"""
Reference-frame transitions for patched-conics SOI handling.

When a body enters a planet's sphere of influence its orbital
elements must be re-expressed relative to the planet.  On exit
the reverse transition occurs.
"""

from typing import Tuple

from orbital_elements import OrbitalElements, orbital_elements_from_cartesian


def sun_state_to_planet_orbit(
    body_x: float,
    body_y: float,
    body_vx: float,
    body_vy: float,
    planet_x: float,
    planet_y: float,
    planet_vx: float,
    planet_vy: float,
    mu_planet: float,
    epoch: float,
) -> OrbitalElements:
    """
    Convert a body's sun-frame state to a planet-relative orbit.

    Parameters
    ----------
    body_*  — body position & velocity in sun frame
    planet_* — planet position & velocity in sun frame
    mu_planet — planet's gravitational parameter
    epoch — time of transition

    Returns
    -------
    OrbitalElements describing the body's trajectory around the planet.
    """
    x_rel = body_x - planet_x
    y_rel = body_y - planet_y
    vx_rel = body_vx - planet_vx
    vy_rel = body_vy - planet_vy
    return orbital_elements_from_cartesian(
        x_rel, y_rel, vx_rel, vy_rel, mu_planet, epoch,
    )


def planet_orbit_to_sun_state(
    orbit_planet: OrbitalElements,
    planet_x: float,
    planet_y: float,
    planet_vx: float,
    planet_vy: float,
    t: float,
) -> Tuple[float, float, float, float]:
    """
    Convert a planet-relative orbit back to sun-frame state at time t.

    Returns (x, y, vx, vy) in sun frame.
    """
    x_rel, y_rel, vx_rel, vy_rel = orbit_planet.compute_state_at(t)
    return (
        x_rel + planet_x,
        y_rel + planet_y,
        vx_rel + planet_vx,
        vy_rel + planet_vy,
    )


def planet_orbit_to_sun_orbit(
    orbit_planet: OrbitalElements,
    planet_x: float,
    planet_y: float,
    planet_vx: float,
    planet_vy: float,
    mu_sun: float,
    t: float,
) -> OrbitalElements:
    """
    Full round-trip: planet-relative orbit → sun-frame orbital elements.

    Used after SOI exit to put the body back into a heliocentric orbit.
    """
    x_sun, y_sun, vx_sun, vy_sun = planet_orbit_to_sun_state(
        orbit_planet, planet_x, planet_y, planet_vx, planet_vy, t,
    )
    return orbital_elements_from_cartesian(
        x_sun, y_sun, vx_sun, vy_sun, mu_sun, t,
    )