Function intersect

external/.d3.js:11006–11068

(a, b, two)

  // 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$2(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$1(delta - pi$1) < epsilon$1,
        meridian = polar || delta < epsilon$1;

    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$1(q[0] - lambda0) < epsilon$1 ? phi0 : phi1)
          : phi0 <= q[1] && q[1] <= phi1
        : delta > pi$1 ^ (lambda0 <= q[0] && q[0] <= lambda1)) {