//! Rust interface for [GeographicLib](https://geographiclib.sourceforge.io/html/) for geodesic calculations
//!
//! **Note**: Copied directly from [geodesic.h](https://geographiclib.sourceforge.io/html/C/geodesic_8h.html). Much more and better information can be found there.
//! 
//! This an implementation in C (with a Rust Interface) of the geodesic algorithms described in
//! 
//! - [C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87, 43–55 (2013); DOI: 10.1007/s00190-012-0578-z; addenda: geod-addenda.html.](https://dx.doi.org/10.1007/s00190-012-0578-z)
//!
//!
//! # Example
//!
//! ```rust
//! use geographiclib::Geodesic;
//! let g = Geodesic::wgs84();
//! let (lat1, lon1) = (37.87622, -122.23558); // Berkeley, California
//! let (lat2, lon2) = (-9.4047, 147.1597);    // Port Moresby, New Guinea
//! let (d_deg, d_m, az1, az2) = g.inverse(lat1, lon1, lat2, lon2);
//! 
//! assert_eq!(d_deg, 96.39996198449684); // Distance in degrees
//! assert_eq!(d_m, 10700471.955233702);  // Distance in meters
//! assert_eq!(az1, -96.91639942294974);  // Azimuth at (lat1, lon1)
//! assert_eq!(az2, -127.32548874543627); // Azimuth at (lat2, lon2)
//! ```
//!
//! # Rationale
//! 
//! The principal advantages of these algorithms over previous ones (e.g., Vincenty, 1975) are
//!
//!    - accurate to round off for |f| < 1/50;
//!    - the solution of the inverse problem is always found;
//!    - differential and integral properties of geodesics are computed.
//!
//! The shortest path between two points on the ellipsoid at (lat1, lon1) and (lat2, lon2) is called the geodesic. Its length is s12 and the geodesic from point 1 to point 2 has forward azimuths azi1 and azi2 at the two end points.
//!
//! Traditionally two geodesic problems are considered:
//!
//!    - [direct](struct.Geodesic.html#method.direct) – given lat1, lon1, s12, and azi1, determine lat2, lon2, and azi2.
//!    - [inverse](struct.Geodesic.html#method.inverse) – given lat1, lon1, and lat2, lon2, determine s12, azi1, and azi2.
//!
//! The ellipsoid is specified by its equatorial radius a (typically in meters) and flattening f. The routines are accurate to round off with double precision arithmetic provided that |f| < 1/50; for the WGS84 ellipsoid, the errors are less than 15 nanometers. (Reasonably accurate results are obtained for |f| < 1/5.) For a prolate ellipsoid, specify f < 0. 
//!
//!

// For the GeographicLib routines (Legacy/C 1.49 Feb 18, 2019)
#[link(name="geographiclib", kind="static")]


/// Ellipsoid on which Geodesic Calculations are computed
#[repr(C)]
pub struct Geodesic {
    /// Semi-major axis
    a: f64,
    /// Flattening
    f: f64,
    f1: f64,
    e2: f64,
    ep2: f64,
    n: f64,
    b: f64,
    c2: f64,
    etol2: f64,
    a3x: [f64; 6],
    c3x: [f64; 15],
    c4x: [f64; 21],
}

