xyvs/wakapi-readme-stats
1
0
Fork 0
Code Issues 2 Pull Requests 1 Actions Packages Projects Releases 1 Wiki Activity
Files
194b41124de40276afe3939c23d9cc508760b5a7
wakapi-readme-stats/node_modules/d3-geo-projection/dist/d3-geo-projection.js
prabhatdev 194b41124d Bar graph added.
2020-07-28 00:48:25 +05:30

5008 lines
138 KiB
JavaScript
Raw Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
// https://d3js.org/d3-geo-projection/ v2.9.0 Copyright 2020 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 = sinz_2 / cosz_2,
lnsecz_2 = -log(abs(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)) * (cosz_2 < 0 ? 0.7 : 1);
} while (abs(delta) > epsilon && --i > 0);
var sinz = sin(z);
return [atan2(x * sinz, r * cos(z)), asin(y * sinz / r)];
};
return forward;
}
function airy() {
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];
};
function aitoff() {
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;
if (abs(dPhi) > 2) dPhi /= 2;
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;
}
function armadillo() {
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)),
precision = p.precision();
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);
if (phi0) while (sPhi0 * (lambda -= 3 * sPhi0 * precision) >= -180) {
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)
];
};
function august() {
return d3Geo.geoProjection(augustRaw)
.scale(66.1603);
}
var sqrt8 = sqrt(8),
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];
};
function baker() {
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;
}
function berghaus() {
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 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
];
};
function hammer() {
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);
}
// Approximate Newton-Raphson
// Solve f(x) = y, start from x
function solve(f, y, x) {
var steps = 100, delta, f0, f1;
x = x === undefined ? 0 : +x;
y = +y;
do {
f0 = f(x);
f1 = f(x + epsilon);
if (f0 === f1) f1 = f0 + epsilon;
x -= delta = (-1 * epsilon * (f0 - y)) / (f0 - f1);
} while (steps-- > 0 && abs(delta) > epsilon);
return steps < 0 ? NaN : x;
}
// Approximate Newton-Raphson in 2D
// Solve f(a,b) = [x,y]
function solve2d(f, MAX_ITERATIONS, eps) {
if (MAX_ITERATIONS === undefined) MAX_ITERATIONS = 40;
if (eps === undefined) eps = epsilon2;
return function(x, y, a, b) {
var err2, da, db;
a = a === undefined ? 0 : +a;
b = b === undefined ? 0 : +b;
for (var i = 0; i < MAX_ITERATIONS; i++) {
var p = f(a, b),
// diffs
tx = p[0] - x,
ty = p[1] - y;
if (abs(tx) < eps && abs(ty) < eps) break; // we're there!
// backtrack if we overshot
var h = tx * tx + ty * ty;
if (h > err2) {
a -= da /= 2;
b -= db /= 2;
continue;
}
err2 = h;
// partial derivatives
var ea = (a > 0 ? -1 : 1) * eps,
eb = (b > 0 ? -1 : 1) * eps,
pa = f(a + ea, b),
pb = f(a, b + eb),
dxa = (pa[0] - p[0]) / ea,
dya = (pa[1] - p[1]) / ea,
dxb = (pb[0] - p[0]) / eb,
dyb = (pb[1] - p[1]) / eb,
// determinant
D = dyb * dxa - dya * dxb,
// newton step — or half-step for small D
l = (abs(D) < 0.5 ? 0.5 : 1) / D;
da = (ty * dxb - tx * dyb) * l;
db = (tx * dya - ty * dxa) * l;
a += da;
b += db;
if (abs(da) < eps && abs(db) < eps) break; // we're crawling
}
return [a, b];
};
}
// Bertin 1953 as a modified Briesemeister
// https://bl.ocks.org/Fil/5b9ee9636dfb6ffa53443c9006beb642
function bertin1953Raw() {
var hammer$$1 = hammerRaw(1.68, 2),
fu = 1.4, k = 12;
function forward(lambda, phi) {
if (lambda + phi < -fu) {
var u = (lambda - phi + 1.6) * (lambda + phi + fu) / 8;
lambda += u;
phi -= 0.8 * u * sin(phi + pi / 2);
}
var r = hammer$$1(lambda, phi);
var d = (1 - cos(lambda * phi)) / k;
if (r[1] < 0) {
r[0] *= 1 + d;
}
if (r[1] > 0) {
r[1] *= 1 + d / 1.5 * r[0] * r[0];
}
return r;
}
forward.invert = solve2d(forward);
return forward;
}
function bertin() {
// this projection should not be rotated
