var t = y / 1.70711,
s = sin(quarterPi * t);
return [
x / (0.74482 - 0.34588 * s * s),
2 * atan(t)
];
};
var times = function() {
return d3Geo.geoProjection(timesRaw)
.scale(146.153);
};
// Compute the origin as the midpoint of the two reference points.
// Rotate one of the reference points by the origin.
// Apply the spherical law of sines to compute gamma rotation.
var twoPoint = function(raw, p0, p1) {
var i = d3Geo.geoInterpolate(p0, p1),
o = i(0.5),
a = d3Geo.geoRotation([-o[0], -o[1]])(p0),
b = i.distance / 2,
y = -asin(sin(a[1] * radians) / sin(b)),
R = [-o[0], -o[1], -(a[0] > 0 ? pi - y : y) * degrees],
p = d3Geo.geoProjection(raw(b)).rotate(R),
r = d3Geo.geoRotation(R),
center = p.center;
delete p.rotate;
p.center = function(_) {
return arguments.length ? center(r(_)) : r.invert(center());
};
return p
.clipAngle(90);
};
function twoPointAzimuthalRaw(d) {
var cosd = cos(d);
function forward(lambda, phi) {
var coordinates = d3Geo.geoGnomonicRaw(lambda, phi);
coordinates[0] *= cosd;
return coordinates;
}
forward.invert = function(x, y) {
return d3Geo.geoGnomonicRaw.invert(x / cosd, y);
};
return forward;
}
function twoPointAzimuthalUsa() {
return twoPointAzimuthal([-158, 21.5], [-77, 39])
.clipAngle(60)
.scale(400);
}
function twoPointAzimuthal(p0, p1) {
return twoPoint(twoPointAzimuthalRaw, p0, p1);
}
// TODO clip to ellipse
function twoPointEquidistantRaw(z0) {
if (!(z0 *= 2)) return d3Geo.geoAzimuthalEquidistantRaw;
var lambdaa = -z0 / 2,
lambdab = -lambdaa,
z02 = z0 * z0,
tanLambda0 = tan(lambdab),
S = 0.5 / sin(lambdab);
function forward(lambda, phi) {
var za = acos(cos(phi) * cos(lambda - lambdaa)),
zb = acos(cos(phi) * cos(lambda - lambdab)),
ys = phi < 0 ? -1 : 1;
za *= za, zb *= zb;
return [
(za - zb) / (2 * z0),
ys * sqrt(4 * z02 * zb - (z02 - za + zb) * (z02 - za + zb)) / (2 * z0)
];
}
forward.invert = function(x, y) {
var y2 = y * y,
cosza = cos(sqrt(y2 + (t = x + lambdaa) * t)),
coszb = cos(sqrt(y2 + (t = x + lambdab) * t)),
t,
d;
return [
atan2(d = cosza - coszb, t = (cosza + coszb) * tanLambda0),
(y < 0 ? -1 : 1) * acos(sqrt(t * t + d * d) * S)
];
};
return forward;
}
function twoPointEquidistantUsa() {
return twoPointEquidistant([-158, 21.5], [-77, 39])
.clipAngle(130)
.scale(122.571);
}
function twoPointEquidistant(p0, p1) {
return twoPoint(twoPointEquidistantRaw, p0, p1);
}
function vanDerGrintenRaw(lambda, phi) {
if (abs(phi) < epsilon) return [lambda, 0];
var sinTheta = abs(phi / halfPi),
theta = asin(sinTheta);
if (abs(lambda) < epsilon || abs(abs(phi) - halfPi) < epsilon) return [0, sign(phi) * pi * tan(theta / 2)];
var cosTheta = cos(theta),
A = abs(pi / lambda - lambda / pi) / 2,
A2 = A * A,
G = cosTheta / (sinTheta + cosTheta - 1),
P = G * (2 / sinTheta - 1),
P2 = P * P,
P2_A2 = P2 + A2,
G_P2 = G - P2,
Q = A2 + G;
return [
sign(lambda) * pi * (A * G_P2 + sqrt(A2 * G_P2 * G_P2 - P2_A2 * (G * G - P2))) / P2_A2,
sign(phi) * pi * (P * Q - A * sqrt((A2 + 1) * P2_A2 - Q * Q)) / P2_A2
];
}
vanDerGrintenRaw.invert = function(x, y) {
if (abs(y) < epsilon) return [x, 0];
if (abs(x) < epsilon) return [0, halfPi * sin(2 * atan(y / pi))];
var x2 = (x /= pi) * x,
y2 = (y /= pi) * y,
x2_y2 = x2 + y2,
z = x2_y2 * x2_y2,
c1 = -abs(y) * (1 + x2_y2),
c2 = c1 - 2 * y2 + x2,
c3 = -2 * c1 + 1 + 2 * y2 + z,
d = y2 / c3 + (2 * c2 * c2 * c2 / (c3 * c3 * c3) - 9 * c1 * c2 / (c3 * c3)) / 27,
a1 = (c1 - c2 * c2 / (3 * c3)) / c3,
m1 = 2 * sqrt(-a1 / 3),
theta1 = acos(3 * d / (a1 * m1)) / 3;
return [
pi * (x2_y2 - 1 + sqrt(1 + 2 * (x2 - y2) + z)) / (2 * x),
sign(y) * pi * (-m1 * cos(theta1 + pi / 3) - c2 / (3 * c3))
];
};
var vanDerGrinten = function() {
return d3Geo.geoProjection(vanDerGrintenRaw)
.scale(79.4183);
};
function vanDerGrinten2Raw(lambda, phi) {
if (abs(phi) < epsilon) return [lambda, 0];
var sinTheta = abs(phi / halfPi),
theta = asin(sinTheta);
if (abs(lambda) < epsilon || abs(abs(phi) - halfPi) < epsilon) return [0, sign(phi) * pi * tan(theta / 2)];
var cosTheta = cos(theta),
A = abs(pi / lambda - lambda / pi) / 2,
A2 = A * A,
x1 = cosTheta * (sqrt(1 + A2) - A * cosTheta) / (1 + A2 * sinTheta * sinTheta);
return [
sign(lambda) * pi * x1,
sign(phi) * pi * sqrt(1 - x1 * (2 * A + x1))
];
}
vanDerGrinten2Raw.invert = function(x, y) {
if (!x) return [0, halfPi * sin(2 * atan(y / pi))];
var x1 = abs(x / pi),
A = (1 - x1 * x1 - (y /= pi) * y) / (2 * x1),
A2 = A * A,
B = sqrt(A2 + 1);
return [
sign(x) * pi * (B - A),
sign(y) * halfPi * sin(2 * atan2(sqrt((1 - 2 * A * x1) * (A + B) - x1), sqrt(B + A + x1)))
];
};
var vanDerGrinten2 = function() {
return d3Geo.geoProjection(vanDerGrinten2Raw)
.scale(79.4183);
};
function vanDerGrinten3Raw(lambda, phi) {
if (abs(phi) < epsilon) return [lambda, 0];
var sinTheta = phi / halfPi,
theta = asin(sinTheta);
if (abs(lambda) < epsilon || abs(abs(phi) - halfPi) < epsilon) return [0, pi * tan(theta / 2)];
var A = (pi / lambda - lambda / pi) / 2,
y1 = sinTheta / (1 + cos(theta));
return [
pi * (sign(lambda) * sqrt(A * A + 1 - y1 * y1) - A),
pi * y1
];
}
vanDerGrinten3Raw.invert = function(x, y) {
if (!y) return [x, 0];
var y1 = y / pi,
A = (pi * pi * (1 - y1 * y1) - x * x) / (2 * pi * x);
return [
x ? pi * (sign(x) * sqrt(A * A + 1) - A) : 0,
halfPi * sin(2 * atan(y1))
];
};
var vanDerGrinten3 = function() {
return d3Geo.geoProjection(vanDerGrinten3Raw)
.scale(79.4183);
};
function vanDerGrinten4Raw(lambda, phi) {
if (!phi) return [lambda, 0];
var phi0 = abs(phi);
if (!lambda || phi0 === halfPi) return [0, phi];
var B = phi0 / halfPi,
B2 = B * B,
C = (8 * B - B2 * (B2 + 2) - 5) / (2 * B2 * (B - 1)),
C2 = C * C,
BC = B * C,
B_C2 = B2 + C2 + 2 * BC,
B_3C = B + 3 * C,
lambda0 = lambda / halfPi,
lambda1 = lambda0 + 1 / lambda0,
D = sign(abs(lambda) - halfPi) * sqrt(lambda1 * lambda1 - 4),
D2 = D * D,
F = B_C2 * (B2 + C2 * D2 - 1) + (1 - B2) * (B2 * (B_3C * B_3C + 4 * C2) + 12 * BC * C2 + 4 * C2 * C2),
x1 = (D * (B_C2 + C2 - 1) + 2 * sqrt(F)) / (4 * B_C2 + D2);
return [
sign(lambda) * halfPi * x1,
sign(phi) * halfPi * sqrt(1 + D * abs(x1) - x1 * x1)
];
}
vanDerGrinten4Raw.invert = function(x, y) {
var delta;
if (!x || !y) return [x, y];
y /= pi;
var x1 = sign(x) * x / halfPi,
D = (x1 * x1 - 1 + 4 * y * y) / abs(x1),
D2 = D * D,
B = 2 * y,
i = 50;
do {
var B2 = B * B,
C = (8 * B - B2 * (B2 + 2) - 5) / (2 * B2 * (B - 1)),
C_ = (3 * B - B2 * B - 10) / (2 * B2 * B),
C2 = C * C,
BC = B * C,
B_C = B + C,
B_C2 = B_C * B_C,
B_3C = B + 3 * C,
F = B_C2 * (B2 + C2 * D2 - 1) + (1 - B2) * (B2 * (B_3C * B_3C + 4 * C2) + C2 * (12 * BC + 4 * C2)),
F_ = -2 * B_C * (4 * BC * C2 + (1 - 4 * B2 + 3 * B2 * B2) * (1 + C_) + C2 * (-6 + 14 * B2 - D2 + (-8 + 8 * B2 - 2 * D2) * C_) + BC * (-8 + 12 * B2 + (-10 + 10 * B2 - D2) * C_)),
sqrtF = sqrt(F),
