"""Coordinate conversion helpers used by dataset adapters.

- `ecef_to_wgs84`: closed-form Zhu/Heikkinen conversion (no iteration), accurate
  to centimetres for any point above the Earth's surface.
- `euler_to_quaternion`: aerospace ZYX intrinsic convention (yaw → pitch → roll
  applied to body frame in that order). Inputs in radians.
"""

from __future__ import annotations

import math

# WGS84 constants
_A = 6_378_137.0                 # semi-major axis, metres
_F = 1.0 / 298.257223563         # flattening
_B = _A * (1.0 - _F)             # semi-minor axis
_E2 = 1.0 - (_B * _B) / (_A * _A)   # first eccentricity squared
_EP2 = (_A * _A) / (_B * _B) - 1.0  # second eccentricity squared


def ecef_to_wgs84(x: float, y: float, z: float) -> tuple[float, float, float]:
    """ECEF (metres) → WGS84 (lat° N, lon° E, altitude metres above ellipsoid).

    Uses Heikkinen's closed-form method — no iteration, one pass, centimetre
    accuracy for any realistic aerial vehicle altitude.
    """
    r = math.sqrt(x * x + y * y)
    if r == 0.0:
        # Pole: lon is conventionally 0, lat is ±90 depending on sign of z
        lat = 90.0 if z >= 0 else -90.0
        alt = abs(z) - _B
        return lat, 0.0, alt

    ee = _A * _A - _B * _B
    f = 54.0 * _B * _B * z * z
    g = r * r + (1.0 - _E2) * z * z - _E2 * ee
    c = (_E2 * _E2 * f * r * r) / (g * g * g)
    s = (1.0 + c + math.sqrt(c * c + 2.0 * c)) ** (1.0 / 3.0)
    p = f / (3.0 * (s + 1.0 / s + 1.0) ** 2 * g * g)
    q = math.sqrt(1.0 + 2.0 * _E2 * _E2 * p)
    r0 = -(p * _E2 * r) / (1.0 + q) + math.sqrt(
        0.5 * _A * _A * (1.0 + 1.0 / q)
        - (p * (1.0 - _E2) * z * z) / (q * (1.0 + q))
        - 0.5 * p * r * r
    )
    u = math.sqrt((r - _E2 * r0) ** 2 + z * z)
    v = math.sqrt((r - _E2 * r0) ** 2 + (1.0 - _E2) * z * z)
    z0 = (_B * _B * z) / (_A * v)

    lat = math.degrees(math.atan((z + _EP2 * z0) / r))
    lon = math.degrees(math.atan2(y, x))
    alt = u * (1.0 - (_B * _B) / (_A * v))
    return lat, lon, alt


def euler_to_quaternion(
    roll: float, pitch: float, yaw: float
) -> tuple[float, float, float, float]:
    """Aerospace ZYX intrinsic Euler → (qx, qy, qz, qw).

    Rotation order: yaw (about world z) → pitch (about intermediate y) → roll
    (about body x). All inputs in radians. Output quaternion has unit norm.
    """
    cr = math.cos(roll * 0.5)
    sr = math.sin(roll * 0.5)
    cp = math.cos(pitch * 0.5)
    sp = math.sin(pitch * 0.5)
    cy = math.cos(yaw * 0.5)
    sy = math.sin(yaw * 0.5)

    qw = cr * cp * cy + sr * sp * sy
    qx = sr * cp * cy - cr * sp * sy
    qy = cr * sp * cy + sr * cp * sy
    qz = cr * cp * sy - sr * sp * cy
    return qx, qy, qz, qw