return d3Geo.geoProjection(bertin1953Raw())
.rotate([-16.5, -42])
.scale(176.57)
.center([7.93, 0.09]);
}
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);
function mollweide() {
return d3Geo.geoProjection(mollweideRaw)
.scale(169.529);
}
var k = 2.00276,
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];
};
function boggs() {
return d3Geo.geoProjection(boggsRaw)
.scale(160.857);
}
function parallel1(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];
};
function sinusoidal() {
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;
}
function bonne() {
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;
}
function bottomley() {
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);
function bromley() {
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),
f = chamberlinRaw(pointRadians(r(p0)), pointRadians(r(p1)), pointRadians(r(p2)));
f.invert = solve2d(f);
var p = d3Geo.geoProjection(f).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)];
};
function collignon() {
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;
}
function craig() {
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];
};
function craster() {
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;
}
function cylindricalEqualArea() {
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;
}
function cylindricalStereographic() {
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
];
};
function eckert1() {
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)
];
};
function eckert2() {
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
];
};
function eckert3() {
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))
];
};
function eckert4() {
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
];
};
function eckert5() {
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)
];
};
function eckert6() {
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];
};
function eisenlohr() {
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)];
};
function fahey() {
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];
};
function foucaut() {
return d3Geo.geoProjection(foucautRaw)
.scale(135.264);
}
function foucautSinusoidalRaw(alpha) {
var beta = 1 - alpha,
equatorial = raw(pi, 0)[0] - raw(-pi, 0)[0],
polar = raw(0, halfPi)[1] - raw(0, -halfPi)[1],
ratio = sqrt(2 * polar / equatorial);
function raw(lambda, phi) {
var cosphi = cos(phi),
sinphi = sin(phi);
return [
cosphi / (beta + alpha * cosphi) * lambda,
beta * phi + alpha * sinphi
];
}
function forward(lambda, phi) {
var p = raw(lambda, phi);
return [p[0] * ratio, p[1] / ratio];
}
function forwardMeridian(phi) {
return forward(0, phi)[1];
}
forward.invert = function(x, y) {
var phi = solve(forwardMeridian, y),
lambda = x / ratio * (alpha + beta / cos(phi));
return [lambda, phi];
};
return forward;
}
function foucautSinusoidal() {
var alpha = 0.5,
m = d3Geo.geoProjectionMutator(foucautSinusoidalRaw),
p = m(alpha);
p.alpha = function(_) {
return arguments.length ? m(alpha = +_) : alpha;
};
return p
.scale(168.725);
}
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];
}
function gilbert(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].apply(projection, arguments), 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("angle");
property("clipAngle");
property("clipExtent");
property("fitExtent");
property("fitHeight");
property("fitSize");
property("fitWidth");
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;
}
function gingery() {
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);
}
function ginzburgPolyconicRaw(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);
function ginzburg4() {
return d3Geo.geoProjection(ginzburg4Raw)
.scale(149.995);
}
var ginzburg5Raw = ginzburgPolyconicRaw(2.583819, -0.835827, 0.170354, -0.038094, 1.543313, -0.411435,0.082742);
function ginzburg5() {