f = D * (B_C2 + C2 - 1) + 2 * sqrtF - x1 * (4 * B_C2 + D2),
f_ = D * (2 * C * C_ + 2 * B_C * (1 + C_)) + F_ / sqrtF - 8 * B_C * (D * (-1 + C2 + B_C2) + 2 * sqrtF) * (1 + C_) / (D2 + 4 * B_C2);
B -= delta = f / f_;
} while (delta > epsilon && --i > 0);
return [
sign(x) * (sqrt(D * D + 4) + D) * pi / 4,
halfPi * B
];
};
var vanDerGrinten4 = function() {
return d3Geo.geoProjection(vanDerGrinten4Raw)
.scale(127.16);
};
var A = 4 * pi + 3 * sqrt(3);
var B = 2 * sqrt(2 * pi * sqrt(3) / A);
var wagner4Raw = mollweideBromleyRaw(B * sqrt(3) / pi, B, A / 6);
var wagner4 = function() {
return d3Geo.geoProjection(wagner4Raw)
.scale(176.84);
};
function wagner6Raw(lambda, phi) {
return [lambda * sqrt(1 - 3 * phi * phi / (pi * pi)), phi];
}
wagner6Raw.invert = function(x, y) {
return [x / sqrt(1 - 3 * y * y / (pi * pi)), y];
};
var wagner6 = function() {
return d3Geo.geoProjection(wagner6Raw)
.scale(152.63);
};
function wagner7Raw(lambda, phi) {
var s = 0.90631 * sin(phi),
c0 = sqrt(1 - s * s),
c1 = sqrt(2 / (1 + c0 * cos(lambda /= 3)));
return [
2.66723 * c0 * c1 * sin(lambda),
1.24104 * s * c1
];
}
wagner7Raw.invert = function(x, y) {
var t1 = x / 2.66723,
t2 = y / 1.24104,
p = sqrt(t1 * t1 + t2 * t2),
c = 2 * asin(p / 2);
return [
3 * atan2(x * tan(c), 2.66723 * p),
p && asin(y * sin(c) / (1.24104 * 0.90631 * p))
];
};
var wagner7 = function() {
return d3Geo.geoProjection(wagner7Raw)
.scale(172.632);
};
function wiechelRaw(lambda, phi) {
var cosPhi = cos(phi),
sinPhi = cos(lambda) * cosPhi,
sin1_Phi = 1 - sinPhi,
cosLambda = cos(lambda = atan2(sin(lambda) * cosPhi, -sin(phi))),
sinLambda = sin(lambda);
cosPhi = sqrt(1 - sinPhi * sinPhi);
return [
sinLambda * cosPhi - cosLambda * sin1_Phi,
-cosLambda * cosPhi - sinLambda * sin1_Phi
];
}
wiechelRaw.invert = function(x, y) {
var w = (x * x + y * y) / -2,
k = sqrt(-w * (2 + w)),
b = y * w + x * k,
a = x * w - y * k,
D = sqrt(a * a + b * b);
return [
atan2(k * b, D * (1 + w)),
D ? -asin(k * a / D) : 0
];
};
var wiechel = function() {
return d3Geo.geoProjection(wiechelRaw)
.rotate([0, -90, 45])
.scale(124.75)
.clipAngle(180 - 1e-3);
};
function winkel3Raw(lambda, phi) {
var coordinates = aitoffRaw(lambda, phi);
return [
(coordinates[0] + lambda / halfPi) / 2,
(coordinates[1] + phi) / 2
];
}
winkel3Raw.invert = function(x, y) {
var lambda = x, phi = y, i = 25;
do {
var cosphi = cos(phi),
sinphi = sin(phi),
sin_2phi = sin(2 * phi),
sin2phi = sinphi * sinphi,
cos2phi = cosphi * cosphi,
sinlambda = sin(lambda),
coslambda_2 = cos(lambda / 2),
sinlambda_2 = sin(lambda / 2),
sin2lambda_2 = sinlambda_2 * sinlambda_2,
C = 1 - cos2phi * coslambda_2 * coslambda_2,
E = C ? acos(cosphi * coslambda_2) * sqrt(F = 1 / C) : F = 0,
F,
fx = 0.5 * (2 * E * cosphi * sinlambda_2 + lambda / halfPi) - x,
fy = 0.5 * (E * sinphi + phi) - y,
dxdlambda = 0.5 * F * (cos2phi * sin2lambda_2 + E * cosphi * coslambda_2 * sin2phi) + 0.5 / halfPi,
dxdphi = F * (sinlambda * sin_2phi / 4 - E * sinphi * sinlambda_2),
dydlambda = 0.125 * F * (sin_2phi * sinlambda_2 - E * sinphi * cos2phi * sinlambda),
dydphi = 0.5 * F * (sin2phi * coslambda_2 + E * sin2lambda_2 * cosphi) + 0.5,
denominator = dxdphi * dydlambda - dydphi * dxdlambda,
dlambda = (fy * dxdphi - fx * dydphi) / denominator,
dphi = (fx * dydlambda - fy * dxdlambda) / denominator;
lambda -= dlambda, phi -= dphi;
} while ((abs(dlambda) > epsilon || abs(dphi) > epsilon) && --i > 0);
return [lambda, phi];
};
var winkel3 = function() {
return d3Geo.geoProjection(winkel3Raw)
.scale(158.837);
};
exports.geoAiry = airy;
exports.geoAiryRaw = airyRaw;
exports.geoAitoff = aitoff;
exports.geoAitoffRaw = aitoffRaw;
exports.geoArmadillo = armadillo;
exports.geoArmadilloRaw = armadilloRaw;
exports.geoAugust = august;
exports.geoAugustRaw = augustRaw;
exports.geoBaker = baker;
exports.geoBakerRaw = bakerRaw;
exports.geoBerghaus = berghaus;
exports.geoBerghausRaw = berghausRaw;
exports.geoBoggs = boggs;
exports.geoBoggsRaw = boggsRaw;
exports.geoBonne = bonne;
exports.geoBonneRaw = bonneRaw;
exports.geoBottomley = bottomley;
exports.geoBottomleyRaw = bottomleyRaw;
exports.geoBromley = bromley;
exports.geoBromleyRaw = bromleyRaw;
exports.geoChamberlin = chamberlin;
exports.geoChamberlinRaw = chamberlinRaw;
exports.geoChamberlinAfrica = chamberlinAfrica;
exports.geoCollignon = collignon;
exports.geoCollignonRaw = collignonRaw;
exports.geoCraig = craig;
exports.geoCraigRaw = craigRaw;
exports.geoCraster = craster;
exports.geoCrasterRaw = crasterRaw;
exports.geoCylindricalEqualArea = cylindricalEqualArea;
exports.geoCylindricalEqualAreaRaw = cylindricalEqualAreaRaw;
exports.geoCylindricalStereographic = cylindricalStereographic;
exports.geoCylindricalStereographicRaw = cylindricalStereographicRaw;
exports.geoEckert1 = eckert1;
exports.geoEckert1Raw = eckert1Raw;
exports.geoEckert2 = eckert2;
exports.geoEckert2Raw = eckert2Raw;
exports.geoEckert3 = eckert3;
exports.geoEckert3Raw = eckert3Raw;
exports.geoEckert4 = eckert4;
exports.geoEckert4Raw = eckert4Raw;
exports.geoEckert5 = eckert5;
exports.geoEckert5Raw = eckert5Raw;
exports.geoEckert6 = eckert6;
exports.geoEckert6Raw = eckert6Raw;
exports.geoEisenlohr = eisenlohr;
exports.geoEisenlohrRaw = eisenlohrRaw;
exports.geoFahey = fahey;
exports.geoFaheyRaw = faheyRaw;
exports.geoFoucaut = foucaut;
exports.geoFoucautRaw = foucautRaw;
exports.geoGilbert = gilbert;
exports.geoGingery = gingery;
exports.geoGingeryRaw = gingeryRaw;
exports.geoGinzburg4 = ginzburg4;
exports.geoGinzburg4Raw = ginzburg4Raw;
exports.geoGinzburg5 = ginzburg5;
exports.geoGinzburg5Raw = ginzburg5Raw;
exports.geoGinzburg6 = ginzburg6;
exports.geoGinzburg6Raw = ginzburg6Raw;
exports.geoGinzburg8 = ginzburg8;
exports.geoGinzburg8Raw = ginzburg8Raw;
exports.geoGinzburg9 = ginzburg9;
exports.geoGinzburg9Raw = ginzburg9Raw;
exports.geoGringorten = gringorten;
exports.geoGringortenRaw = gringortenRaw;
exports.geoGuyou = guyou;
exports.geoGuyouRaw = guyouRaw;
exports.geoHammer = hammer;
exports.geoHammerRaw = hammerRaw;
exports.geoHammerRetroazimuthal = hammerRetroazimuthal;
exports.geoHammerRetroazimuthalRaw = hammerRetroazimuthalRaw;
exports.geoHealpix = healpix;
exports.geoHealpixRaw = healpixRaw;
exports.geoHill = hill;
exports.geoHillRaw = hillRaw;
exports.geoHomolosine = homolosine;
exports.geoHomolosineRaw = homolosineRaw;
exports.geoInterrupt = interrupt;
exports.geoInterruptedBoggs = boggs$1;
exports.geoInterruptedHomolosine = homolosine$1;
exports.geoInterruptedMollweide = mollweide$1;
exports.geoInterruptedMollweideHemispheres = mollweideHemispheres;
exports.geoInterruptedSinuMollweide = sinuMollweide$1;
exports.geoInterruptedSinusoidal = sinusoidal$1;
exports.geoKavrayskiy7 = kavrayskiy7;
exports.geoKavrayskiy7Raw = kavrayskiy7Raw;
exports.geoLagrange = lagrange;
