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Contents
import "projection";
function vanDerGrinten4(λ, φ) {
if (!φ) return [λ, 0];
var φ0 = Math.abs(φ);
if (!λ || φ0 === π / 2) return [0, φ];
var B = 2 * φ0 / π,
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,
λ0 = 2 * λ / π,
λ1 = λ0 + 1 / λ0,
D = sgn(Math.abs(λ) - π / 2) * Math.sqrt(λ1 * λ1 - 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 * asqrt(F)) / (4 * B_C2 + D2);
return [
sgn(λ) * π * x1 / 2,
sgn(φ) * π / 2 * asqrt(1 + D * Math.abs(x1) - x1 * x1)
];
}
vanDerGrinten4.invert = function(x, y) {
if (!x || !y) return [x, y];
y /= π;
var x1 = sgn(x) * x * 2 / π,
D = (x1 * x1 - 1 + 4 * y * y) / Math.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 = Math.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 -= δ = f / f_;
} while (δ > ε && --i > 0);
return [
sgn(x) * (Math.sqrt(D * D + 4) + D) * π / 4,
π / 2 * B
];
};
(d3.geo.vanDerGrinten4 = function() { return projection(vanDerGrinten4); }).raw = vanDerGrinten4;
Version data entries
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