intersect.js

import {abs, acos, cos, degrees, epsilon, epsilon2, pi, radians} from "./math.js";
import {cartesian, cartesianCross, cartesianDot, cartesianEqual, cartesianNormalize, spherical} from "./cartesian.js";

export class intersectSegment {
  constructor(from, to) {
    this.from = from, this.to = to;
    this.normal = cartesianCross(from, to);
    this.fromNormal = cartesianCross(this.normal, from);
    this.toNormal = cartesianCross(this.normal, to);
    this.l = acos(cartesianDot(from, to));
  }
}

// >> here a and b are segments processed by intersectSegment
export function intersect(a, b) {
  if (cartesianEqual(a.from, b.from) || cartesianEqual(a.from, b.to)) return a.from;
  if (cartesianEqual(a.to, b.from) || cartesianEqual(a.to, b.to)) return a.to;

  // Slightly faster lookup when there is no intersection
  const lc = (a.l + b.l < pi) ? cos(a.l + b.l) - epsilon : -1;
  if (cartesianDot(a.from, b.from) < lc
  || cartesianDot(a.from, b.to) < lc
  || cartesianDot(a.to, b.from) < lc
  || cartesianDot(a.to, b.to) < lc)
     return;

  const axb = cartesianNormalize(cartesianCross(a.normal, b.normal));
  
  const a0 = cartesianDot(axb, a.fromNormal);
  const a1 = cartesianDot(axb, a.toNormal);
  const b0 = cartesianDot(axb, b.fromNormal);
  const b1 = cartesianDot(axb, b.toNormal);
  
  // check if the candidate lies on both segments
  // or is almost equal to one of the four points
  if (a0 >= 0 && a1 <= 0 && b0 >= 0 && b1 <= 0)
    return axb;

  // same test for the antipode
  if (a0 <= 0 && a1 >= 0 && b0 <= 0 && b1 >= 0)
    return axb.map(d => -d);
}

export function intersectPointOnLine(p, a) {
  const a0 = cartesianDot(p, a.fromNormal);
  const a1 = cartesianDot(p, a.toNormal);
  p = cartesianDot(p, a.normal);
  return abs(p) < epsilon2 && (a0 > -epsilon2 && a1 < epsilon2 || a0 < epsilon2 && a1 > -epsilon2);
}

export const intersectCoincident = {};

export default function(a, b) {
  const ca = a.map(p => cartesian(p.map(d => d * radians)));
  const cb = b.map(p => cartesian(p.map(d => d * radians)));
  const i = intersect(
    new intersectSegment(ca[0], ca[1]),
    new intersectSegment(cb[0], cb[1])
  );
  return i ? spherical(i).map((d) => d * degrees) : null;
}