exports.geoLagrangeRaw = lagrangeRaw;
exports.geoLarrivee = larrivee;
exports.geoLarriveeRaw = larriveeRaw;
exports.geoLaskowski = laskowski;
exports.geoLaskowskiRaw = laskowskiRaw;
exports.geoLittrow = littrow;
exports.geoLittrowRaw = littrowRaw;
exports.geoLoximuthal = loximuthal;
exports.geoLoximuthalRaw = loximuthalRaw;
exports.geoMiller = miller;
exports.geoMillerRaw = millerRaw;
exports.geoModifiedStereographic = modifiedStereographic;
exports.geoModifiedStereographicRaw = modifiedStereographicRaw;
exports.geoModifiedStereographicAlaska = modifiedStereographicAlaska;
exports.geoModifiedStereographicGs48 = modifiedStereographicGs48;
exports.geoModifiedStereographicGs50 = modifiedStereographicGs50;
exports.geoModifiedStereographicMiller = modifiedStereographicMiller;
exports.geoModifiedStereographicLee = modifiedStereographicLee;
exports.geoMollweide = mollweide;
exports.geoMollweideRaw = mollweideRaw;
exports.geoMtFlatPolarParabolic = mtFlatPolarParabolic;
exports.geoMtFlatPolarParabolicRaw = mtFlatPolarParabolicRaw;
exports.geoMtFlatPolarQuartic = mtFlatPolarQuartic;
exports.geoMtFlatPolarQuarticRaw = mtFlatPolarQuarticRaw;
exports.geoMtFlatPolarSinusoidal = mtFlatPolarSinusoidal;
exports.geoMtFlatPolarSinusoidalRaw = mtFlatPolarSinusoidalRaw;
exports.geoNaturalEarth = naturalEarth;
exports.geoNaturalEarthRaw = naturalEarthRaw;
exports.geoNaturalEarth2 = naturalEarth2;
exports.geoNaturalEarth2Raw = naturalEarth2Raw;
exports.geoNellHammer = nellHammer;
exports.geoNellHammerRaw = nellHammerRaw;
exports.geoPatterson = patterson;
exports.geoPattersonRaw = pattersonRaw;
exports.geoPolyconic = polyconic;
exports.geoPolyconicRaw = polyconicRaw;
exports.geoPolyhedral = polyhedral;
exports.geoPolyhedralButterfly = butterfly;
exports.geoPolyhedralCollignon = collignon$1;
exports.geoPolyhedralWaterman = waterman;
exports.geoProject = index;
exports.geoGringortenQuincuncial = gringorten$1;
exports.geoPeirceQuincuncial = peirce;
exports.geoPierceQuincuncial = peirce;
exports.geoQuantize = quantize;
exports.geoQuincuncial = quincuncial;
exports.geoRectangularPolyconic = rectangularPolyconic;
exports.geoRectangularPolyconicRaw = rectangularPolyconicRaw;
exports.geoRobinson = robinson;
exports.geoRobinsonRaw = robinsonRaw;
exports.geoSatellite = satellite;
exports.geoSatelliteRaw = satelliteRaw;
exports.geoSinuMollweide = sinuMollweide;
exports.geoSinuMollweideRaw = sinuMollweideRaw;
exports.geoSinusoidal = sinusoidal;
exports.geoSinusoidalRaw = sinusoidalRaw;
exports.geoStitch = stitch;
exports.geoTimes = times;
exports.geoTimesRaw = timesRaw;
exports.geoTwoPointAzimuthal = twoPointAzimuthal;
exports.geoTwoPointAzimuthalRaw = twoPointAzimuthalRaw;
exports.geoTwoPointAzimuthalUsa = twoPointAzimuthalUsa;
exports.geoTwoPointEquidistant = twoPointEquidistant;
exports.geoTwoPointEquidistantRaw = twoPointEquidistantRaw;
exports.geoTwoPointEquidistantUsa = twoPointEquidistantUsa;
exports.geoVanDerGrinten = vanDerGrinten;
exports.geoVanDerGrintenRaw = vanDerGrintenRaw;
exports.geoVanDerGrinten2 = vanDerGrinten2;
exports.geoVanDerGrinten2Raw = vanDerGrinten2Raw;
exports.geoVanDerGrinten3 = vanDerGrinten3;
exports.geoVanDerGrinten3Raw = vanDerGrinten3Raw;
exports.geoVanDerGrinten4 = vanDerGrinten4;
exports.geoVanDerGrinten4Raw = vanDerGrinten4Raw;
exports.geoWagner4 = wagner4;
exports.geoWagner4Raw = wagner4Raw;
exports.geoWagner6 = wagner6;
exports.geoWagner6Raw = wagner6Raw;
exports.geoWagner7 = wagner7;
exports.geoWagner7Raw = wagner7Raw;
exports.geoWiechel = wiechel;
exports.geoWiechelRaw = wiechelRaw;
exports.geoWinkel3 = winkel3;
exports.geoWinkel3Raw = winkel3Raw;
Object.defineProperty(exports, '__esModule', { value: true });
})));
Raw
d3-geo.js
// https://d3js.org/d3-geo/ Version 1.6.4. Copyright 2017 Mike Bostock.
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports, require('d3-array')) :
typeof define === 'function' && define.amd ? define(['exports', 'd3-array'], factory) :
(factory((global.d3 = global.d3 || {}),global.d3));
}(this, function (exports,d3Array) { 'use strict';
// 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 epsilon2 = 1e-12;
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 ceil = Math.ceil;
var exp = Math.exp;
var log = Math.log;
var pow = Math.pow;
var sin = Math.sin;
var sign = Math.sign || function(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; };
var sqrt = Math.sqrt;
var tan = Math.tan;
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 haversin(x) {
return (x = sin(x / 2)) * 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 area(object) {
areaSum.reset();
geoStream(object, areaStream);
return areaSum * 2;
}
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;
}
function cartesianEqual(a, b) {
var dx = b[0] - a[0],
dy = b[1] - a[1],
dz = b[2] - a[2];
return dx * dx + dy * dy + dz * dz < epsilon2 * epsilon2;
}
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;
}
function rangeCompare(a, b) {
return a[0] - b[0];
}
function rangeContains(range, x) {
return range[0] <= range[1] ? range[0] <= x && x <= range[1] : x < range[0] || range[1] < x;
}
function bounds(feature) {
var i, n, a, b, merged, deltaMax, delta;
phi1 = lambda1 = -(lambda0$1 = phi0 = Infinity);
ranges = [];
geoStream(feature, boundsStream);
// First, sort ranges by their minimum longitudes.
if (n = ranges.length) {
ranges.sort(rangeCompare);
// Then, merge any ranges that overlap.
for (i = 1, a = ranges[0], merged = [a]; i < n; ++i) {
b = ranges[i];
if (rangeContains(a, b[0]) || rangeContains(a, b[1])) {
if (angle(a[0], b[1]) > angle(a[0], a[1])) a[1] = b[1];
if (angle(b[0], a[1]) > angle(a[0], a[1])) a[0] = b[0];
} else {
merged.push(a = b);
}
}
// Finally, find the largest gap between the merged ranges.
// The final bounding box will be the inverse of this gap.
for (deltaMax = -Infinity, n = merged.length - 1, i = 0, a = merged[n]; i <= n; a = b, ++i) {
b = merged[i];
if ((delta = angle(a[1], b[0])) > deltaMax) deltaMax = delta, lambda0$1 = b[0], lambda1 = a[1];
}
}
ranges = range$1 = null;
return lambda0$1 === Infinity || phi0 === Infinity
? [[NaN, NaN], [NaN, NaN]]
: [[lambda0$1, phi0], [lambda1, phi1]];
}
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 centroid(object) {
W0 = W1 =
X0 = Y0 = Z0 =
X1 = Y1 = Z1 =
X2 = Y2 = Z2 = 0;
geoStream(object, centroidStream);
var x = X2,
y = Y2,
z = Z2,
m = x * x + y * y + z * z;
// If the area-weighted ccentroid is undefined, fall back to length-weighted ccentroid.
if (m < epsilon2) {
x = X1, y = Y1, z = Z1;
// If the feature has zero length, fall back to arithmetic mean of point vectors.
if (W1 < epsilon) x = X0, y = Y0, z = Z0;
m = x * x + y * y + z * z;
// If the feature still has an undefined ccentroid, then return.
