Kerkovits projectionA map of AfricaCupola ProjectionClipping spherical polygonsA conformal AiroceanFill with strokeMarkley’s tetrahedral mapSynchronized projectionsSatellite GLSLVan Der Grinten IV GLSLVan Der Grinten III GLSLVan Der Grinten II GLSLWinkel Tripel GLSLLee Modified Stereographic GLSLMiller Oblated Stereographic GLSLModified Stereographic GS48 GLSLModified Stereographic GS50 GLSLFoucaut GLSLLagrange GLSLKavrayskiy VII GLSLEisenlohr GLSLEckert VI GLSLEckert V GLSLEckert IV GLSLEckert III GLSLEckert II GLSLEckert I GLSLBertin1953 GLSLRobinson GLSLMiller GLSLRectangular Polyconic GLSLPatterson GLSLPolyconic GLSLLoximuthal GLSLCylindrical Stereographic GLSLCylindrical Equal-Area GLSLTransverse Fahey GLSLFahey GLSLCollignon GLSLBromley GLSLBottomley GLSLHammer GLSLBonne GLSLBoggs GLSLBerghaus GLSLBaker Transverse GLSLBaker GLSLAugust GLSLAiry GLSLAitoff GLSLArmadillo GLSLLarrivée GLSLCylindrical Equal-Area GLSLAzimuthal Equidistant GLSLLittrow GLSLVan Der Grinten GLSLEquirectangular GLSLConic Conformal GLSLConic Equidistant GLSLAlbers GLSLConic Equal-Area GLSLEqual Earth GLSLTimes GLSLWagner IV GLSLWagner VI GLSLWagner VII GLSLWiechel GLSLAtlantis GLSLMollweide GLSLMercator GLSLTransverse Mercator GLSLCordiform GLSLWebMercator to globeVersor zooming for Three.jsAzimuthal Equal-Area GLSLBriesemeister GLSLRectilinear GLSLPhytoplanktonDanseiji projectionsTransverse MollweideThe 2D approximate Newton-Raphson methodInverting Lee’s Tetrahedral projectionAmerican PolyconicThe complex logarithm projectionRaster projection with GPU.jsH3 hexagons & geoContoursModified Stereographic ProjectionsFisheye Conformal Map (Cox)Fisheye Conformal MapFisheye Conformal Map (Tetrahedral)Reproject elevation tiles — worldTransverse projectionsThe Imago projectionD3 ProjectionsImago Projection Distorsion AnalysisEPSG:5530Imago tilingCordiform map projections 💛💗💖MultiPolygon clippingThe Nicolosi Globular ProjectionFisheye GlobeHerbert Bayer’s Pacific OceanThe Behrmann projectionOronce Finé’s triangle projectionDa Vinci’s octant projectionThe Lotus projection (1958)The Voronoi projectionUsing proj4js with D3 and PlotMurphey Butterfly ProjectionEquateur & tropiquesVega projectionsMercator projection of a Mercator globeThe truth about the Mercator projectionOcean-centric Mollweide projectionBuckminster Fuller’s triangle transformationExperimental two world projectionsTobler’s hyperelliptical projection (1973)Jacques Bertin’s projection (1953)A map without Antarctica (Bertin1953 projection)Square Root Azimuthal projectionThe Log-Azimuthal projectionPeirce Quincuncial Projection, centered on the South PoleTranslucent Earth (Satellite projection)Lee’s conformal projection in a tetrahedronAirocean projectionCubic projectionsCox conformal projection in a triangleIcosahedral projectionsDodecahedral projectionThe Cahill-Keyes projection (1975)Polyhedral projections with d3-geo-polygonWagner customizable projectionParametrized Equal Earth ProjectionTissot's indicatrixAn equal-area projection for the cubic EarthBase map
The Hufnagel projection system
// test the inverse
projection
.invert(projection([10, -34]))
.map(d => d.toFixed(8))
.join(", ")
hufnagel = {
const { abs, asin, cos, sign, sin, sqrt } = Math;
const projectionMutator = d3.geoProjectionMutator;
const epsilon = 1e-6,
pi = Math.PI,
degrees = 180 / pi,
radians = pi / 180;
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() {
// default is Hufnagel XI: 0/-0.111/90/2
var a = 0,
b = -0.111,
psiMax = 90 * radians,
ratio = 2,
mutate = projectionMutator(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(179.801);
}
// Newton-Raphson
// Solve f(x) = y, start from x = 0
function solve(f, y = 0, x = 0, steps = 100) {
var delta, f0, f1;
do {
f0 = f(x);
f1 = f(x + epsilon);
if (f0 === f1) f1 = f0 + epsilon;
delta = (epsilon * (f0 - y)) / (f0 - f1);
if (abs(delta) > 0.1) delta = 0.1 * sign(delta);
x += delta;
} while (steps-- > 0 && abs(delta) > epsilon);
return steps < 0 ? NaN : x;
}
return (d3.geoHufnagel = hufnagel);
}
projection = {
hufnagel; // bind the projection to the d3 symbol
return d3
.geoHufnagel()
.precision(0.1)
.rotate([-10, 0]);
}
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