"""Fast 2D LiDAR simulator for the Gymnasium env.

Raycasts against sheep (discs) and static world geometry. For rectangular
fields this is axis-aligned walls + gate posts; for round fields it is a
circular wall + gate posts. The env reproduces the false-positive cluster
distribution Webots produces from real 3D geometry.

Returns a range array matching the Webots Lidar device:
180 rays, 140° FOV centred on forward, 12 m max range, 5 mm noise.
See ``protos/ShepherdDog.proto``.
"""

from __future__ import annotations

import math

import numpy as np

from herding.world.geometry import (
    FIELD_SHAPE, FIELD_ROUND_R,
    FIELD_X, FIELD_Y,
    GATE_X, GATE_Y,
    PEN_X, PEN_Y,
)


# Match protos/ShepherdDog.proto Lidar device — extended to 360° for
# full situational awareness. The original Webots device is 140° FOV /
# 180 rays; we use 360 rays for full-circle coverage.
LIDAR_N_RAYS = 360
LIDAR_FOV = 2.0 * math.pi  # 360° full circle
LIDAR_MAX_RANGE = 12.0
LIDAR_NOISE = 0.005    # m, gaussian std

# Sheep cross-section in the LiDAR plane (horizontal cylinder approx).
SHEEP_RADIUS = 0.30
POST_RADIUS = 0.25


# ---------------------------------------------------------------------------
# Rectangular-field static geometry
# ---------------------------------------------------------------------------
_VERTICAL_WALLS_RECT = (
    ( 15.0, -15.0,  15.0),  # field east
    (-15.0, -15.0,  15.0),  # field west
    ( 10.0, -22.0, -15.0),  # pen west
    ( 13.0, -22.0, -15.0),  # pen east
)

_HORIZONTAL_WALLS_RECT = (
    ( 15.0, -15.0,  15.0),  # field north
    (-15.0, -15.0,  10.0),  # field south-west of gate
    (-15.0,  13.0,  15.0),  # field south-east of gate
    (-22.0,  10.0,  13.0),  # pen south
)

_POSTS_RECT = np.array([
    ( 10.0, -15.0), ( 13.0, -15.0),
    ( 15.0,  15.0), ( 15.0, -15.0),
    (-15.0,  15.0), (-15.0, -15.0),
], dtype=np.float64)


# ---------------------------------------------------------------------------
# Round-field static geometry
# ---------------------------------------------------------------------------
# Circular wall with gate gap. Gate posts at the edges of the gate gap.
_gate_cx = 0.5 * (GATE_X[0] + GATE_X[1])
_POSTS_ROUND = np.array([
    (GATE_X[0], GATE_Y),
    (GATE_X[1], GATE_Y),
], dtype=np.float64)

# Pen walls for round field
_VERTICAL_WALLS_ROUND = (
    (GATE_X[0], PEN_Y[0], GATE_Y),   # pen west
    (GATE_X[1], PEN_Y[0], GATE_Y),   # pen east
)
_HORIZONTAL_WALLS_ROUND = (
    (PEN_Y[0], GATE_X[0], GATE_X[1]),  # pen south
)


def _build_static_geometry():
    """Select the correct static geometry for the active field shape."""
    if FIELD_SHAPE == "field_round":
        return (
            _VERTICAL_WALLS_ROUND,
            _HORIZONTAL_WALLS_ROUND,
            _POSTS_ROUND,
            FIELD_ROUND_R,
        )
    return (
        _VERTICAL_WALLS_RECT,
        _HORIZONTAL_WALLS_RECT,
        _POSTS_RECT,
        None,  # no circular wall
    )


_VERTS, _HORIZS, _POSTS, _CIRC_R = _build_static_geometry()


# ---------------------------------------------------------------------------
# Ray helpers
# ---------------------------------------------------------------------------
def ray_angles(n: int = LIDAR_N_RAYS, fov: float = LIDAR_FOV) -> np.ndarray:
    """Local-frame ray angles, CCW from forward, sweeping +fov/2 → -fov/2."""
    return np.linspace(fov / 2.0, -fov / 2.0, n, dtype=np.float64)