if (m < epsilon2) return [NaN, NaN];
}
return [atan2(y, x) * degrees, asin(z / sqrt(m)) * degrees];
}
function constant(x) {
return function() {
return x;
};
}
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;
}
function rotation(rotate) {
rotate = rotateRadians(rotate[0] * radians, rotate[1] * radians, rotate.length > 2 ? rotate[2] * radians : 0);
function forward(coordinates) {
coordinates = rotate(coordinates[0] * radians, coordinates[1] * radians);
return coordinates[0] *= degrees, coordinates[1] *= degrees, coordinates;
}
forward.invert = function(coordinates) {
coordinates = rotate.invert(coordinates[0] * radians, coordinates[1] * radians);
return coordinates[0] *= degrees, coordinates[1] *= degrees, coordinates;
};
return forward;
}
// 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 circle() {
var center = constant([0, 0]),
radius = constant(90),
precision = constant(6),
ring,
rotate,
stream = {point: point};
function point(x, y) {
ring.push(x = rotate(x, y));
x[0] *= degrees, x[1] *= degrees;
}
function circle() {
var c = center.apply(this, arguments),
r = radius.apply(this, arguments) * radians,
p = precision.apply(this, arguments) * radians;
ring = [];
rotate = rotateRadians(-c[0] * radians, -c[1] * radians, 0).invert;
circleStream(stream, r, p, 1);
c = {type: "Polygon", coordinates: [ring]};
ring = rotate = null;
return c;
}
circle.center = function(_) {
return arguments.length ? (center = typeof _ === "function" ? _ : constant([+_[0], +_[1]]), circle) : center;
};
circle.radius = function(_) {
return arguments.length ? (radius = typeof _ === "function" ? _ : constant(+_), circle) : radius;
};
circle.precision = function(_) {
return arguments.length ? (precision = typeof _ === "function" ? _ : constant(+_), circle) : precision;
};
return circle;
}
function clipBuffer() {
var lines = [],
line;
return {
point: function(x, y, i, t) {
var point = [x, y];
// when called by clipPolygon, store index and t
if (arguments.length > 2) { point.index = i; point.t = t; }
line.push(point);
},
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 clipRejoin(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 = d3Array.merge(segments)).length;
if (cleanInside || visible) {
stream.polygonStart();
if (cleanInside) {
stream.lineStart();
interpolate(null, null, 1, stream);
stream.lineEnd();
}
if (visible) {
clipRejoin(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;
};
}
function extent() {
var x0 = 0,
y0 = 0,
x1 = 960,
y1 = 500,
cache,
cacheStream,
clip;
return clip = {
stream: function(stream) {
return cache && cacheStream === stream ? cache : cache = clipExtent(x0, y0, x1, y1)(cacheStream = stream);
},
extent: function(_) {
return arguments.length ? (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1], cache = cacheStream = null, clip) : [[x0, y0], [x1, y1]];
}
};
}
var sum = adder();
function polygonContains(polygon, point) {
var lambda = point[0],
phi = point[1],
normal = [sin(lambda), -cos(lambda), 0],
angle = 0,
winding = 0;
sum.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.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 < -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 length(object) {
lengthSum.reset();
geoStream(object, lengthStream);
return +lengthSum;
}
var coordinates = [null, null];
var object = {type: "LineString", coordinates: coordinates};
function distance(a, b) {
coordinates[0] = a;
coordinates[1] = b;
return length(object);
}
var containsObjectType = {
Feature: function(object, point) {
return containsGeometry(object.geometry, point);
},
FeatureCollection: function(object, point) {
var features = object.features, i = -1, n = features.length;
while (++i < n) if (containsGeometry(features[i].geometry, point)) return true;
return false;
}
};
var containsGeometryType = {
Sphere: function() {
return true;
},
Point: function(object, point) {
return containsPoint(object.coordinates, point);
},
MultiPoint: function(object, point) {
var coordinates = object.coordinates, i = -1, n = coordinates.length;
while (++i < n) if (containsPoint(coordinates[i], point)) return true;
return false;
},
LineString: function(object, point) {
return containsLine(object.coordinates, point);
},
MultiLineString: function(object, point) {
var coordinates = object.coordinates, i = -1, n = coordinates.length;
while (++i < n) if (containsLine(coordinates[i], point)) return true;
return false;
},
Polygon: function(object, point) {
return containsPolygon(object.coordinates, point);
},
MultiPolygon: function(object, point) {
var coordinates = object.coordinates, i = -1, n = coordinates.length;
while (++i < n) if (containsPolygon(coordinates[i], point)) return true;
return false;
},
GeometryCollection: function(object, point) {
var geometries = object.geometries, i = -1, n = geometries.length;
while (++i < n) if (containsGeometry(geometries[i], point)) return true;
return false;
}
};
function containsGeometry(geometry, point) {
return geometry && containsGeometryType.hasOwnProperty(geometry.type)
? containsGeometryType[geometry.type](geometry, point)
: false;
}
function containsPoint(coordinates, point) {
return distance(coordinates, point) === 0;
}
function containsLine(coordinates, point) {
var ab = distance(coordinates[0], coordinates[1]),
ao = distance(coordinates[0], point),
ob = distance(point, coordinates[1]);
return ao + ob <= ab + epsilon;
}
function containsPolygon(coordinates, point) {
return !!polygonContains(coordinates.map(ringRadians), pointRadians(point));
}
function ringRadians(ring) {
return ring = ring.map(pointRadians), ring.pop(), ring;
}
function pointRadians(point) {
return [point[0] * radians, point[1] * radians];
}
function contains(object, point) {
return (object && containsObjectType.hasOwnProperty(object.type)
? containsObjectType[object.type]
: containsGeometry)(object, point);
}
function graticuleX(y0, y1, dy) {
var y = d3Array.range(y0, y1 - epsilon, dy).concat(y1);
return function(x) { return y.map(function(y) { return [x, y]; }); };
}
function graticuleY(x0, x1, dx) {
var x = d3Array.range(x0, x1 - epsilon, dx).concat(x1);
return function(y) { return x.map(function(x) { return [x, y]; }); };
}
function graticule() {
var x1, x0, X1, X0,
y1, y0, Y1, Y0,
dx = 10, dy = dx, DX = 90, DY = 360,
x, y, X, Y,
precision = 2.5;
function graticule() {
return {type: "MultiLineString", coordinates: lines()};
}
function lines() {
return d3Array.range(ceil(X0 / DX) * DX, X1, DX).map(X)
.concat(d3Array.range(ceil(Y0 / DY) * DY, Y1, DY).map(Y))
.concat(d3Array.range(ceil(x0 / dx) * dx, x1, dx).filter(function(x) { return abs(x % DX) > epsilon; }).map(x))
.concat(d3Array.range(ceil(y0 / dy) * dy, y1, dy).filter(function(y) { return abs(y % DY) > epsilon; }).map(y));
}
graticule.lines = function() {
return lines().map(function(coordinates) { return {type: "LineString", coordinates: coordinates}; });
};
graticule.outline = function() {
return {
type: "Polygon",
coordinates: [
X(X0).concat(
Y(Y1).slice(1),
X(X1).reverse().slice(1),
Y(Y0).reverse().slice(1))
]
};
};
graticule.extent = function(_) {
if (!arguments.length) return graticule.extentMinor();
return graticule.extentMajor(_).extentMinor(_);
};
graticule.extentMajor = function(_) {
if (!arguments.length) return [[X0, Y0], [X1, Y1]];
X0 = +_[0][0], X1 = +_[1][0];
Y0 = +_[0][1], Y1 = +_[1][1];
if (X0 > X1) _ = X0, X0 = X1, X1 = _;
if (Y0 > Y1) _ = Y0, Y0 = Y1, Y1 = _;
return graticule.precision(precision);
};
graticule.extentMinor = function(_) {
if (!arguments.length) return [[x0, y0], [x1, y1]];
x0 = +_[0][0], x1 = +_[1][0];
y0 = +_[0][1], y1 = +_[1][1];
if (x0 > x1) _ = x0, x0 = x1, x1 = _;
if (y0 > y1) _ = y0, y0 = y1, y1 = _;
return graticule.precision(precision);
};
graticule.step = function(_) {
if (!arguments.length) return graticule.stepMinor();
return graticule.stepMajor(_).stepMinor(_);
};
graticule.stepMajor = function(_) {
if (!arguments.length) return [DX, DY];
DX = +_[0], DY = +_[1];
return graticule;
};
graticule.stepMinor = function(_) {
if (!arguments.length) return [dx, dy];
dx = +_[0], dy = +_[1];
return graticule;
};
graticule.precision = function(_) {
if (!arguments.length) return precision;
precision = +_;
x = graticuleX(y0, y1, 90);
y = graticuleY(x0, x1, precision);
X = graticuleX(Y0, Y1, 90);
Y = graticuleY(X0, X1, precision);
return graticule;
};
return graticule
.extentMajor([[-180, -90 + epsilon], [180, 90 - epsilon]])
.extentMinor([[-180, -80 - epsilon], [180, 80 + epsilon]]);
}
function graticule10() {
return graticule()();
}
function interpolate(a, b) {
var x0 = a[0] * radians,
y0 = a[1] * radians,
x1 = b[0] * radians,
y1 = b[1] * radians,
cy0 = cos(y0),
sy0 = sin(y0),
cy1 = cos(y1),
sy1 = sin(y1),
kx0 = cy0 * cos(x0),
ky0 = cy0 * sin(x0),
kx1 = cy1 * cos(x1),
ky1 = cy1 * sin(x1),
d = 2 * asin(sqrt(haversin(y1 - y0) + cy0 * cy1 * haversin(x1 - x0))),
k = sin(d);
var interpolate = d ? function(t) {
var B = sin(t *= d) / k,
A = sin(d - t) / k,
x = A * kx0 + B * kx1,
y = A * ky0 + B * ky1,
z = A * sy0 + B * sy1;
return [
atan2(y, x) * degrees,
atan2(z, sqrt(x * x + y * y)) * degrees
];
} : function() {
return [x0 * degrees, y0 * degrees];
};
interpolate.distance = d;
return interpolate;
}
function identity(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 = {
_radius: 4.5,
_circle: circle$1(4.5),
pointRadius: function(_) {
if ((_ = +_) !== this._radius) this._radius = _, this._circle = null;
return 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: {
if (this._circle == null) this._circle = circle$1(this._radius);
this._string.push("M", x, ",", y, this._circle);
break;
}
}
},
result: function() {
if (this._string.length) {
var result = this._string.join("");
this._string = [];
return result;
} else {
return null;
}
}
};
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 index(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) : (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, sort) {
if (typeof sort === "undefined") sort = compareIntersection;
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 = d3Array.merge(segments);
var startInside = polygonContains(polygon, rotatedStart);
if (segments.length) {
if (!polygonStarted) sink.polygonStart(), polygonStarted = true;
clipRejoin(segments, sort, 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, close) {
ring.push([lambda, phi]);
var point = rotate(lambda, phi);
ringSink.point(point[0], point[1], close);
}
function ringStart() {
ringSink.lineStart();
ring = [];
}
function ringEnd() {
pointRing(ring[0][0], ring[0][1], true);
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]);
}
/*
* a clip function
*
* this one doesn't do anything but complies with the preclip API
*
*/
function clipNone(rotate, stream) {
var _stream = {
point: function(x,y) {
var r = rotate(x,y);
return stream.point(r[0],r[1]);
},
lineStart: stream.lineStart,
lineEnd: stream.lineEnd,
polygonStart: stream.polygonStart,
polygonEnd: stream.polygonEnd,
sphere: sphere(stream)
};
return _stream;
}
function sphere(stream) {
return function() {
var phi = 1 * halfPi;
stream.lineStart();
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);
stream.lineEnd();
}
}
function clipAntimeridian() {
// 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 clipLine(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 interpolate(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 visible() {
return true;
}
return clip(visible, clipLine, interpolate, [-pi, -halfPi]);
}
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 (!point2 || 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
n2 = cartesianCross(pa, pb),
n2n2 = cartesianDot(n2, n2),
n1n2 = n2[0], // cartesianDot(n1, n2),
determinant = n2n2 - n1n2 * n1n2;
// Two polar points.
