AlexAegis/loreplotter

import { Vector3 } from 'three';

export interface Circle {
    center: Vector3;
    radius: number; // In kilometer
}

/**
 * 1)
 * @param c1 first circle, radius in km, center in geocentric coordinates
 * @param c2 second circle, radius in km, center in geocentric coordinates
 * @param radius by default the earths default radius in KM
 */
export function intersection(c1: Circle, c2: Circle, radius: number): Array<Vector3> {
    const intersections: Array<Vector3> = [];

    // project to (x,y,z) with unit radius
    const x1: Vector3 = c1.center.clone().normalize();
    const x2: Vector3 = c2.center.clone().normalize();
    // convert radii to radians:
    const r1: number = c1.radius / radius;
    const r2: number = c2.radius / radius;
    // compute the unique point x0
    const q: number = x1.clone().dot(x2);
    const q2: number = q * q;
    if (q2 === 1) {
        // no solution: circle centers are either the same or antipodal
        return intersections;
    }
    const a: number = (Math.cos(r1) - q * Math.cos(r2)) / (1 - q2);
    const b: number = (Math.cos(r2) - q * Math.cos(r1)) / (1 - q2);
    const x0: Vector3 = x1
        .clone()
        .multiplyScalar(a)
        .add(x2.clone().multiplyScalar(b));

    // we only have a solution if x0 is within the sphere - if not,
    // the circles are not touching.
    const x02: number = x0.clone().dot(x0);
    if (x02 > 1) {
        // no solution: circles not touching
        return intersections;
    }

    // get the normal vector:
    const n: Vector3 = x1
        .clone()
        .cross(x2)
        .normalize();
    const n2: number = n.clone().dot(n);
    if (n2 === 0) {
        // no solution: circle centers are either the same or antipodal
        return intersections;
    }

    // find intersections:
    const t: number = Math.sqrt((1 - x0.clone().dot(x0)) / n2);
    intersections.push(x0.clone().add(n.clone().multiplyScalar(t)));
    if (t > 0) {
        // there's only multiple solutions if t > 0
        intersections.push(x0.clone().add(n.clone().multiplyScalar(-t)));
    }
    return intersections;
}