/// Used Ellipsoids and Historical Ones
///
///
///  Name           | Semi Major Axis (m) | Inverse Flattening | Notes
/// --------------- | ------------------- | ------------------ | -----
///  WGS84          |  6,378,137.0        | 298.257,223,563    | &gamma;
///  Bessel         |  6,377,397.155      | 299.152,812,8      | &gamma;
///  Hayford        |  6,378,388.0        | 297.0              | &gamma;
///  International  |  6,378,388.0        | 297.0              | &gamma;
///  Krassovsky     |  6,378,245.0        | 298.3              | &gamma;
///  WGS66          |  6,378,145.0        | 298.25             | &gamma;
///  WGS72          |  6,378,135.0        | 298.26             | &gamma;
///  GRS80          |  6,378,137.0        | 298.257,222,101    | &gamma;
///  Mercury        |  2,439,700.0        | &infin; (1/0)      | &alpha;
///  Venus          |  6,051,800.0        | &infin; (1/0)      | &alpha;
///  Mars           |  3,396,190.0        | 169.894447         | &alpha;
///  Jupiter        | 71,492,000.0        | 15.41440           | &alpha;
///  Saturn         | 60,268,000.0        | 10.20799           | &alpha;
///  Uranus         | 25,559,000.0        | 43.6160            | &alpha;
///  Neptune        | 24,764,000.0        | 58.5437            | &alpha;
///  Pluto          |  1,195,000.0        | &infin; (1/0)      | &alpha;
///  Miranda        |    240,300.0        | 32.47297           | &alpha;
///
///  &alpha; [Seidelmann et al. (2007), Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006](dx.doi.org/10.1007/s10569-007-9072-y)
///
///  &gamma; [Historical Ellipsoids](https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids)
///


pub enum Ellipsoid {
    /// [World Geodetic System: WGS 84](https://en.wikipedia.org/wiki/World_Geodetic_System#A_new_World_Geodetic_System:_WGS_84)
    ///
    /// This is probably what you want
    WGS84,
    /// [Bessel Ellipsoid](https://en.wikipedia.org/wiki/Bessel_ellipsoid) (1841)
    Bessel,
    /// [Hayford Ellipsoid](https://en.wikipedia.org/wiki/Hayford_ellipsoid) (1910)
    Hayford,
    /// [International Ellipsoid](https://en.wikipedia.org/wiki/Hayford_ellipsoid) (1924)
    ///
    /// Also known as the Hayford Ellipsoid
    International,
    /// [Krassovsky Ellipsoid](https://en.wikipedia.org/wiki/SK-42_reference_system) (1940)
    ///
    /// Also know as the SK-42 reference system
    Krassovsky,
    /// [World Geodetic System 1966](https://en.wikipedia.org/wiki/World_Geodetic_System#The_United_States_Department_of_Defense_World_Geodetic_System_1966) (1966)
    WGS66,
    /// [World Geodetic System 1972](https://en.wikipedia.org/wiki/World_Geodetic_System#The_United_States_Department_of_Defense_World_Geodetic_System_1972)
    WGS72,
    /// (Geodetic Reference System 1980)[https://en.wikipedia.org/wiki/Geodetic_Reference_System_1980]
    GRS80,
    Mercury,
    Venus,
    Mars,
    Jupiter,
    Saturn,
    Uranus,
    Neptune,
    Pluto,
    Miranda
}

impl Ellipsoid {
    fn value(&self) -> (f64, f64) {
        match *self {
            Ellipsoid::WGS84         => ( 6_378_137.0,   1.0 / 298.257_223_563),
            Ellipsoid::Bessel        => ( 6_377_397.155, 1.0 / 299.152_812_8  ),
            Ellipsoid::Hayford       => ( 6_378_388.0,   1.0 / 297.0),
            Ellipsoid::International => ( 6_378_388.0,   1.0 / 297.0),
            Ellipsoid::Krassovsky    => ( 6_378_245.0,   1.0 / 298.3),
            Ellipsoid::WGS66         => ( 6_378_145.0,   1.0 / 298.25),
            Ellipsoid::WGS72         => ( 6_378_135.0,   1.0 / 298.26),
            Ellipsoid::GRS80         => ( 6_378_137.0,   1.0 / 298.257_222_101),
            Ellipsoid::Mercury       => ( 2_439_700.0,   0.0),
            Ellipsoid::Venus         => ( 6_051_800.0,   0.0),
            Ellipsoid::Mars          => ( 3_396_190.0,   1.0 / 169.894_447),
            Ellipsoid::Jupiter       => (71_492_000.0,   1.0 / 15.41440),
            Ellipsoid::Saturn        => (60_268_000.0,   1.0 / 10.20799),
            Ellipsoid::Uranus        => (25_559_000.0,   1.0 / 43.6160),
            Ellipsoid::Neptune       => (24_764_000.0,   1.0 / 58.5437),
            Ellipsoid::Pluto         => ( 1_195_000.0,   0.0),
            Ellipsoid::Miranda       => (   240_300.0,   1.0 / 32.47297),
        }
    }
}