if (!determinant) return !two && a;
var c1 = cr * n2n2 / determinant,
c2 = -cr * n1n2 / determinant,
n1xn2 = cartesianCross(n1, n2),
A = cartesianScale(n1, c1),
B = cartesianScale(n2, c2);
cartesianAddInPlace(A, B);
// Solve |p(t)|^2 = 1.
var u = n1xn2,
w = cartesianDot(A, u),
uu = cartesianDot(u, u),
t2 = w * w - uu * (cartesianDot(A, A) - 1);
if (t2 < 0) return;
var t = sqrt(t2),
q = cartesianScale(u, (-w - t) / uu);
cartesianAddInPlace(q, A);
q = spherical(q);
if (!two) return q;
// Two intersection points.
var lambda0 = a[0],
lambda1 = b[0],
phi0 = a[1],
phi1 = b[1],
z;
if (lambda1 < lambda0) z = lambda0, lambda0 = lambda1, lambda1 = z;
var delta = lambda1 - lambda0,
polar = abs(delta - pi) < epsilon,
meridian = polar || delta < epsilon;
if (!polar && phi1 < phi0) z = phi0, phi0 = phi1, phi1 = z;
// Check that the first point is between a and b.
if (meridian
? polar
? phi0 + phi1 > 0 ^ q[1] < (abs(q[0] - lambda0) < epsilon ? phi0 : phi1)
: phi0 <= q[1] && q[1] <= phi1
: delta > pi ^ (lambda0 <= q[0] && q[0] <= lambda1)) {
var q1 = cartesianScale(u, (-w + t) / uu);
cartesianAddInPlace(q1, A);
return [q, spherical(q1)];
}
}
// Generates a 4-bit vector representing the location of a point relative to
// the small circle's bounding box.
function code(lambda, phi) {
var r = smallRadius ? radius : pi - radius,
code = 0;
if (lambda < -r) code |= 1; // left
else if (lambda > r) code |= 2; // right
if (phi < -r) code |= 4; // below
else if (phi > r) code |= 8; // above
return code;
}
return clip(visible, clipLine, interpolate, smallRadius ? [0, -radius] : [-pi, radius - pi]);
}
function intersectSegment(from, to) {
this.from = from, this.to = to;
this.normal = cartesianCross(from, to);
this.fromNormal = cartesianCross(this.normal, from);
this.toNormal = cartesianCross(this.normal, to);
}
// >> here a and b are segments processed by intersectSegment
function intersect(a, b) {
var axb = cartesianCross(a.normal, b.normal);
cartesianNormalizeInPlace(axb);
var a0 = cartesianDot(axb, a.fromNormal),
a1 = cartesianDot(axb, a.toNormal),
b0 = cartesianDot(axb, b.fromNormal),
b1 = cartesianDot(axb, b.toNormal);
if (a0 > -epsilon2 && a1 < epsilon2 && b0 > -epsilon2 && b1 < epsilon2) return axb;
if (a0 < epsilon2 && a1 > -epsilon2 && b0 < epsilon2 && b1 > -epsilon2) {
axb[0] = -axb[0], axb[1] = -axb[1], axb[2] = -axb[2];
return axb;
}
}
function intersectPointOnLine(p, a) {
var a0 = cartesianDot(p, a.fromNormal),
a1 = cartesianDot(p, a.toNormal);
p = cartesianDot(p, a.normal);
return abs(p) < epsilon2 && (a0 > -epsilon2 && a1 < epsilon2 || a0 < epsilon2 && a1 > -epsilon2);
}
var intersectCoincident = {};
// todo: publicly expose d3.geoIntersect(segment0, segment1) ??
// cf. https://github.com/d3/d3/commit/3dbdf87974dc2588c29db0533a8500ccddb25daa#diff-65daf69cea7d039d72c1eca7c13326b0
/*
import "distance";
*/
// clipPolygon
function clipPolygon (polygon) {
var segments = [];
polygon = polygon.map(function(ring) {
var c, c0;
ring = ring.map(function(point, i) {
c = cartesian(point = [point[0] * radians, point[1] * radians]);
if (i) segments.push(new intersectSegment(c0, c));
c0 = c;
return point;
});
ring.pop();
return ring;
});
function visible(lambda, phi) {
return polygonContains(polygon, [lambda, phi]);
}
function clipLine(stream) {
var point0,
lambda00,
phi00,
v00,
v0,
clean;
return {
lineStart: function() {
point0 = null;
clean = 1;
},
point: function(lambda, phi, close) {
if (close) lambda = lambda00, phi = phi00;
var point = cartesian([lambda, phi]),
v = v0,
intersection,
i, j, s, t;
if (point0) {
var segment = new intersectSegment(point0, point),
intersections = [];
for (i = 0, j = 100; i < segments.length && j > 0; ++i) {
s = segments[i];
intersection = intersect(segment, s);
if (intersection) {
if (intersection === intersectCoincident ||
cartesianEqual(intersection, point0) || cartesianEqual(intersection, point) ||
cartesianEqual(intersection, s.from) || cartesianEqual(intersection, s.to)) {
t = 1e-4;
lambda = (lambda + 3 * pi + (Math.random() < .5 ? t : -t)) % (2 * pi) - pi;
phi = Math.min(pi / 2 - 1e-4, Math.max(1e-4 - pi / 2, phi + (Math.random() < .5 ? t : -t)));
segment = new intersectSegment(point0, point = cartesian([lambda, phi]));
i = -1, --j;
intersections.length = 0;
continue;
}
var sph = spherical(intersection);
intersection.distance = clipPolygonDistance(point0, intersection);
intersection.index = i;
intersection.t = clipPolygonDistance(s.from, intersection);
intersection[0] = sph[0], intersection[1] = sph[1], intersection.pop();
intersections.push(intersection);
}
}
if (intersections.length) {
clean = 0;
intersections.sort(function(a, b) { return a.distance - b.distance; });
for (i = 0; i < intersections.length; ++i) {
intersection = intersections[i];
if (v = !v) {
stream.lineStart();
stream.point(intersection[0], intersection[1], intersection.index, intersection.t);
} else {
stream.point(intersection[0], intersection[1], intersection.index, intersection.t);
stream.lineEnd();
}
}
}
if (v) stream.point(lambda, phi);
} else {
for (i = 0, j = 100; i < segments.length && j > 0; ++i) {
s = segments[i];
if (intersectPointOnLine(point, s)) {
t = 1e-4;
lambda = (lambda + 3 * pi + (Math.random() < .5 ? t : -t)) % (2 * pi) - pi;
phi = Math.min(pi / 2 - 1e-4, Math.max(1e-4 - pi / 2, phi + (Math.random() < .5 ? t : -t)));
point = cartesian([lambda, phi]);
i = -1, --j;
}
}
if (v00 = v = visible(lambda00 = lambda, phi00 = phi)) stream.lineStart(), stream.point(lambda, phi);
}
point0 = point, v0 = v;
},
lineEnd: function() {
if (v0) stream.lineEnd();
},
// Rejoin first and last segments if there were intersections and the first
// and last points were visible.
clean: function() {
return clean | ((v00 && v0) << 1);
}
};
}
function interpolate(from, to, direction, stream) {
if (from == null) {
var n = polygon.length;
polygon.forEach(function(ring, i) {
ring.forEach(function(point) { stream.point(point[0], point[1]); });
if (i < n - 1) stream.lineEnd(), stream.lineStart();
});
} else if (from.index !== to.index && from.index != null && to.index != null) {
for (var i = from.index; i !== to.index; i = (i + direction + segments.length) % segments.length) {
var segment = segments[i],
point = spherical(direction > 0 ? segment.to : segment.from);
stream.point(point[0], point[1]);
}
}
}
return clip(visible, clipLine, interpolate, polygon[0][0], clipPolygonSort);
}
function clipPolygonSort(a, b) {
a = a.x, b = b.x;
return a.index - b.index || a.t - b.t;
}
// Geodesic coordinates for two 3D points.