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);
function ginzburg6() {
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];
};
function ginzburg8() {
return d3Geo.geoProjection(ginzburg8Raw)
.scale(131.747);
}
var ginzburg9Raw = ginzburgPolyconicRaw(2.6516, -0.76534, 0.19123, -0.047094, 1.36289, -0.13965,0.031762);
function ginzburg9() {
return d3Geo.geoProjection(ginzburg9Raw)
.scale(131.087);
}
function squareRaw(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];
}
function gringorten() {
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
];
};
function guyou() {
return d3Geo.geoProjection(squareRaw(guyouRaw))
.scale(151.496);
}
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)
];
};
}
function hammerRetroazimuthal() {
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 K = 3,
healpixParallel = asin(1 - 1 / K) * degrees,
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 sphereTop(x, i) {
return [x, i & 1 ? 90 - epsilon : healpixParallel];
}
function sphereBottom(x, i) {
return [x, i & 1 ? -90 + epsilon : -healpixParallel];
}
function sphereNudge(d) {
return [d[0] * (1 - epsilon), d[1]];
}
function sphere(step) {
var c = [].concat(
d3Array.range(-180, 180 + step / 2, step).map(sphereTop),
d3Array.range(180, -180 - step / 2, -step).map(sphereBottom)
);
return {
type: "Polygon",
coordinates: [step === 180 ? c.map(sphereNudge) : c]
};
}
function healpix() {
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;
}
function hill() {
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);
};
function sinuMollweide() {
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);
};
function homolosine() {
return d3Geo.geoProjection(homolosineRaw)
.scale(152.63);
}
function hufnagelRaw(a, b, psiMax, ratio) {
var k = sqrt(
(4 * pi) /
(2 * psiMax +
(1 + a - b / 2) * sin(2 * psiMax) +
((a + b) / 2) * sin(4 * psiMax) +
(b / 2) * sin(6 * psiMax))
),
c = sqrt(
ratio *
sin(psiMax) *
sqrt((1 + a * cos(2 * psiMax) + b * cos(4 * psiMax)) / (1 + a + b))
),
M = psiMax * mapping(1);
function radius(psi) {
return sqrt(1 + a * cos(2 * psi) + b * cos(4 * psi));
}
function mapping(t) {
var psi = t * psiMax;
return (
(2 * psi +
(1 + a - b / 2) * sin(2 * psi) +
((a + b) / 2) * sin(4 * psi) +
(b / 2) * sin(6 * psi)) /
psiMax
);
}
function inversemapping(psi) {
return radius(psi) * sin(psi);
}
var forward = function(lambda, phi) {
var psi = psiMax * solve(mapping, (M * sin(phi)) / psiMax, phi / pi);
if (isNaN(psi)) psi = psiMax * sign(phi);
var kr = k * radius(psi);
return [((kr * c * lambda) / pi) * cos(psi), (kr / c) * sin(psi)];
};
forward.invert = function(x, y) {
var psi = solve(inversemapping, (y * c) / k);
return [
(x * pi) / (cos(psi) * k * c * radius(psi)),
asin((psiMax * mapping(psi / psiMax)) / M)
];
};
if (psiMax === 0) {
k = sqrt(ratio / pi);
forward = function(lambda, phi) {
return [lambda * k, sin(phi) / k];
};
forward.invert = function(x, y) {
return [x / k, asin(y * k)];
};
}
return forward;
}
function hufnagel() {
var a = 1,
b = 0,
psiMax = 45 * radians,
ratio = 2,
mutate = d3Geo.geoProjectionMutator(hufnagelRaw),
projection = mutate(a, b, psiMax, ratio);
projection.a = function(_) {
return arguments.length ? mutate((a = +_), b, psiMax, ratio) : a;
};
projection.b = function(_) {
return arguments.length ? mutate(a, (b = +_), psiMax, ratio) : b;
};
projection.psiMax = function(_) {
return arguments.length
? mutate(a, b, (psiMax = +_ * radians), ratio)
: psiMax * degrees;
};
projection.ratio = function(_) {
return arguments.length ? mutate(a, b, psiMax, (ratio = +_)) : ratio;
};
return projection.scale(180.739);
}
// https://github.com/scijs/integrate-adaptive-simpson
// This algorithm adapted from pseudocode in:
// http://www.math.utk.edu/~ccollins/refs/Handouts/rich.pdf
function adsimp (f, a, b, fa, fm, fb, V0, tol, maxdepth, depth, state) {
if (state.nanEncountered) {
