/*
 * od_math.h -- Orbital determination math: element converters and
 *              inverse coordinate transforms
 *
 * Implements the inverse pipeline for observation-to-TLE fitting:
 *   ECI ↔ Keplerian ↔ equinoctial (Vallado 2008 Eq. 1-5)
 *   Brouwer ↔ Kozai mean motion (inverse of sxpall_common_init)
 *   ECEF → TEME, topocentric → ECEF (inverse coord transforms)
 *
 * All propagation-side constants use WGS-72 from norad_in.h.
 * Coordinate output constants use WGS-84 from types.h.
 */

#ifndef PG_ORRERY_OD_MATH_H
#define PG_ORRERY_OD_MATH_H

#include <math.h>

/*
 * Equinoctial elements (Vallado 2008 Eq. 1-5)
 *
 * Singularity-free for e < 1, i < 180 deg. The DC solver
 * perturbs these instead of classical elements, avoiding
 * ill-conditioned Jacobians near circular or equatorial orbits.
 */
typedef struct
{
    double n;       /* mean motion, rad/min */
    double af;      /* e * cos(omega + RAAN) */
    double ag;      /* e * sin(omega + RAAN) */
    double chi;     /* tan(i/2) * cos(RAAN) */
    double psi;     /* tan(i/2) * sin(RAAN) */
    double L0;      /* mean longitude at epoch: M + omega + RAAN */
    double bstar;   /* drag coefficient (7th state, optional) */
} od_equinoctial_t;

/*
 * Classical Keplerian elements (osculating)
 *
 * Intermediate representation between ECI state vectors
 * and equinoctial elements. All angles in radians.
 */
typedef struct
{
    double n;       /* mean motion, rad/min */
    double ecc;     /* eccentricity */
    double inc;     /* inclination, radians */
    double raan;    /* right ascension of ascending node, radians */
    double argp;    /* argument of perigee, radians */
    double M;       /* mean anomaly at epoch, radians */
    double bstar;   /* drag coefficient */
} od_keplerian_t;

/* ── Element conversion functions ──────────────────────── */

/*
 * ECI state vector (TEME, km, km/s) → classical Keplerian
 *
 * Uses WGS-72 mu (398600.8 km^3/s^2) for consistency with SGP4.
 * Returns 0 on success, -1 on degenerate orbit.
 */
int od_eci_to_keplerian(const double pos[3], const double vel[3],
                        od_keplerian_t *kep);

/*
 * Classical Keplerian → ECI state vector (TEME, km, km/s)
 *
 * Inverse of od_eci_to_keplerian. Uses WGS-72 mu.
 */
void od_keplerian_to_eci(const od_keplerian_t *kep,
                         double pos[3], double vel[3]);

/*
 * Classical Keplerian ↔ equinoctial element conversion
 * (Vallado 2008 Eq. 1-5 and their inverses)
 */
void od_keplerian_to_equinoctial(const od_keplerian_t *kep,
                                 od_equinoctial_t *eq);
void od_equinoctial_to_keplerian(const od_equinoctial_t *eq,
                                 od_keplerian_t *kep);

/*
 * Brouwer ↔ Kozai mean motion conversion
 *
 * TLEs store Kozai mean motion. SGP4 converts to Brouwer internally
 * via sxpall_common_init() (common.c:36-54). We need the inverse
 * to synthesize a TLE from fitted Brouwer elements.
 *
 * Newton-Raphson, converges in 2-4 iterations to |delta| < 1e-14.
 */
double od_kozai_to_brouwer_n(double n_kozai, double ecc, double inc);
double od_brouwer_to_kozai_n(double n_brouwer, double ecc, double inc);

/* ── Inverse coordinate transforms ────────────────────── */

/*
 * ECEF → TEME (inverse of teme_to_ecef in coord_funcs.c:84-105)
 * Rotate by +GMST, add Earth rotation to velocity.
 */
void od_ecef_to_teme(const double pos_ecef[3], const double vel_ecef[3],
                     double gmst,
                     double pos_teme[3], double vel_teme[3]);

/*
 * Topocentric (az, el, range) + observer → ECEF satellite position
 * Inverse of ecef_to_topocentric in coord_funcs.c:165-190.
 *
 * Returns satellite ECEF position in km. Velocity is not recoverable
 * from a single topocentric observation without range rate.
 */
void od_topocentric_to_ecef(double az, double el, double range_km,
                            const double obs_ecef[3],
                            double obs_lat, double obs_lon,
                            double sat_ecef[3]);

/*
 * Observer (WGS-84 lat/lon radians, alt meters) → ECEF vector in km.
 * Duplicated from coord_funcs.c to avoid symbol coupling.
 */
void od_observer_to_ecef(double lat, double lon, double alt_m,
                         double pos_ecef[3]);

/*
 * GMST from Julian date (Vallado Eq. 3-47).
 * Duplicated from coord_funcs.c.
 */
double od_gmst_from_jd(double jd);

/* ── RA/Dec utilities (angles-only mode) ───────────────── */

/*
 * RA/Dec (radians) → unit line-of-sight vector (equatorial TEME).
 */
void od_radec_to_los(double ra, double dec, double los[3]);

/*
 * TEME satellite pos + observer ECEF + GMST → RA/Dec (radians).
 * Computes observer-relative direction in inertial (TEME) frame.
 * TEME ≈ J2000 equatorial for our accuracy needs (~1 arcsec offset
 * from nutation, well below TLE accuracy floor of ~1 km ≈ 20 arcsec at LEO).
 */
void od_teme_to_radec(const double pos_teme[3], const double obs_ecef[3],
                      double gmst, double *ra, double *dec);

/*
 * Normalize angle to [0, 2*pi)
 */
static inline double
od_normalize_angle(double a)
{
    a = fmod(a, 2.0 * M_PI);
    if (a < 0.0)
        a += 2.0 * M_PI;
    return a;
}

#endif /* PG_ORRERY_OD_MATH_H */