function clipPolygonDistance(a, b) {
var axb = cartesianCross(a, b);
return atan2(sqrt(cartesianDot(axb, axb)), cartesianDot(a, b));
}
function transform(methods) {
return {
stream: transformer(methods)
};
}
function transformer(methods) {
return function(stream) {
var s = new TransformStream;
for (var key in methods) s[key] = methods[key];
s.stream = stream;
return s;
};
}
function TransformStream() {}
TransformStream.prototype = {
constructor: TransformStream,
point: function(x, y) { this.stream.point(x, y); },
sphere: function() { this.stream.sphere(); },
lineStart: function() { this.stream.lineStart(); },
lineEnd: function() { this.stream.lineEnd(); },
polygonStart: function() { this.stream.polygonStart(); },
polygonEnd: function() { this.stream.polygonEnd(); }
};
function fitExtent(projection, extent, object) {
var w = extent[1][0] - extent[0][0],
h = extent[1][1] - extent[0][1],
clip = projection.clipExtent && projection.clipExtent();
projection
.scale(150)
.translate([0, 0]);
if (clip != null) projection.clipExtent(null);
geoStream(object, projection.stream(boundsStream$1));
var b = boundsStream$1.result(),
k = Math.min(w / (b[1][0] - b[0][0]), h / (b[1][1] - b[0][1])),
x = +extent[0][0] + (w - k * (b[1][0] + b[0][0])) / 2,
y = +extent[0][1] + (h - k * (b[1][1] + b[0][1])) / 2;
if (clip != null) projection.clipExtent(clip);
return projection
.scale(k * 150)
.translate([x, y]);
}
function fitSize(projection, size, object) {
return fitExtent(projection, [[0, 0], size], object);
}
var maxDepth = 16;
var cosMinDistance = cos(30 * radians);
// cos(minimum angular distance)
function resample(project, delta2) {
return +delta2 ? resample$1(project, delta2) : resampleNone(project);
}
function resampleNone(project) {
return transformer({
point: function(x, y) {
x = project(x, y);
this.stream.point(x[0], x[1]);
}
});
}
function resample$1(project, delta2) {
function resampleLineTo(x0, y0, lambda0, a0, b0, c0, x1, y1, lambda1, a1, b1, c1, depth, stream) {
var dx = x1 - x0,
dy = y1 - y0,
d2 = dx * dx + dy * dy;
if (d2 > 4 * delta2 && depth--) {
var a = a0 + a1,
b = b0 + b1,
c = c0 + c1,
m = sqrt(a * a + b * b + c * c),
phi2 = asin(c /= m),
lambda2 = abs(abs(c) - 1) < epsilon || abs(lambda0 - lambda1) < epsilon ? (lambda0 + lambda1) / 2 : atan2(b, a),
p = project(lambda2, phi2),
x2 = p[0],
y2 = p[1],
dx2 = x2 - x0,
dy2 = y2 - y0,
dz = dy * dx2 - dx * dy2;
if (dz * dz / d2 > delta2 // perpendicular projected distance
|| abs((dx * dx2 + dy * dy2) / d2 - 0.5) > 0.3 // midpoint close to an end
|| a0 * a1 + b0 * b1 + c0 * c1 < cosMinDistance) { // angular distance
resampleLineTo(x0, y0, lambda0, a0, b0, c0, x2, y2, lambda2, a /= m, b /= m, c, depth, stream);
stream.point(x2, y2);
resampleLineTo(x2, y2, lambda2, a, b, c, x1, y1, lambda1, a1, b1, c1, depth, stream);
}
}
}
return function(stream) {
var lambda00, x00, y00, a00, b00, c00, // first point
lambda0, x0, y0, a0, b0, c0; // previous point
var resampleStream = {
point: point,
lineStart: lineStart,
lineEnd: lineEnd,
polygonStart: function() { stream.polygonStart(); resampleStream.lineStart = ringStart; },
polygonEnd: function() { stream.polygonEnd(); resampleStream.lineStart = lineStart; }
};
function point(x, y) {
x = project(x, y);
stream.point(x[0], x[1]);
}
function lineStart() {
x0 = NaN;
resampleStream.point = linePoint;
stream.lineStart();
}
function linePoint(lambda, phi) {
var c = cartesian([lambda, phi]), p = project(lambda, phi);
resampleLineTo(x0, y0, lambda0, a0, b0, c0, x0 = p[0], y0 = p[1], lambda0 = lambda, a0 = c[0], b0 = c[1], c0 = c[2], maxDepth, stream);
stream.point(x0, y0);
}
function lineEnd() {
resampleStream.point = point;
stream.lineEnd();
}
function ringStart() {
lineStart();
resampleStream.point = ringPoint;
resampleStream.lineEnd = ringEnd;
}
function ringPoint(lambda, phi) {
linePoint(lambda00 = lambda, phi), x00 = x0, y00 = y0, a00 = a0, b00 = b0, c00 = c0;
resampleStream.point = linePoint;
}
function ringEnd() {
resampleLineTo(x0, y0, lambda0, a0, b0, c0, x00, y00, lambda00, a00, b00, c00, maxDepth, stream);
resampleStream.lineEnd = lineEnd;
lineEnd();
}
return resampleStream;
};
}
var transformRadians = transformer({
point: function(x, y) {
this.stream.point(x * radians, y * radians);
}
});
function projection(project) {
return projectionMutator(function() { return project; })();
}
function projectionMutator(projectAt) {
var project,
k = 150, // scale
x = 480, y = 250, // translate
dx, dy, lambda = 0, phi = 0, // center
deltaLambda = 0, deltaPhi = 0, deltaGamma = 0, rotate, projectRotate, // rotate
preclip = clipAntimeridian(), // default clip
theta = null, // clip angle
polygon = null, // clip polygon
x0 = null, y0, x1, y1, postclip = identity, // clip extent
delta2 = 0.5, projectResample = resample(projectTransform, delta2), // precision
cache,
cacheStream;
function projection(point) {
point = projectRotate(point[0] * radians, point[1] * radians);
return [point[0] * k + dx, dy - point[1] * k];
}
function invert(point) {
point = projectRotate.invert((point[0] - dx) / k, (dy - point[1]) / k);
return point && [point[0] * degrees, point[1] * degrees];
}
function projectTransform(x, y) {
return x = project(x, y), [x[0] * k + dx, dy - x[1] * k];
}
projection.stream = function(stream) {
return cache && cacheStream === stream ? cache : cache = transformRadians(preclip(rotate, projectResample(postclip(cacheStream = stream))));
};
projection.clipAngle = function(_) {
return arguments.length ? (preclip = +_ > 0 ? clipCircle(theta = _ * radians, 6 * radians) : (theta = null, clipNone), reset()) : theta * degrees;
};
projection.clipExtent = function(_) {
return arguments.length ? (postclip = _ == null ? (x0 = y0 = x1 = y1 = null, identity) : clipExtent(x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1]), reset()) : x0 == null ? null : [[x0, y0], [x1, y1]];
};
projection.clipPolygon = function(_) {
return arguments.length ? (preclip = _.length ? clipPolygon(polygon = _) : (polygon = theta = null, clipAntimeridian()), reset()) : polygon;
};
projection.scale = function(_) {
return arguments.length ? (k = +_, recenter()) : k;
};
projection.translate = function(_) {
return arguments.length ? (x = +_[0], y = +_[1], recenter()) : [x, y];
};
projection.center = function(_) {
return arguments.length ? (lambda = _[0] % 360 * radians, phi = _[1] % 360 * radians, recenter()) : [lambda * degrees, phi * degrees];
};
projection.rotate = function(_) {
return arguments.length ? (deltaLambda = _[0] % 360 * radians, deltaPhi = _[1] % 360 * radians, deltaGamma = _.length > 2 ? _[2] % 360 * radians : 0, recenter()) : [deltaLambda * degrees, deltaPhi * degrees, deltaGamma * degrees];
};
projection.precision = function(_) {
return arguments.length ? (projectResample = resample(projectTransform, delta2 = _ * _), reset()) : sqrt(delta2);
};
projection.fitExtent = function(extent, object) {
return fitExtent(projection, extent, object);
};
projection.fitSize = function(size, object) {
return fitSize(projection, size, object);
};
function recenter() {
projectRotate = compose(rotate = rotateRadians(deltaLambda, deltaPhi, deltaGamma), project);
var center = project(lambda, phi);
dx = x - center[0] * k;
dy = y + center[1] * k;
return reset();
}
function reset() {
cache = cacheStream = null;
return projection;
}
return function() {
project = projectAt.apply(this, arguments);
projection.invert = project.invert && invert;
return recenter();
};
}
function conicProjection(projectAt) {
var phi0 = 0,
phi1 = pi / 3,
m = projectionMutator(projectAt),
p = m(phi0, phi1);
p.parallels = function(_) {
return arguments.length ? m(phi0 = _[0] * radians, phi1 = _[1] * radians) : [phi0 * degrees, phi1 * degrees];
};
return p;
}
function cylindricalEqualAreaRaw(phi0) {
var cosPhi0 = cos(phi0);
function forward(lambda, phi) {
return [lambda * cosPhi0, sin(phi) / cosPhi0];
}
forward.invert = function(x, y) {
return [x / cosPhi0, asin(y * cosPhi0)];
};
return forward;
}
function conicEqualAreaRaw(y0, y1) {
var sy0 = sin(y0), n = (sy0 + sin(y1)) / 2;
// Are the parallels symmetrical around the Equator?
if (abs(n) < epsilon) return cylindricalEqualAreaRaw(y0);
var c = 1 + sy0 * (2 * n - sy0), r0 = sqrt(c) / n;
function project(x, y) {
var r = sqrt(c - 2 * n * sin(y)) / n;
return [r * sin(x *= n), r0 - r * cos(x)];
}
project.invert = function(x, y) {
var r0y = r0 - y;
return [atan2(x, abs(r0y)) / n * sign(r0y), asin((c - (x * x + r0y * r0y) * n * n) / (2 * n))];
};
return project;
}
function conicEqualArea() {
return conicProjection(conicEqualAreaRaw)
.scale(155.424)
.center([0, 33.6442]);
}
function albers() {
return conicEqualArea()
.parallels([29.5, 45.5])
.scale(1070)
.translate([480, 250])
.rotate([96, 0])
.center([-0.6, 38.7]);
}
// The projections must have mutually exclusive clip regions on the sphere,
// as this will avoid emitting interleaving lines and polygons.
