/**
 * Takes a {@link Point} and calculates the location of a destination point given a distance in
 * degrees, radians, miles, or kilometers; and bearing in degrees.
 * This uses the [Haversine formula](http://en.wikipedia.org/wiki/Haversine_formula) to account for global curvature.
 *
 * @name destination
 * @param {Coord} origin starting point
 * @param {number} distance distance from the origin point
 * @param {number} bearing ranging from -180 to 180
 * @param {Object} [options={}] Optional parameters
 * @param {string} [options.units='kilometers'] miles, kilometers, degrees, or radians
 * @param {Object} [options.properties={}] Translate properties to Point
 * @returns {Feature<Point>} destination point
 * @example
 * var point = turf.point([-75.343, 39.984]);
 * var distance = 50;
 * var bearing = 90;
 * var options = {units: 'miles'};
 *
 * var destination = turf.destination(point, distance, bearing, options);
 *
 * //addToMap
 * var addToMap = [point, destination]
 * destination.properties['marker-color'] = '#f00';
 * point.properties['marker-color'] = '#0f0';
 */
export default function destination<P = Properties>(
    origin: Coord,
    distance: number,
    bearing: number,
    options: {
        units?: Units,
        properties?: P,
    } = {},
): Feature<Point, P> {
    // Handle input
    const coordinates1 = getCoord(origin);
    const longitude1 = degreesToRadians(coordinates1[0]);
    const latitude1 = degreesToRadians(coordinates1[1]);
    const bearingRad = degreesToRadians(bearing);
    const radians = lengthToRadians(distance, options.units);

    // Main
    const latitude2 = Math.asin(Math.sin(latitude1) * Math.cos(radians) +
        Math.cos(latitude1) * Math.sin(radians) * Math.cos(bearingRad));
    const longitude2 = longitude1 + Math.atan2(Math.sin(bearingRad) * Math.sin(radians) * Math.cos(latitude1),
        Math.cos(radians) - Math.sin(latitude1) * Math.sin(latitude2));
    const lng = radiansToDegrees(longitude2);
    const lat = radiansToDegrees(latitude2);

    return point([lng, lat], options.properties);
}

/**
 * Returns the destination point having travelled along a rhumb line from origin point the given
 * distance on the  given bearing.
 * Adapted from Geodesy: http://www.movable-type.co.uk/scripts/latlong.html#rhumblines
 *
 * @private
 * @param   {Array<number>} origin - point
 * @param   {number} distance - Distance travelled, in same units as earth radius (default: metres).
 * @param   {number} bearing - Bearing in degrees from north.
 * @param   {number} [radius=6371e3] - (Mean) radius of earth (defaults to radius in metres).
 * @returns {Array<number>} Destination point.
 */
function calculateRhumbDestination(origin: number[], distance: number, bearing: number, radius?: number) {
    // φ => phi
    // Îť => lambda
    // ψ => psi
    // Δ => Delta
    // δ => delta
    // θ => theta

    radius = (radius === undefined) ? earthRadius : Number(radius);

    const delta = distance / radius; // angular distance in radians
    const lambda1 = origin[0] * Math.PI / 180; // to radians, but without normalize to 𝜋
    const phi1 = degreesToRadians(origin[1]);
    const theta = degreesToRadians(bearing);

    const DeltaPhi = delta * Math.cos(theta);
    let phi2 = phi1 + DeltaPhi;

    // check for some daft bugger going past the pole, normalise latitude if so
    if (Math.abs(phi2) > Math.PI / 2) { phi2 = phi2 > 0 ? Math.PI - phi2 : -Math.PI - phi2; }

    const DeltaPsi = Math.log(Math.tan(phi2 / 2 + Math.PI / 4) / Math.tan(phi1 / 2 + Math.PI / 4));
    // E-W course becomes ill-conditioned with 0/0
    const q = Math.abs(DeltaPsi) > 10e-12 ? DeltaPhi / DeltaPsi : Math.cos(phi1);

    const DeltaLambda = delta * Math.sin(theta) / q;
    const lambda2 = lambda1 + DeltaLambda;

    return [((lambda2 * 180 / Math.PI) + 540) % 360 - 180, phi2 * 180 / Math.PI]; // normalise to −180..+180°
}

//http://en.wikipedia.org/wiki/Haversine_formula
//http://www.movable-type.co.uk/scripts/latlong.html