return NaN;
}
var h, f1, f2, sl, sr, s2, m, V1, V2, err;
h = b - a;
f1 = f(a + h * 0.25);
f2 = f(b - h * 0.25);
// Simple check for NaN:
if (isNaN(f1)) {
state.nanEncountered = true;
return;
}
// Simple check for NaN:
if (isNaN(f2)) {
state.nanEncountered = true;
return;
}
sl = h * (fa + 4 * f1 + fm) / 12;
sr = h * (fm + 4 * f2 + fb) / 12;
s2 = sl + sr;
err = (s2 - V0) / 15;
if (depth > maxdepth) {
state.maxDepthCount++;
return s2 + err;
} else if (Math.abs(err) < tol) {
return s2 + err;
} else {
m = a + h * 0.5;
V1 = adsimp(f, a, m, fa, f1, fm, sl, tol * 0.5, maxdepth, depth + 1, state);
if (isNaN(V1)) {
state.nanEncountered = true;
return NaN;
}
V2 = adsimp(f, m, b, fm, f2, fb, sr, tol * 0.5, maxdepth, depth + 1, state);
if (isNaN(V2)) {
state.nanEncountered = true;
return NaN;
}
return V1 + V2;
}
}
function integrate (f, a, b, tol, maxdepth) {
var state = {
maxDepthCount: 0,
nanEncountered: false
};
if (tol === undefined) {
tol = 1e-8;
}
if (maxdepth === undefined) {
maxdepth = 20;
}
var fa = f(a);
var fm = f(0.5 * (a + b));
var fb = f(b);
var V0 = (fa + 4 * fm + fb) * (b - a) / 6;
var result = adsimp(f, a, b, fa, fm, fb, V0, tol, maxdepth, 1, state);
/*
if (state.maxDepthCount > 0 && console && console.warn) {
console.warn('integrate-adaptive-simpson: Warning: maximum recursion depth (' + maxdepth + ') reached ' + state.maxDepthCount + ' times');
}
if (state.nanEncountered && console && console.warn) {
console.warn('integrate-adaptive-simpson: Warning: NaN encountered. Halting early.');
}
*/
return result;
}
function hyperellipticalRaw(alpha, k, gamma) {
function elliptic (f) {
return alpha + (1 - alpha) * pow(1 - pow(f, k), 1 / k);
}
function z(f) {
return integrate(elliptic, 0, f, 1e-4);
}
var G = 1 / z(1),
n = 1000,
m = (1 + 1e-8) * G,
approx = [];
for (var i = 0; i <= n; i++)
approx.push(z(i / n) * m);
function Y(sinphi) {
var rmin = 0, rmax = n, r = n >> 1;
do {
if (approx[r] > sinphi) rmax = r; else rmin = r;
r = (rmin + rmax) >> 1;
} while (r > rmin);
var u = approx[r + 1] - approx[r];
if (u) u = (sinphi - approx[r + 1]) / u;
return (r + 1 + u) / n;
}
var ratio = 2 * Y(1) / pi * G / gamma;
var forward = function(lambda, phi) {
var y = Y(abs(sin(phi))),
x = elliptic(y) * lambda;
y /= ratio;
return [ x, (phi >= 0) ? y : -y ];
};
forward.invert = function(x, y) {
var phi;
y *= ratio;
if (abs(y) < 1) phi = sign(y) * asin(z(abs(y)) * G);
return [ x / elliptic(abs(y)), phi ];
};
return forward;
}
function hyperelliptical() {
var alpha = 0,
k = 2.5,
gamma = 1.183136, // affine = sqrt(2 * gamma / pi) = 0.8679
m = d3Geo.geoProjectionMutator(hyperellipticalRaw),
p = m(alpha, k, gamma);
p.alpha = function(_) {
return arguments.length ? m(alpha = +_, k, gamma) : alpha;
};
p.k = function(_) {
return arguments.length ? m(alpha, k = +_, gamma) : k;
};
p.gamma = function(_) {
return arguments.length ? m(alpha, k, gamma = +_) : gamma;
};
return p
.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)]
};
}
function interrupt(project, lobes, inverse) {
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;
}
if (inverse) {
forward.invert = inverse(forward);
} else 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]]
]];
function boggs$1() {
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]]
]];
function homolosine$1() {
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]]
]];
function mollweide$1() {
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]]
]];
function mollweideHemispheres() {
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]]
]];
function sinuMollweide$1() {
return interrupt(sinuMollweideRaw, lobes$4, solve2d)
.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]]
]];
function sinusoidal$1() {
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];
};
function kavrayskiy7() {
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;
}