function multiplex(streams) {
var n = streams.length;
return {
point: function(x, y) { var i = -1; while (++i < n) streams[i].point(x, y); },
sphere: function() { var i = -1; while (++i < n) streams[i].sphere(); },
lineStart: function() { var i = -1; while (++i < n) streams[i].lineStart(); },
lineEnd: function() { var i = -1; while (++i < n) streams[i].lineEnd(); },
polygonStart: function() { var i = -1; while (++i < n) streams[i].polygonStart(); },
polygonEnd: function() { var i = -1; while (++i < n) streams[i].polygonEnd(); }
};
}
// A composite projection for the United States, configured by default for
// 960×500. The projection also works quite well at 960×600 if you change the
// scale to 1285 and adjust the translate accordingly. The set of standard
// parallels for each region comes from USGS, which is published here:
// http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html#albers
function albersUsa() {
var cache,
cacheStream,
lower48 = albers(), lower48Point,
alaska = conicEqualArea().rotate([154, 0]).center([-2, 58.5]).parallels([55, 65]), alaskaPoint, // EPSG:3338
hawaii = conicEqualArea().rotate([157, 0]).center([-3, 19.9]).parallels([8, 18]), hawaiiPoint, // ESRI:102007
point, pointStream = {point: function(x, y) { point = [x, y]; }};
function albersUsa(coordinates) {
var x = coordinates[0], y = coordinates[1];
return point = null,
(lower48Point.point(x, y), point)
|| (alaskaPoint.point(x, y), point)
|| (hawaiiPoint.point(x, y), point);
}
albersUsa.invert = function(coordinates) {
var k = lower48.scale(),
t = lower48.translate(),
x = (coordinates[0] - t[0]) / k,
y = (coordinates[1] - t[1]) / k;
return (y >= 0.120 && y < 0.234 && x >= -0.425 && x < -0.214 ? alaska
: y >= 0.166 && y < 0.234 && x >= -0.214 && x < -0.115 ? hawaii
: lower48).invert(coordinates);
};
albersUsa.stream = function(stream) {
return cache && cacheStream === stream ? cache : cache = multiplex([lower48.stream(cacheStream = stream), alaska.stream(stream), hawaii.stream(stream)]);
};
albersUsa.precision = function(_) {
if (!arguments.length) return lower48.precision();
lower48.precision(_), alaska.precision(_), hawaii.precision(_);
return reset();
};
albersUsa.scale = function(_) {
if (!arguments.length) return lower48.scale();
lower48.scale(_), alaska.scale(_ * 0.35), hawaii.scale(_);
return albersUsa.translate(lower48.translate());
};
albersUsa.translate = function(_) {
if (!arguments.length) return lower48.translate();
var k = lower48.scale(), x = +_[0], y = +_[1];
lower48Point = lower48
.translate(_)
.clipExtent([[x - 0.455 * k, y - 0.238 * k], [x + 0.455 * k, y + 0.238 * k]])
.stream(pointStream);
alaskaPoint = alaska
.translate([x - 0.307 * k, y + 0.201 * k])
.clipExtent([[x - 0.425 * k + epsilon, y + 0.120 * k + epsilon], [x - 0.214 * k - epsilon, y + 0.234 * k - epsilon]])
.stream(pointStream);
hawaiiPoint = hawaii
.translate([x - 0.205 * k, y + 0.212 * k])
.clipExtent([[x - 0.214 * k + epsilon, y + 0.166 * k + epsilon], [x - 0.115 * k - epsilon, y + 0.234 * k - epsilon]])
.stream(pointStream);
return reset();
};
albersUsa.fitExtent = function(extent, object) {
return fitExtent(albersUsa, extent, object);
};
albersUsa.fitSize = function(size, object) {
return fitSize(albersUsa, size, object);
};
function reset() {
cache = cacheStream = null;
return albersUsa;
}
return albersUsa.scale(1070);
}
function azimuthalRaw(scale) {
return function(x, y) {
var cx = cos(x),
cy = cos(y),
k = scale(cx * cy);
return [
k * cy * sin(x),
k * sin(y)
];
}
}
function azimuthalInvert(angle) {
return function(x, y) {
var z = sqrt(x * x + y * y),
c = angle(z),
sc = sin(c),
cc = cos(c);
return [
atan2(x * sc, z * cc),
asin(z && y * sc / z)
];
}
}
var azimuthalEqualAreaRaw = azimuthalRaw(function(cxcy) {
return sqrt(2 / (1 + cxcy));
});
azimuthalEqualAreaRaw.invert = azimuthalInvert(function(z) {
return 2 * asin(z / 2);
});
function azimuthalEqualArea() {
return projection(azimuthalEqualAreaRaw)
.scale(124.75)
.clipAngle(180 - 1e-3);
}
var azimuthalEquidistantRaw = azimuthalRaw(function(c) {
return (c = acos(c)) && c / sin(c);
});
azimuthalEquidistantRaw.invert = azimuthalInvert(function(z) {
return z;
});
function azimuthalEquidistant() {
return projection(azimuthalEquidistantRaw)
.scale(79.4188)
.clipAngle(180 - 1e-3);
}
function mercatorRaw(lambda, phi) {
return [lambda, log(tan((halfPi + phi) / 2))];
}
mercatorRaw.invert = function(x, y) {
return [x, 2 * atan(exp(y)) - halfPi];
};
function mercator() {
return mercatorProjection(mercatorRaw)
.scale(961 / tau);
}
function mercatorProjection(project) {
var m = projection(project),
center = m.center,
scale = m.scale,
translate = m.translate,
clipExtent = m.clipExtent,
x0 = null, y0, x1, y1; // clip extent
m.scale = function(_) {
return arguments.length ? (scale(_), reclip()) : scale();
};
m.translate = function(_) {
return arguments.length ? (translate(_), reclip()) : translate();
};
m.center = function(_) {
return arguments.length ? (center(_), reclip()) : center();
};
m.clipExtent = function(_) {
return arguments.length ? ((_ == null ? x0 = y0 = x1 = y1 = null : (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1])), reclip()) : x0 == null ? null : [[x0, y0], [x1, y1]];
};
function reclip() {
var k = pi * scale(),
t = m(rotation(m.rotate()).invert([0, 0]));
return clipExtent(x0 == null
? [[t[0] - k, t[1] - k], [t[0] + k, t[1] + k]] : project === mercatorRaw
? [[Math.max(t[0] - k, x0), y0], [Math.min(t[0] + k, x1), y1]]
: [[x0, Math.max(t[1] - k, y0)], [x1, Math.min(t[1] + k, y1)]]);
}
return reclip();
}
function tany(y) {
return tan((halfPi + y) / 2);
}
function conicConformalRaw(y0, y1) {
var cy0 = cos(y0),
n = y0 === y1 ? sin(y0) : log(cy0 / cos(y1)) / log(tany(y1) / tany(y0)),
f = cy0 * pow(tany(y0), n) / n;
if (!n) return mercatorRaw;
function project(x, y) {
if (f > 0) { if (y < -halfPi + epsilon) y = -halfPi + epsilon; }
else { if (y > halfPi - epsilon) y = halfPi - epsilon; }
var r = f / pow(tany(y), n);
return [r * sin(n * x), f - r * cos(n * x)];
}
project.invert = function(x, y) {
var fy = f - y, r = sign(n) * sqrt(x * x + fy * fy);
return [atan2(x, abs(fy)) / n * sign(fy), 2 * atan(pow(f / r, 1 / n)) - halfPi];
};
return project;
}
function conicConformal() {
return conicProjection(conicConformalRaw)
.scale(109.5)
.parallels([30, 30]);
}
function equirectangularRaw(lambda, phi) {
return [lambda, phi];
}
equirectangularRaw.invert = equirectangularRaw;
function equirectangular() {
return projection(equirectangularRaw)
.scale(152.63);
}
function conicEquidistantRaw(y0, y1) {
var cy0 = cos(y0),
n = y0 === y1 ? sin(y0) : (cy0 - cos(y1)) / (y1 - y0),
g = cy0 / n + y0;
if (abs(n) < epsilon) return equirectangularRaw;
function project(x, y) {
var gy = g - y, nx = n * x;
return [gy * sin(nx), g - gy * cos(nx)];
}
project.invert = function(x, y) {
var gy = g - y;
return [atan2(x, abs(gy)) / n * sign(gy), g - sign(n) * sqrt(x * x + gy * gy)];
};
return project;
}
function conicEquidistant() {
return conicProjection(conicEquidistantRaw)
.scale(131.154)
.center([0, 13.9389]);
}
function gnomonicRaw(x, y) {
var cy = cos(y), k = cos(x) * cy;
return [cy * sin(x) / k, sin(y) / k];
}
gnomonicRaw.invert = azimuthalInvert(atan);
function gnomonic() {
return projection(gnomonicRaw)
.scale(144.049)
.clipAngle(60);
}
function scaleTranslate(kx, ky, tx, ty) {
return kx === 1 && ky === 1 && tx === 0 && ty === 0 ? identity : transformer({
point: function(x, y) {
this.stream.point(x * kx + tx, y * ky + ty);
}
});
}
function identity$1() {
var k = 1, tx = 0, ty = 0, sx = 1, sy = 1, transform = identity, // scale, translate and reflect
x0 = null, y0, x1, y1, clip = identity, // clip extent
cache,
cacheStream,
projection;
function reset() {
cache = cacheStream = null;
return projection;
}
return projection = {
stream: function(stream) {
return cache && cacheStream === stream ? cache : cache = transform(clip(cacheStream = stream));
},
clipExtent: function(_) {
return arguments.length ? (clip = _ == null ? (x0 = y0 = x1 = y1 = null, identity) : clipExtent(x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1]), reset()) : x0 == null ? null : [[x0, y0], [x1, y1]];
},
scale: function(_) {
return arguments.length ? (transform = scaleTranslate((k = +_) * sx, k * sy, tx, ty), reset()) : k;
},
translate: function(_) {
