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64 lines
1.6 KiB
64 lines
1.6 KiB
import {geoProjection as projection} from "d3-geo";
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import {abs, cos, halfPi, pi, sign, sin, sqrt} from "./math.js";
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import {solve} from "./newton.js";
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// Based on Torben Jansen's implementation
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// https://beta.observablehq.com/@toja/nicolosi-globular-projection
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// https://beta.observablehq.com/@toja/nicolosi-globular-inverse
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export function nicolosiRaw(lambda, phi) {
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var sinPhi = sin(phi),
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q = cos(phi),
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s = sign(lambda);
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if (lambda === 0 || abs(phi) === halfPi) return [0, phi];
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else if (phi === 0) return [lambda, 0];
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else if (abs(lambda) === halfPi) return [lambda * q, halfPi * sinPhi];
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var b = pi / (2 * lambda) - (2 * lambda) / pi,
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c = (2 * phi) / pi,
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d = (1 - c * c) / (sinPhi - c);
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var b2 = b * b,
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d2 = d * d,
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b2d2 = 1 + b2 / d2,
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d2b2 = 1 + d2 / b2;
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var M = ((b * sinPhi) / d - b / 2) / b2d2,
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N = ((d2 * sinPhi) / b2 + d / 2) / d2b2,
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m = M * M + (q * q) / b2d2,
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n = N * N - ((d2 * sinPhi * sinPhi) / b2 + d * sinPhi - 1) / d2b2;
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return [
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halfPi * (M + sqrt(m) * s),
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halfPi * (N + sqrt(n < 0 ? 0 : n) * sign(-phi * b) * s)
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];
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}
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nicolosiRaw.invert = function(x, y) {
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x /= halfPi;
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y /= halfPi;
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var x2 = x * x,
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y2 = y * y,
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x2y2 = x2 + y2,
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pi2 = pi * pi;
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return [
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x ? (x2y2 -1 + sqrt((1 - x2y2) * (1 - x2y2) + 4 * x2)) / (2 * x) * halfPi : 0,
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solve(function(phi) {
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return (
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x2y2 * (pi * sin(phi) - 2 * phi) * pi +
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4 * phi * phi * (y - sin(phi)) +
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2 * pi * phi -
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pi2 * y
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);
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}, 0)
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];
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};
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export default function() {
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return projection(nicolosiRaw)
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.scale(127.267);
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}
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