impl std::fmt::Display for Geodesic {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "Geodesic {{ a: {}, f: {} }}", self.a, self.f)
    }
}
impl std::fmt::Debug for Geodesic {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "Geodesic {{ a: {}, f: {} }}", self.a, self.f)
    }
}

extern {
    fn geod_init(g: *mut Geodesic, a: f64, f: f64);
    fn geod_inverse(g: *const Geodesic,
                    lat1: f64, lon1: f64,
                    lat2: f64, lon2: f64,
                    ps12: *mut f64,
                    pazi1: *mut f64,
                    pazi2: *mut f64) -> f64;
    fn geod_direct(g: *const Geodesic,
                   lat1: f64, lon1: f64,
                   azi1: f64, s12: f64,
                   plat2: *mut f64,
                   plon2: *mut f64,
                   pazi2: *mut f64);
}

impl Geodesic {
    /// Create a new WGS84 Ellipsoid
    ///
    /// - Semi-major Axis: 6_378_137.0
    /// - Flattening: 1.0/298.257_223_563
    ///
    pub fn wgs84() -> Self {
        let a = 6_378_137.0;
        let f = 1.0/298.257_223_563; /* WGS84 */
        Self::new(a,f)
    }
    /// Create a new Ellipsoid from currently existing versions
    ///
    /// For a complete list see the [Ellipsoid](enum.Ellipsoid.html) enum
    ///
    pub fn ellipsoid(name: Ellipsoid) -> Self {
        let (a,f) = name.value();
        Self::new(a,f)
    }
    /// Create new Ellipsoid with semi-major axis `a` in meters and a flattening `f`
    ///
    /// Most users will likely want either [wgs84](struct.Geodesic.html#method.wgs84)
    ///  or [ellipsoid](struct.Geodesic.html#method.ellipsoid) for well defined
    ///  and recongized Ellipsoids
    ///
    /// ```rust
    /// use geographiclib::Geodesic;
    /// let g = Geodesic::new(6_378_145.0, 1.0/298.25);
    /// println!("{}", g);
    /// // Geodesic { a: 6378145, f: 0.003352891869237217 }
    /// ```
    pub fn new(a: f64, f: f64) -> Self {
        unsafe {
            let mut g = std::mem::uninitialized::<Geodesic>();
            geod_init(&mut g as *mut Geodesic, a, f);
            g
        }
    }