return arguments.length ? (transform = scaleTranslate(k * sx, k * sy, tx = +_[0], ty = +_[1]), reset()) : [tx, ty];
},
reflectX: function(_) {
return arguments.length ? (transform = scaleTranslate(k * (sx = _ ? -1 : 1), k * sy, tx, ty), reset()) : sx < 0;
},
reflectY: function(_) {
return arguments.length ? (transform = scaleTranslate(k * sx, k * (sy = _ ? -1 : 1), tx, ty), reset()) : sy < 0;
},
fitExtent: function(extent, object) {
return fitExtent(projection, extent, object);
},
fitSize: function(size, object) {
return fitSize(projection, size, object);
}
};
}
function orthographicRaw(x, y) {
return [cos(y) * sin(x), sin(y)];
}
orthographicRaw.invert = azimuthalInvert(asin);
function orthographic() {
return projection(orthographicRaw)
.scale(249.5)
.clipAngle(90 + epsilon);
}
function stereographicRaw(x, y) {
var cy = cos(y), k = 1 + cos(x) * cy;
return [cy * sin(x) / k, sin(y) / k];
}
stereographicRaw.invert = azimuthalInvert(function(z) {
return 2 * atan(z);
});
function stereographic() {
return projection(stereographicRaw)
.scale(250)
.clipAngle(142);
}
function transverseMercatorRaw(lambda, phi) {
return [log(tan((halfPi + phi) / 2)), -lambda];
}
transverseMercatorRaw.invert = function(x, y) {
return [-y, 2 * atan(exp(x)) - halfPi];
};
function transverseMercator() {
var m = mercatorProjection(transverseMercatorRaw),
center = m.center,
rotate = m.rotate;
m.center = function(_) {
return arguments.length ? center([-_[1], _[0]]) : (_ = center(), [_[1], -_[0]]);
};
m.rotate = function(_) {
return arguments.length ? rotate([_[0], _[1], _.length > 2 ? _[2] + 90 : 90]) : (_ = rotate(), [_[0], _[1], _[2] - 90]);
};
return rotate([0, 0, 90])
.scale(159.155);
}
exports.geoArea = area;
exports.geoBounds = bounds;
exports.geoCentroid = centroid;
exports.geoCircle = circle;
exports.geoClipExtent = extent;
exports.geoContains = contains;
exports.geoDistance = distance;
exports.geoGraticule = graticule;
exports.geoGraticule10 = graticule10;
exports.geoInterpolate = interpolate;
exports.geoLength = length;
exports.geoPath = index;
exports.geoAlbers = albers;
exports.geoAlbersUsa = albersUsa;
exports.geoAzimuthalEqualArea = azimuthalEqualArea;
exports.geoAzimuthalEqualAreaRaw = azimuthalEqualAreaRaw;
exports.geoAzimuthalEquidistant = azimuthalEquidistant;
exports.geoAzimuthalEquidistantRaw = azimuthalEquidistantRaw;
exports.geoConicConformal = conicConformal;
exports.geoConicConformalRaw = conicConformalRaw;
exports.geoConicEqualArea = conicEqualArea;
exports.geoConicEqualAreaRaw = conicEqualAreaRaw;
exports.geoConicEquidistant = conicEquidistant;
exports.geoConicEquidistantRaw = conicEquidistantRaw;
exports.geoEquirectangular = equirectangular;
exports.geoEquirectangularRaw = equirectangularRaw;
exports.geoGnomonic = gnomonic;
exports.geoGnomonicRaw = gnomonicRaw;
exports.geoIdentity = identity$1;
exports.geoProjection = projection;
exports.geoProjectionMutator = projectionMutator;
exports.geoMercator = mercator;
exports.geoMercatorRaw = mercatorRaw;
exports.geoOrthographic = orthographic;
exports.geoOrthographicRaw = orthographicRaw;
exports.geoStereographic = stereographic;
exports.geoStereographicRaw = stereographicRaw;
exports.geoTransverseMercator = transverseMercator;
exports.geoTransverseMercatorRaw = transverseMercatorRaw;
exports.geoRotation = rotation;
exports.geoStream = geoStream;
exports.geoTransform = transform;
Object.defineProperty(exports, '__esModule', { value: true });
}));
Raw
index.html
<!DOCTYPE html>
<head>
<meta charset="utf-8">
<link rel="stylesheet" type="text/css" href="map.css">
<title>Earth in an Icosahedron</title>
</head>
<body>
<div id="map"></div>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://d3js.org/topojson.v2.min.js"></script>
<script src="d3-geo.js"></script>
<script src="d3-geo-projection.js"></script>
<script src="versor.js"></script>
<script src="map.js"></script>
Raw
map.css
body {
background: #fff;
}
#top {
width: 960px;
height: 100px;
margin: 0 auto;
position: relative;
}
#heading {
position: absolute;
top: 30px;
left: 350px;
width: 420px;
}
#heading h1 {
font-size: 3.5em;
margin: 0;
}
/*#mapinacube {
margin: -120px 0 -100px -200px;
float: left;
}
*/
h2 {
clear: left;
}
.author a, .meta a {
color: #000;
}
.author, .meta {
color: #666;
font-style: italic;
font-size: small;
}
.globe {
cursor: move;
}
.background {
stroke: none;
fill: #ccf;
}
.outline {
stroke: #000;
stroke-width: 1px;
fill: none;
}
.graticule {
stroke: #000;
stroke-width: .25px;
stroke-opacity: .5;
fill: none;
}
.land {
stroke: #000;
stroke-width: .5px;
fill: #9f9;
}
.boundary {
stroke: #000;
stroke-width: .5px;
stroke-opacity: .7;
fill: none;
}
.face {
stroke: #000;
stroke-width: .5px;
stroke-dasharray: 8,3;
fill: none;
}
.vertex {
fill: #000;
}
Raw
map.js
// imports
var atan = Math.atan,
abs = Math.abs,
ε = 1e-6,
π = Math.PI,
degrees = 180 / π,
θ = atan(0.5) * degrees;
// manually rotate/guessed from JvW article
var r = [-85.76422660821149, -47.20427493656335, -83.97741129030045];
var d3Geo = d3,
polyhedral = d3.geoPolyhedral;
var width = 900,
height = 400,
margin = 5,
rotate = [0, 0, 0];
// construction inspired by
// https://en.wikipedia.org/wiki/Regular_icosahedron#Spherical_coordinates
var vertices = [
[0, 90],
[0, -90]
].concat(d3.range(10).map(function(i) {
// var φ = i * 36;
var φ = ((i * 36) + 180) % 360 - 180;
return [φ, i & 1 ? θ : -θ];
}));
var polyhedron = [
[ 0, 3, 11],
[ 0, 5, 3],
[ 0, 7, 5],
[ 0, 9, 7],
[ 0, 11, 9], // North
[ 2, 11, 3],
[ 3, 4, 2],
[ 4, 3, 5],
[ 5, 6, 4],
[ 6, 5, 7],
[ 7, 8, 6],
[ 8, 7, 9],
[ 9, 10, 8],
[10, 9, 11],
[11, 2, 10], // Equator
[ 1, 2, 4],
[ 1, 4, 6],
[ 1, 6, 8],
[ 1, 8, 10],
[ 1, 10, 2] // South
].map(function(face) {
return face.map(function(i) {
return vertices[i];
});
});
// add centroid
polyhedron.forEach(function(face) {
face.centroid = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face});
});
var jvw_icosahedron = function(faceProjection) {
faceProjection = faceProjection || function(face) {
var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face});
if (abs(abs(c[1]) - 90) < ε) c[0] = 0;
return d3Geo.geoGnomonic().scale(1).translate([0, 0]).rotate([-c[0], -c[1]]);
};
var faces = polyhedron.map(function(face) {
var polygon = face.slice();
polygon.push(polygon[0]);
return {
face: face,
contains: function(lambda, phi) {
return d3Geo.geoContains({ type: "Polygon", coordinates: [ polygon ] },
[lambda * degrees, phi * degrees]);
},
project: faceProjection(face)
};
});
// Connect each face to a parent face.
[
// N
-1, // 0
0, // 1
9, // 2
2, // 3
0, // 4
// Eq
0, // 5
5, // 6
6, // 7
7, // 8
8, // 9
9, // 10
10, // 11
11, // 12
4, // 13
5, // 14
// S
6, // 15
8, // 16
18, // 17
19, // 18
14, // 19
].forEach(function (d, i) {
var node = faces[d];
node && (node.children || (node.children = [])).push(faces[i]);
});
function face(λ, φ) {
for (var i = 0; i < faces.length; i++) {
if (faces[i].contains(λ, φ)) return faces[i];
}
}
// Polyhedral projection
var proj = polyhedral(
faces[0], // the root face
face, // a function that return a face give coords
0 // rotation of the root face in the projected (pixel) space
)
.rotate(rotate)
.clipAngle(-1) // as suggested by Fil
.fitExtent(
[
[margin, margin],
[width - margin, height - margin]
],
{type:"Sphere"}
);
proj.faces = faces;
return proj;
}
d3.geoPolyhedralJakvanWijIcosahedron = jvw_icosahedron;
// map in an icosahedron.
var projection = d3.geoPolyhedralJakvanWijIcosahedron();
var path = d3.geoPath().projection(projection);
var graticule = d3.geoGraticule();
var svg = d3.select("#map").append("svg")
.attr("width", width)
.attr("height", height);
svg.append("path")
.datum({type: "Sphere"})
.attr("class", "background")
.attr("d", path);
svg.append("path")
.datum(graticule)
.attr("class", "graticule")
.attr("d", path);
svg.append("path")
.datum({type: "Sphere"})
.attr("class", "outline")
.attr("d", path);
d3.json("world-110m.json", function(error, world) {
var land = topojson.feature(world, world.objects.land);
svg
.insert("path", ".graticule")
.datum(land)
.attr("class", "land")
.attr("d", path);
});
var render = function() {
svg.selectAll('path').attr('d', path);
};
projection.rotate(r) && render()
d3.select(self.frameElement).style("height", height + "px");
Display the source blob
Display the rendered blob
Raw
world-110m.json
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