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Contents
import "projection";
import "elliptic";
import "quincuncial";
// √k' tn(½K - w) = exp(-ζ).
function guyou(λ, φ) {
var k_ = (Math.SQRT2 - 1) / (Math.SQRT2 + 1),
k = Math.sqrt(1 - k_ * k_),
K = ellipticF(π / 2, k * k),
f = -1;
var ψ = Math.log(Math.tan(π / 4 + Math.abs(φ) / 2)),
r = Math.exp(f * ψ) / Math.sqrt(k_),
at = guyouComplexAtan(r * Math.cos(f * λ), r * Math.sin(f * λ)),
t = ellipticFi(at[0], at[1], k * k);
return [-t[1], sgn(φ) * (.5 * K - t[0])];
}
function guyouComplexAtan(x, y) {
var x2 = x * x,
y_1 = y + 1,
t = 1 - x2 - y * y;
return [
sgn(x) * π / 4 - .5 * Math.atan2(t, 2 * x),
-.25 * Math.log(t * t + 4 * x2) + .5 * Math.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
];
}
guyou.invert = function(x, y) {
var k_ = (Math.SQRT2 - 1) / (Math.SQRT2 + 1),
k = Math.sqrt(1 - k_ * k_),
K = ellipticF(π / 2, k * k),
f = -1;
var j = ellipticJi(.5 * K - y, -x, k * k),
tn = guyouComplexDivide(j[0], j[1]),
λ = Math.atan2(tn[1], tn[0]) / f;
return [
λ,
2 * Math.atan(Math.exp(.5 / f * Math.log(k_ * tn[0] * tn[0] + k_ * tn[1] * tn[1]))) - π / 2
];
};
d3.geo.guyou = quincuncialProjection(guyou);
Version data entries
4 entries across 4 versions & 1 rubygems