    /// Compute distance and azimuth from (`lat1`,`lon1`) to (`lat2`,`lon2`)
    ///
    /// # Arguments
    ///   - lat1: Latitude of 1st point [degrees] [-90., 90.]
    ///   - lon1: Longitude of 1st point [degrees] [-180., 180.]
    ///   - lat2: Latitude of 2nd point [degrees] [-90. 90]
    ///   - lon2: Longitude of 2nd point [degrees] [-180., 180.]
    ///
    /// # Returns
    ///   - a12 - Distance from 1st to 2nd point [degrees]
    ///   - s12 - Distance from 1st to 2nd point [degrees]
    ///   - azi1 - Azimuth at 1st point [degrees]
    ///   - azi2 - Azimuth at 2nd point [degrees]
    ///
    /// If either point is at a pole, the azimuth is defined by keeping the
    ///   longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+.
    ///
    /// The solution to the inverse problem is found using Newton's method.
    ///  If this fails to converge (this is very unlikely in geodetic applications
    ///  but does occur for very eccentric ellipsoids), then the bisection method
    ///  is used to refine the solution.
    ///
    /// ```rust
    /// // Example, determine the distance between JFK and Singapore Changi Airport:
    /// use geographiclib::Geodesic;
    /// let g = Geodesic::wgs84();
    /// let (jfk_lat, jfk_lon) = (40.64, -73.78);
    /// let (sin_lat, sin_lon) = (1.36, 103.99);
    /// let (d, m, a1, a2) = g.inverse(jfk_lat, jfk_lon, sin_lat, sin_lon);
    /// assert_eq!(d,  138.0511907301622);  // Distance degrees
    /// assert_eq!(m,  15347512.94051294);  // Distance meters
    /// assert_eq!(a1, 3.3057734780176125); // Azimuth at 1st point
    /// assert_eq!(a2, 177.48784020815515); // Azimuth at 2nd point (forward)
    /// ```
    ///
    pub fn inverse(&self, lat1: f64, lon1: f64, lat2: f64, lon2: f64) -> (f64, f64, f64, f64) {
        let mut ps12  = 0.0;
        let mut pazi1 = 0.0;
        let mut pazi2 = 0.0;
        let a12 = unsafe {
            geod_inverse(self as *const Geodesic,
                         lat1, lon1, lat2, lon2,
                         &mut ps12 as *mut f64,
                         &mut pazi1 as *mut f64,
                         &mut pazi2 as *mut f64)
        };
        (a12, ps12, pazi1, pazi2)
    }
    /// Compute a new location (`lat2`,`lon2`) from (`lat1`,`lon1`) a distance `s12` at an azimuth of `azi1`
    ///
    /// # Arguments
    ///   - lat1 - Latitude of 1st point [degrees] [-90.,90.]
    ///   - lon1 - Longitude of 1st point [degrees] [-180., 180.]
    ///   - azi1 - Azimuth at 1st point [degrees] [-180., 180.]
    ///   - s12 - Distance from 1st to 2nd point [meters] Value may be negative
    ///
    /// # Returns
    ///   - lat2 - Latitude of 2nd point [degrees]
    ///   - lon2 - Longitude of 2nd point [degrees]
    ///   - azi2 - Azimuth at 2nd point
    ///
    /// If either point is at a pole, the azimuth is defined by keeping the
    ///  longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+.
    ///  An arc length greater that 180° signifies a geodesic which is not a
    ///  shortest path. (For a prolate ellipsoid, an additional condition is
    ///  necessary for a shortest path: the longitudinal extent must not
    ///  exceed of 180°.)
    ///
    /// ```rust
    /// // Example, determine the point 10000 km NE of JFK:
    /// use geographiclib::Geodesic;
    /// let g = Geodesic::wgs84();
    /// let (lat,lon,az) = g.direct(40.64, -73.78, 45.0, 10e6);
    /// assert_eq!(lat, 32.621100463725796);
    /// assert_eq!(lon, 49.05248709295982);
    /// assert_eq!(az,  140.4059858768007);
    /// ```
    ///
    pub fn direct(&self, lat1: f64, lon1: f64, azi1: f64, s12: f64) -> (f64, f64, f64) {
        let mut plat2 = 0.0;
        let mut plon2 = 0.0;
        let mut pazi2 = 0.0;
        unsafe {
            geod_direct(self as *const Geodesic,
                        lat1, lon1, azi1, s12,
                        &mut plat2 as &mut f64,
                        &mut plon2 as &mut f64,
                        &mut pazi2 as &mut f64)
        };
        (plat2, plon2, pazi2)
    }
}


