d3-geo-polygon/src/polygonContains.js

Clipping and geometric operations for spherical polygons.

import {Adder} from "d3-array";
import {cartesian, cartesianCross, cartesianNormalize} from "./cartesian.js";
import {asin, atan2, cos, epsilon, pi, quarterPi, sin, tau} from "./math.js";

export default function(polygon, point) {
  const lambda = point[0];
  const phi = point[1];
  const normal = [sin(lambda), -cos(lambda), 0];
  let angle = 0;
  let winding = 0;

  const sum = new Adder();

  for (let i = 0, n = polygon.length; i < n; ++i) {
    if (!(m = (ring = polygon[i]).length)) continue;
    var ring,
        m,
        point0 = ring[m - 1],
        lambda0 = point0[0],
        phi0 = point0[1] / 2 + quarterPi,
        sinPhi0 = sin(phi0),
        cosPhi0 = cos(phi0);

    for (let j = 0; j < m; ++j, lambda0 = lambda1, sinPhi0 = sinPhi1, cosPhi0 = cosPhi1, point0 = point1) {
      var point1 = ring[j],
          lambda1 = point1[0],
          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) {
        const arc = cartesianNormalize(cartesianCross(cartesian(point0), cartesian(point1)));
        const intersection = cartesianNormalize(cartesianCross(normal, arc));
        const 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 < -epsilon) ^ (winding & 1);
}