function lagrange() {
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];
};
function larrivee() {
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];
};
function laskowski() {
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,
x2_y2_1 = x2 + y2_1,
cosPhi = x
? sqrt1_2 * sqrt((x2_y2_1 - sqrt(x2_y2_1 * x2_y2_1 - 4 * x2)) / x2)
: 1 / sqrt(y2_1);
return [
asin(x * cosPhi),
sign(y) * acos(cosPhi)
];
};
function littrow() {
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;
}
function loximuthal() {
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];
};
function miller() {
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]],
gs48 = [[0.98879, 0], [0, 0], [-0.050909, 0], [0, 0], [0.075528, 0]],
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]],
miller$1 = [[0.9245, 0], [0, 0], [0.01943, 0]],
lee = [[0.721316, 0], [0, 0], [-0.00881625, -0.00617325]];
function modifiedStereographicAlaska() {
return modifiedStereographic(alaska, [152, -64])
.scale(1400)
.center([-160.908, 62.4864])
.clipAngle(30)
.angle(7.8);
}
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),
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)
];
};
function mtFlatPolarParabolic() {
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))
];
};
function mtFlatPolarQuartic() {
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))
];
};
function mtFlatPolarSinusoidal() {
return d3Geo.geoProjection(mtFlatPolarSinusoidalRaw)
.scale(166.518);
}
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
];
};
function naturalEarth2() {
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
];
};
function nellHammer() {
return d3Geo.geoProjection(nellHammerRaw)
.scale(152.63);
}
var lobes$6 = [[ // 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]]
]];
function quarticAuthalic() {
return interrupt(hammerRaw(Infinity), lobes$6)
.rotate([20, 0])
.scale(152.63);
}
// Based on Torben Jansen's implementation
// https://beta.observablehq.com/@toja/nicolosi-globular-projection
// https://beta.observablehq.com/@toja/nicolosi-globular-inverse
function nicolosiRaw(lambda, phi) {
var sinPhi = sin(phi),
q = cos(phi),
s = sign(lambda);
if (lambda === 0 || abs(phi) === halfPi) return [0, phi];
else if (phi === 0) return [lambda, 0];
else if (abs(lambda) === halfPi) return [lambda * q, halfPi * sinPhi];
var b = pi / (2 * lambda) - (2 * lambda) / pi,
c = (2 * phi) / pi,
d = (1 - c * c) / (sinPhi - c);
var b2 = b * b,
d2 = d * d,
b2d2 = 1 + b2 / d2,
d2b2 = 1 + d2 / b2;
var M = ((b * sinPhi) / d - b / 2) / b2d2,
N = ((d2 * sinPhi) / b2 + d / 2) / d2b2,
m = M * M + (q * q) / b2d2,
n = N * N - ((d2 * sinPhi * sinPhi) / b2 + d * sinPhi - 1) / d2b2;
return [
halfPi * (M + sqrt(m) * s),
halfPi * (N + sqrt(n < 0 ? 0 : n) * sign(-phi * b) * s)
];
}
nicolosiRaw.invert = function(x, y) {
x /= halfPi;
y /= halfPi;
var x2 = x * x,
y2 = y * y,
x2y2 = x2 + y2,
pi2 = pi * pi;
return [
x ? (x2y2 -1 + sqrt((1 - x2y2) * (1 - x2y2) + 4 * x2)) / (2 * x) * halfPi : 0,
solve(function(phi) {
return (
x2y2 * (pi * sin(phi) - 2 * phi) * pi +
4 * phi * phi * (y - sin(phi)) +
2 * pi * phi -
pi2 * y
);
}, 0)
];
};
function nicolosi() {
return d3Geo.geoProjection(nicolosiRaw)
.scale(127.267);
}
// 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,
pattersonK2 = 0.23185,
pattersonK3 = -0.14499,
pattersonK4 = 0.02406,
pattersonC1 = pattersonK1,
pattersonC2 = 5 * pattersonK2,
pattersonC3 = 7 * pattersonK3,
pattersonC4 = 9 * pattersonK4,
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];
};
function patterson() {
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(y) * sign(x) * (acos(abs(x * tanPhi)) + halfPi)) / sin(phi),
phi
];
};
function polyconic() {
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].
function matrix(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 root face [deprecated by .angle()].