#[cfg(test)]
mod tests {

    #[test]
    fn dist_az_test() {
        struct TestCase {
            pub lat1: f64,
            pub lon1: f64,
            pub azi1: f64,
            pub lat2: f64,
            pub lon2: f64,
            pub azi2: f64,
            pub s12: f64,
            pub a12: f64,
            pub m12: f64,
            pub mm12: f64, // M12
            pub mm21: f64, // M21
            pub ss12: f64, // S12
        }
        impl TestCase {
            fn vec(v: &[f64]) -> Self {
                Self { lat1: v[0], lon1: v[1],  azi1: v[2],
                       lat2: v[3], lon2: v[4],  azi2: v[5],
                       s12:  v[6], a12:  v[7],  m12:  v[8],
                       mm12: v[9], mm21: v[10], ss12: v[11]
                }
            }
        }
        
        let testcases = [
            TestCase::vec(&[35.60777, -139.44815, 111.098748429560326,
                            -11.17491, -69.95921, 129.289270889708762,
                            8935244.5604818305, 80.50729714281974,
                            6273170.2055303837,
                            0.16606318447386067, 0.16479116945612937,
                            12841384694976.432]),
            TestCase::vec(&[55.52454, 106.05087, 22.020059880982801,
                            77.03196, 197.18234, 109.112041110671519,
                            4105086.1713924406, 36.892740690445894,
                            3828869.3344387607,
                            0.80076349608092607, 0.80101006984201008,
                            61674961290615.615]),
            TestCase::vec(&[-21.97856, 142.59065, -32.44456876433189,
                            41.84138, 98.56635, -41.84359951440466,
                            8394328.894657671, 75.62930491011522,
                            6161154.5773110616,
                            0.24816339233950381, 0.24930251203627892,
                            -6637997720646.717]),
            TestCase::vec(&[-66.99028, 112.2363, 173.73491240878403,
                            -12.70631, 285.90344, 2.512956620913668,
                            11150344.2312080241, 100.278634181155759,
                            6289939.5670446687,
                            -0.17199490274700385, -0.17722569526345708,
                            -121287239862139.744]),
            TestCase::vec(&[-17.42761, 173.34268, -159.033557661192928,
                            -15.84784, 5.93557, -20.787484651536988,
                            16076603.1631180673, 144.640108810286253,
                            3732902.1583877189,
                            -0.81273638700070476, -0.81299800519154474,
                            97825992354058.708]),
            TestCase::vec(&[32.84994, 48.28919, 150.492927788121982,
                            -56.28556, 202.29132, 48.113449399816759,
                            16727068.9438164461, 150.565799985466607,
                            3147838.1910180939,
                            -0.87334918086923126, -0.86505036767110637,
                            -72445258525585.010]),
            TestCase::vec(&[6.96833, 52.74123, 92.581585386317712,
                            -7.39675, 206.17291, 90.721692165923907,
                            17102477.2496958388, 154.147366239113561,
                            2772035.6169917581,
                            -0.89991282520302447, -0.89986892177110739,
                            -1311796973197.995]),
            TestCase::vec(&[-50.56724, -16.30485, -105.439679907590164,
                            -33.56571, -94.97412, -47.348547835650331,
                            6455670.5118668696, 58.083719495371259,
                            5409150.7979815838,
                            0.53053508035997263, 0.52988722644436602,
                            41071447902810.047]),
            TestCase::vec(&[-58.93002, -8.90775, 140.965397902500679,
                            -8.91104, 133.13503, 19.255429433416599,
                            11756066.0219864627, 105.755691241406877,
                            6151101.2270708536,
                            -0.26548622269867183, -0.27068483874510741,
                            -86143460552774.735]),
            TestCase::vec(&[-68.82867, -74.28391, 93.774347763114881,
                            -50.63005, -8.36685, 34.65564085411343,
                            3956936.926063544, 35.572254987389284,
                            3708890.9544062657,
                            0.81443963736383502, 0.81420859815358342,
                            -41845309450093.787]),
            TestCase::vec(&[-10.62672, -32.0898, -86.426713286747751,