/**
 * Calculates the distance between two {@link Point|points} in degrees, radians, miles, or kilometers.
 * This uses the [Haversine formula](http://en.wikipedia.org/wiki/Haversine_formula) to account for global curvature.
 *
 * @name distance
 * @param {Coord} from origin point
 * @param {Coord} to destination point
 * @param {Object} [options={}] Optional parameters
 * @param {string} [options.units='kilometers'] can be degrees, radians, miles, or kilometers
 * @returns {number} distance between the two points
 * @example
 * var from = turf.point([-75.343, 39.984]);
 * var to = turf.point([-75.534, 39.123]);
 * var options = {units: 'miles'};
 *
 * var distance = turf.distance(from, to, options);
 *
 * //addToMap
 * var addToMap = [from, to];
 * from.properties.distance = distance;
 * to.properties.distance = distance;
 */
function distance(from: Coord, to: Coord, options: {
    units?: Units,
} = {}) {
    var coordinates1 = getCoord(from);
    var coordinates2 = getCoord(to);
    var dLat = degreesToRadians((coordinates2[1] - coordinates1[1]));
    var dLon = degreesToRadians((coordinates2[0] - coordinates1[0]));
    var lat1 = degreesToRadians(coordinates1[1]);
    var lat2 = degreesToRadians(coordinates2[1]);

    var a = Math.pow(Math.sin(dLat / 2), 2) +
          Math.pow(Math.sin(dLon / 2), 2) * Math.cos(lat1) * Math.cos(lat2);

    return radiansToLength(2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a)), options.units);
}

/**
 * Returns the bearing from ‘this’ point to destination point along a rhumb line.
 * Adapted from Geodesy: https://github.com/chrisveness/geodesy/blob/master/latlon-spherical.js
 *
 * @private
 * @param   {Array<number>} from - origin point.
 * @param   {Array<number>} to - destination point.
 * @returns {number} Bearing in degrees from north.
 * @example
 * var p1 = new LatLon(51.127, 1.338);
 * var p2 = new LatLon(50.964, 1.853);
 * var d = p1.rhumbBearingTo(p2); // 116.7 m
 */
function calculateRhumbBearing(from: number[], to: number[]) {
    // φ => phi
    // Δλ => deltaLambda
    // Δψ => deltaPsi
    // θ => theta
    const phi1 = degreesToRadians(from[1]);
    const phi2 = degreesToRadians(to[1]);
    let deltaLambda = degreesToRadians((to[0] - from[0]));
    // if deltaLambdaon over 180° take shorter rhumb line across the anti-meridian:
    if (deltaLambda > Math.PI) { deltaLambda -= 2 * Math.PI; }
    if (deltaLambda < -Math.PI) { deltaLambda += 2 * Math.PI; }

    const deltaPsi = Math.log(Math.tan(phi2 / 2 + Math.PI / 4) / Math.tan(phi1 / 2 + Math.PI / 4));

    const theta = Math.atan2(deltaLambda, deltaPsi);

    return (radiansToDegrees(theta) + 360) % 360;
}

// http://en.wikipedia.org/wiki/Haversine_formula
// http://www.movable-type.co.uk/scripts/latlong.html

/**
 * Takes two {@link Point|points} and finds the geographic bearing between them,
 * i.e. the angle measured in degrees from the north line (0 degrees)
 *
 * @name bearing
 * @param {Coord} start starting Point
 * @param {Coord} end ending Point
 * @param {Object} [options={}] Optional parameters
 * @param {boolean} [options.final=false] calculates the final bearing if true
 * @returns {number} bearing in decimal degrees, between -180 and 180 degrees (positive clockwise)
 * @example
 * var point1 = turf.point([-75.343, 39.984]);
 * var point2 = turf.point([-75.534, 39.123]);
 *
 * var bearing = turf.bearing(point1, point2);
 *
 * //addToMap
 * var addToMap = [point1, point2]
 * point1.properties['marker-color'] = '#f00'
 * point2.properties['marker-color'] = '#0f0'
 * point1.properties.bearing = bearing
 */
export default function bearing(start: Coord, end: Coord, options: {
    final?: boolean,
} = {}): number {
    // Reverse calculation
    if (options.final === true) { return calculateFinalBearing(start, end); }

    const coordinates1 = getCoord(start);
    const coordinates2 = getCoord(end);

    const lon1 = degreesToRadians(coordinates1[0]);
    const lon2 = degreesToRadians(coordinates2[0]);
    const lat1 = degreesToRadians(coordinates1[1]);
    const lat2 = degreesToRadians(coordinates2[1]);
    const a = Math.sin(lon2 - lon1) * Math.cos(lat2);
    const b = Math.cos(lat1) * Math.sin(lat2) -
        Math.sin(lat1) * Math.cos(lat2) * Math.cos(lon2 - lon1);

    return radiansToDegrees(Math.atan2(a, b));
}