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import {Adder} from "d3-array";
import {cartesian, cartesianCross, cartesianNormalizeInPlace} from "./cartesian.js";
import {abs, asin, atan2, cos, epsilon, epsilon2, halfPi, pi, quarterPi, sign, sin, tau} from "./math.js";
function longitude(point) {
return abs(point[0]) <= pi ? point[0] : sign(point[0]) * ((abs(point[0]) + pi) % tau - pi);
}
export default function(polygon, point) {
var lambda = longitude(point),
phi = point[1],
sinPhi = sin(phi),
normal = [sin(lambda), -cos(lambda), 0],
angle = 0,
winding = 0;
var sum = new Adder();
if (sinPhi === 1) phi = halfPi + epsilon;
else if (sinPhi === -1) phi = -halfPi - epsilon;
for (var i = 0, n = polygon.length; i < n; ++i) {
if (!(m = (ring = polygon[i]).length)) continue;
var ring,
m,
point0 = ring[m - 1],
lambda0 = longitude(point0),
phi0 = point0[1] / 2 + quarterPi,
sinPhi0 = sin(phi0),
cosPhi0 = cos(phi0);
for (var j = 0; j < m; ++j, lambda0 = lambda1, sinPhi0 = sinPhi1, cosPhi0 = cosPhi1, point0 = point1) {
var point1 = ring[j],
lambda1 = longitude(point1),
phi1 = point1[1] / 2 + quarterPi,
sinPhi1 = sin(phi1),
cosPhi1 = cos(phi1),
delta = lambda1 - lambda0,
sign = delta >= 0 ? 1 : -1,
absDelta = sign * delta,
antimeridian = absDelta > pi,
k = sinPhi0 * sinPhi1;
sum.add(atan2(k * sign * sin(absDelta), cosPhi0 * cosPhi1 + k * cos(absDelta)));
angle += antimeridian ? delta + sign * tau : delta;
// Are the longitudes either side of the point’s meridian (lambda),
// and are the latitudes smaller than the parallel (phi)?
if (antimeridian ^ lambda0 >= lambda ^ lambda1 >= lambda) {
var arc = cartesianCross(cartesian(point0), cartesian(point1));
cartesianNormalizeInPlace(arc);
var intersection = cartesianCross(normal, arc);
cartesianNormalizeInPlace(intersection);
var phiArc = (antimeridian ^ delta >= 0 ? -1 : 1) * asin(intersection[2]);
if (phi > phiArc || phi === phiArc && (arc[0] || arc[1])) {
winding += antimeridian ^ delta >= 0 ? 1 : -1;
}
}
}
}
// First, determine whether the South pole is inside or outside:
//
// It is inside if:
// * the polygon winds around it in a clockwise direction.
// * the polygon does not (cumulatively) wind around it, but has a negative
// (counter-clockwise) area.
//
// Second, count the (signed) number of times a segment crosses a lambda
// from the point to the South pole. If it is zero, then the point is the
// same side as the South pole.
return (angle < -epsilon || angle < epsilon && sum < -epsilon2) ^ (winding & 1);
}