                            5.883, -134.31681, -80.473780971034875,
                            11470869.3864563009, 103.387395634504061,
                            6184411.6622659713,
                            -0.23138683500430237, -0.23155097622286792,
                            4198803992123.548]),
            TestCase::vec(&[-21.76221, 166.90563, 29.319421206936428,
                            48.72884, 213.97627, 43.508671946410168,
                            9098627.3986554915, 81.963476716121964,
                            6299240.9166992283,
                            0.13965943368590333, 0.14152969707656796,
                            10024709850277.476]),
            TestCase::vec(&[-19.79938, -174.47484, 71.167275780171533,
                            -11.99349, -154.35109, 65.589099775199228,
                            2319004.8601169389, 20.896611684802389,
                            2267960.8703918325,
                            0.93427001867125849, 0.93424887135032789,
                            -3935477535005.785]),
            TestCase::vec(&[-11.95887, -116.94513, 92.712619830452549,
                            4.57352, 7.16501, 78.64960934409585,
                            13834722.5801401374, 124.688684161089762,
                            5228093.177931598,
                            -0.56879356755666463, -0.56918731952397221,
                            -9919582785894.853]),
            TestCase::vec(&[-87.85331, 85.66836, -65.120313040242748,
                            66.48646, 16.09921, -4.888658719272296,
                            17286615.3147144645, 155.58592449699137,
                            2635887.4729110181,
                            -0.90697975771398578, -0.91095608883042767,
                            42667211366919.534]),
            TestCase::vec(&[1.74708, 128.32011, -101.584843631173858,
                            -11.16617, 11.87109, -86.325793296437476,
                            12942901.1241347408, 116.650512484301857,
                            5682744.8413270572,
                            -0.44857868222697644, -0.44824490340007729,
                            10763055294345.653]),
            TestCase::vec(&[-25.72959, -144.90758, -153.647468693117198,
                            -57.70581, -269.17879, -48.343983158876487,
                            9413446.7452453107, 84.664533838404295,
                            6356176.6898881281,
                            0.09492245755254703, 0.09737058264766572,
                            74515122850712.444]),
            TestCase::vec(&[-41.22777, 122.32875, 14.285113402275739,
                            -7.57291, 130.37946, 10.805303085187369,
                            3812686.035106021, 34.34330804743883,
                            3588703.8812128856,
                            0.82605222593217889, 0.82572158200920196,
                            -2456961531057.857]),
            TestCase::vec(&[11.01307, 138.25278, 79.43682622782374,
                            6.62726, 247.05981, 103.708090215522657,
                            11911190.819018408, 107.341669954114577,
                            6070904.722786735,
                            -0.29767608923657404, -0.29785143390252321,
                            17121631423099.696]),
            TestCase::vec(&[-29.47124, 95.14681, -163.779130441688382,
                            -27.46601, -69.15955, -15.909335945554969,
                            13487015.8381145492, 121.294026715742277,
                            5481428.9945736388,
                            -0.51527225545373252, -0.51556587964721788,
                            104679964020340.318])
        ];
        let g = crate::Geodesic::wgs84();
        for t in &testcases {
            let (a,s,azi1,azi2) = g.inverse(t.lat1, t.lon1, t.lat2, t.lon2);
            assert!((s - t.s12).abs() < 1e-8, "{} {}", s, t.s12);
            assert!((a - t.a12).abs() < 1e-13, "{} {}", a, t.a12);
            assert!((azi1 - t.azi1).abs() < 1e-13, "{} {}", azi1, t.azi1);
            assert!((azi2 - t.azi2).abs() < 1e-13, "{} {}", azi2, t.azi2);
        }
        let (a,s,az1,az2) = g.inverse(0.0, 0.0, 0.0, 10.0);
        let a0 = 10.033640898209764;
        let s0 = 1113194.9079327357;
        assert!((a - a0).abs() < 1e-8, "{} {}", a, a0);
        assert!((s - s0).abs() < 1e-5, "{} {}", s, s0);
        assert_eq!(az1, 90.0);
        assert_eq!(az2, 90.0);
    }

    #[test]
    fn test_debug() {
        use crate::Geodesic;
        let g = Geodesic::new(6_378_145.0, 1.0/298.25);
        assert_eq!(format!("{}", g), "Geodesic { a: 6378145, f: 0.003352891869237217 }");
    }
}