function polyhedral(root, face, r) {
recurse(root, {transform: null});
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;
proj.stream = function(stream) {
var rotate = proj.rotate(),
rotateStream = stream_(stream),
sphereStream = (proj.rotate([0, 0]), stream_(stream));
proj.rotate(rotate);
rotateStream.sphere = function() {
sphereStream.polygonStart();
sphereStream.lineStart();
outline(sphereStream, root);
sphereStream.lineEnd();
sphereStream.polygonEnd();
};
return rotateStream;
};
return proj.angle(r == null ? -30 : r * degrees);
}
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];
});
});
function butterfly(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];
})
.angle(-30)
.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);
};
function collignon$1(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];
})
.angle(-30)
.scale(121.906)
.center([0, 48.5904]);
}
function waterman(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)
.angle(-30)
.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)
];
}
function noop() {}
function clockwise(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;
}
function contains(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;
}
function index(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 = [],
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]};
}
};
function quincuncial(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);
}
function gringorten$1() {
return quincuncial(gringortenRaw)
.scale(176.423);
}
function peirce() {
return quincuncial(guyouRaw)
.scale(111.48);
}
function quantize(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 quantizePointsNoDuplicates(input) {
var point0 = quantizePoint(input[0]);
var output = [point0];
for (var i = 1; i < input.length; i++) {
var point = quantizePoint(input[i]);
if (point.length > 2 || point[0] != point0[0] || point[1] != point0[1]) {
output.push(point);
point0 = point;
}
}
if (output.length === 1 && input.length > 1) {
output.push(quantizePoint(input[input.length - 1]));
}
return output;
}
function quantizePolygon(input) {
return input.map(quantizePointsNoDuplicates);
}
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": output = {type: input.type, coordinates: quantizePoints(input.coordinates)}; break;
case "LineString": output = {type: input.type, coordinates: quantizePointsNoDuplicates(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;
}
function rectangularPolyconic() {
return parallel1(rectangularPolyconicRaw)
.scale(131.215);
}
var K$1 = [
[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$1.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$1[i0])[0],
ay = k[1],
bx = (k = K$1[++i0])[0],
by = k[1],
cx = (k = K$1[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$1[i0][1],
by = K$1[i0 + 1][1],
cy = K$1[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$1[i0][1];
by = K$1[i0 + 1][1];
cy = K$1[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$1[i0][0],
bx = K$1[i0 + 1][0],
cx = K$1[min(19, i0 + 2)][0];
return [
x / (bx + di * (cx - ax) / 2 + di * di * (cx - 2 * bx + ax) / 2),
phi * radians
];
};
function robinson() {
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;
}
function satellite() {
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,
epsilonInverse = 1e4,
x0 = -180, x0e = x0 + epsilon$1,
x1 = 180, x1e = x1 - epsilon$1,
y0 = -90, y0e = y0 + epsilon$1,
y1 = 90, 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;
}
function stitch(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)
];
};
function times() {
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.
function twoPoint(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))
];
};
function vanDerGrinten() {
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)))
];
};
function vanDerGrinten2() {
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))
];
};
function vanDerGrinten3() {
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
];
};
function vanDerGrinten4() {
return d3Geo.geoProjection(vanDerGrinten4Raw)
.scale(127.16);
}
function wagnerFormula(cx, cy, m1, m2, n) {
function forward(lambda, phi) {
var s = m1 * sin(m2 * phi),
c0 = sqrt(1 - s * s),
c1 = sqrt(2 / (1 + c0 * cos(lambda *= n)));
return [
cx * c0 * c1 * sin(lambda),
cy * s * c1
];
}
forward.invert = function(x, y) {
var t1 = x / cx,
t2 = y / cy,
p = sqrt(t1 * t1 + t2 * t2),
c = 2 * asin(p / 2);
return [
atan2(x * tan(c), cx * p) / n,
p && asin(y * sin(c) / (cy * m1 * p)) / m2
];
};
return forward;
}
function wagnerRaw(poleline, parallels, inflation, ratio) {
// 60 is always used as reference parallel
var phi1 = pi / 3;
// sanitizing the input values
// poleline and parallels may approximate but never equal 0
poleline = max(poleline, epsilon);
parallels = max(parallels, epsilon);
// poleline must be <= 90; parallels may approximate but never equal 180
poleline = min(poleline, halfPi);
parallels = min(parallels, pi - epsilon);
// 0 <= inflation <= 99.999
inflation = max(inflation, 0);
inflation = min(inflation, 100 - epsilon);
// ratio > 0.
