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circle.js 5.83 KiB
import {cartesian, cartesianAddInPlace, cartesianCross, cartesianDot, cartesianScale, spherical} from "../cartesian";
import {circleStream} from "../circle";
import {abs, cos, epsilon, pi, sqrt} from "../math";
import pointEqual from "../pointEqual";
import clip from "./index";
export default function(radius, delta) {
  var cr = cos(radius),
      smallRadius = cr > 0,
      notHemisphere = abs(cr) > epsilon; // TODO optimise for this common case
  function interpolate(from, to, direction, stream) {
    circleStream(stream, radius, delta, direction, from, to);
  function visible(lambda, phi) {
    return cos(lambda) * cos(phi) > cr;
  // Takes a line and cuts into visible segments. Return values used for polygon
  // clipping: 0 - there were intersections or the line was empty; 1 - no
  // intersections 2 - there were intersections, and the first and last segments
  // should be rejoined.
  function clipLine(stream) {
    var point0, // previous point
        c0, // code for previous point
        v0, // visibility of previous point
        v00, // visibility of first point
        clean; // no intersections
    return {
      lineStart: function() {
        v00 = v0 = false;
        clean = 1;
      point: function(lambda, phi) {
        var point1 = [lambda, phi],
            point2,
            v = visible(lambda, phi),
            c = smallRadius
              ? v ? 0 : code(lambda, phi)
              : v ? code(lambda + (lambda < 0 ? pi : -pi), phi) : 0;
        if (!point0 && (v00 = v0 = v)) stream.lineStart();
        // Handle degeneracies.
        // TODO ignore if not clipping polygons.
        if (v !== v0) {
          point2 = intersect(point0, point1);
          if (!point2 || pointEqual(point0, point2) || pointEqual(point1, point2)) {
            point1[0] += epsilon;
            point1[1] += epsilon;
            v = visible(point1[0], point1[1]);
        if (v !== v0) {
          clean = 0;
          if (v) {
            // outside going in
            stream.lineStart();
            point2 = intersect(point1, point0);
            stream.point(point2[0], point2[1]);
          } else {
            // inside going out
            point2 = intersect(point0, point1);
            stream.point(point2[0], point2[1]);
            stream.lineEnd();
          point0 = point2;
        } else if (notHemisphere && point0 && smallRadius ^ v) {
          var t;
          // If the codes for two points are different, or are both zero,
          // and there this segment intersects with the small circle.
if (!(c & c0) && (t = intersect(point1, point0, true))) { clean = 0; if (smallRadius) { stream.lineStart(); stream.point(t[0][0], t[0][1]); stream.point(t[1][0], t[1][1]); stream.lineEnd(); } else { stream.point(t[1][0], t[1][1]); stream.lineEnd(); stream.lineStart(); stream.point(t[0][0], t[0][1]); } } } if (v && (!point0 || !pointEqual(point0, point1))) { stream.point(point1[0], point1[1]); } point0 = point1, v0 = v, c0 = c; }, lineEnd: function() { if (v0) stream.lineEnd(); point0 = null; }, // Rejoin first and last segments if there were intersections and the first // and last points were visible. clean: function() { return clean | ((v00 && v0) << 1); } }; } // Intersects the great circle between a and b with the clip circle. function intersect(a, b, two) { var pa = cartesian(a), pb = cartesian(b); // We have two planes, n1.p = d1 and n2.p = d2. // Find intersection line p(t) = c1 n1 + c2 n2 + t (n1 ⨯ n2). var n1 = [1, 0, 0], // normal n2 = cartesianCross(pa, pb), n2n2 = cartesianDot(n2, n2), n1n2 = n2[0], // cartesianDot(n1, n2), determinant = n2n2 - n1n2 * n1n2; // Two polar points. if (!determinant) return !two && a; var c1 = cr * n2n2 / determinant, c2 = -cr * n1n2 / determinant, n1xn2 = cartesianCross(n1, n2), A = cartesianScale(n1, c1), B = cartesianScale(n2, c2); cartesianAddInPlace(A, B); // Solve |p(t)|^2 = 1. var u = n1xn2, w = cartesianDot(A, u), uu = cartesianDot(u, u), t2 = w * w - uu * (cartesianDot(A, A) - 1); if (t2 < 0) return; var t = sqrt(t2), q = cartesianScale(u, (-w - t) / uu); cartesianAddInPlace(q, A); q = spherical(q); if (!two) return q;
// Two intersection points. var lambda0 = a[0], lambda1 = b[0], phi0 = a[1], phi1 = b[1], z; if (lambda1 < lambda0) z = lambda0, lambda0 = lambda1, lambda1 = z; var delta = lambda1 - lambda0, polar = abs(delta - pi) < epsilon, meridian = polar || delta < epsilon; if (!polar && phi1 < phi0) z = phi0, phi0 = phi1, phi1 = z; // Check that the first point is between a and b. if (meridian ? polar ? phi0 + phi1 > 0 ^ q[1] < (abs(q[0] - lambda0) < epsilon ? phi0 : phi1) : phi0 <= q[1] && q[1] <= phi1 : delta > pi ^ (lambda0 <= q[0] && q[0] <= lambda1)) { var q1 = cartesianScale(u, (-w + t) / uu); cartesianAddInPlace(q1, A); return [q, spherical(q1)]; } } // Generates a 4-bit vector representing the location of a point relative to // the small circle's bounding box. function code(lambda, phi) { var r = smallRadius ? radius : pi - radius, code = 0; if (lambda < -r) code |= 1; // left else if (lambda > r) code |= 2; // right if (phi < -r) code |= 4; // below else if (phi > r) code |= 8; // above return code; } return clip(visible, clipLine, interpolate, smallRadius ? [0, -radius] : [-pi, radius - pi]); }