// sensible values, i.e. something that renders a map which still can be
// recognized as world map, are e.g. 20 <= ratio <= 1000.
ratio = max(ratio, epsilon);
// convert values from boehm notation
// areal inflation e.g. from 0 to 1 or 20 to 1.2:
var vinflation = inflation/100 + 1;
// axial ratio e.g. from 200 to 2:
var vratio = ratio / 100;
// the other ones are a bit more complicated...
var m2 = acos(vinflation * cos(phi1)) / phi1,
m1 = sin(poleline) / sin(m2 * halfPi),
n = parallels / pi,
k = sqrt(vratio * sin(poleline / 2) / sin(parallels / 2)),
cx = k / sqrt(n * m1 * m2),
cy = 1 / (k * sqrt(n * m1 * m2));
return wagnerFormula(cx, cy, m1, m2, n);
}
function wagner() {
// default values generate wagner8
var poleline = 65 * radians,
parallels = 60 * radians,
inflation = 20,
ratio = 200,
mutate = d3Geo.geoProjectionMutator(wagnerRaw),
projection = mutate(poleline, parallels, inflation, ratio);
projection.poleline = function(_) {
return arguments.length ? mutate(poleline = +_ * radians, parallels, inflation, ratio) : poleline * degrees;
};
projection.parallels = function(_) {
return arguments.length ? mutate(poleline, parallels = +_ * radians, inflation, ratio) : parallels * degrees;
};
projection.inflation = function(_) {
return arguments.length ? mutate(poleline, parallels, inflation = +_, ratio) : inflation;
};
projection.ratio = function(_) {
return arguments.length ? mutate(poleline, parallels, inflation, ratio = +_) : ratio;
};
return projection
.scale(163.775);
}
function wagner7() {
return wagner()
.poleline(65)
.parallels(60)
.inflation(0)
.ratio(200)
.scale(172.633);
}
var A = 4 * pi + 3 * sqrt(3),
B = 2 * sqrt(2 * pi * sqrt(3) / A);
var wagner4Raw = mollweideBromleyRaw(B * sqrt(3) / pi, B, A / 6);
function wagner4() {
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];
};
function wagner6() {
return d3Geo.geoProjection(wagner6Raw)
.scale(152.63);
}
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
];
};
function wiechel() {
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];
};
function winkel3() {
return d3Geo.geoProjection(winkel3Raw)
.scale(158.837);
}
exports.geoNaturalEarth = d3Geo.geoNaturalEarth1;
exports.geoNaturalEarthRaw = d3Geo.geoNaturalEarth1Raw;
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.geoBertin1953 = bertin;
exports.geoBertin1953Raw = bertin1953Raw;
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.geoFoucautSinusoidal = foucautSinusoidal;
exports.geoFoucautSinusoidalRaw = foucautSinusoidalRaw;
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.geoHufnagel = hufnagel;
exports.geoHufnagelRaw = hufnagelRaw;
exports.geoHyperelliptical = hyperelliptical;
exports.geoHyperellipticalRaw = hyperellipticalRaw;
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.geoNaturalEarth2 = naturalEarth2;
exports.geoNaturalEarth2Raw = naturalEarth2Raw;
exports.geoNellHammer = nellHammer;
exports.geoNellHammerRaw = nellHammerRaw;
exports.geoInterruptedQuarticAuthalic = quarticAuthalic;
exports.geoNicolosi = nicolosi;
exports.geoNicolosiRaw = nicolosiRaw;
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.geoWagner = wagner;
exports.geoWagner7 = wagner7;
exports.geoWagnerRaw = wagnerRaw;
exports.geoWagner4 = wagner4;
exports.geoWagner4Raw = wagner4Raw;
exports.geoWagner6 = wagner6;
exports.geoWagner6Raw = wagner6Raw;
exports.geoWiechel = wiechel;
exports.geoWiechelRaw = wiechelRaw;
exports.geoWinkel3 = winkel3;
exports.geoWinkel3Raw = winkel3Raw;
Object.defineProperty(exports, '__esModule', { value: true });
})));
Reference in New Issue View Git Blame Copy Permalink