_ANGLES = ray_angles()
_COS = np.cos(_ANGLES)
_SIN = np.sin(_ANGLES)


def _raycast_static(
    ox: float, oy: float, cos_w: np.ndarray, sin_w: np.ndarray,
) -> np.ndarray:
    """Per-ray distance to the nearest wall or post hit (∞ if none)."""
    n_rays = cos_w.shape[0]
    best = np.full(n_rays, np.inf, dtype=np.float64)

    EPS = 1e-3
    safe_cos = np.where(np.abs(cos_w) < 1e-9, 1e-9, cos_w)
    safe_sin = np.where(np.abs(sin_w) < 1e-9, 1e-9, sin_w)

    # Vertical walls (x = const)
    for wx, ymin, ymax in _VERTS:
        t = (wx - ox) / safe_cos
        y_at = oy + t * sin_w
        valid = (t > EPS) & (y_at >= ymin - EPS) & (y_at <= ymax + EPS)
        cand = np.where(valid, t, np.inf)
        np.minimum(best, cand, out=best)

    # Horizontal walls (y = const)
    for wy, xmin, xmax in _HORIZS:
        t = (wy - oy) / safe_sin
        x_at = ox + t * cos_w
        valid = (t > EPS) & (x_at >= xmin - EPS) & (x_at <= xmax + EPS)
        cand = np.where(valid, t, np.inf)
        np.minimum(best, cand, out=best)

    # Circular wall (round field only)
    if _CIRC_R is not None:
        # Ray: P(t) = O + t·D.  ||P(t)||² = R²
        # t² - 2t(O·D) + (||O||² - R²) = 0
        # a = 1 (rays are unit), b = -2(O·D), c = ||O||² - R²
        a = 1.0  # cos_w² + sin_w² = 1
        b = -(ox * cos_w + oy * sin_w)
        c = ox * ox + oy * oy - _CIRC_R * _CIRC_R
        disc = b * b - a * c
        valid_disc = disc >= 0.0
        sqrt_disc = np.sqrt(np.maximum(disc, 0.0))
        # Two intersection candidates: t = (-b ± sqrt(disc)) / a
        t1 = -b - sqrt_disc
        t2 = -b + sqrt_disc
        # We want the smallest positive t.
        t1_valid = valid_disc & (t1 > EPS)
        t2_valid = valid_disc & (t2 > EPS)
        t_circ = np.where(t1_valid, t1, np.where(t2_valid, t2, np.inf))

        # Exclude rays that hit the gate gap: the hit point must not lie
        # in the gate column (between GATE_X and above GATE_Y).
        hx = ox + t_circ * cos_w
        hy = oy + t_circ * sin_w
        in_gate = ((hx > GATE_X[0]) & (hx < GATE_X[1]) &
                   (hy > GATE_Y - 2.0) & (hy < GATE_Y + 2.0))
        t_circ = np.where(in_gate, np.inf, t_circ)
        np.minimum(best, t_circ, out=best)

    # Posts (treat as discs)
    if _POSTS.size:
        px = _POSTS[:, 0] - ox
        py = _POSTS[:, 1] - oy
        t_post = np.outer(px, cos_w) + np.outer(py, sin_w)
        d2 = (px ** 2 + py ** 2)[:, None]
        perp2 = d2 - t_post ** 2
        R2 = POST_RADIUS ** 2
        hit = (perp2 < R2) & (t_post > 0.0)
        half = np.sqrt(np.clip(R2 - perp2, 0.0, None))
        cand = np.where(hit, t_post - half, np.inf)
        nearest = cand.min(axis=0)
        np.minimum(best, nearest, out=best)

    return best


def simulate_scan(
    dog_x: float, dog_y: float, dog_heading: float,
    sheep_xy: list[tuple[float, float]],
    noise: float = LIDAR_NOISE,
    max_range: float = LIDAR_MAX_RANGE,
    rng: np.random.Generator | None = None,
) -> np.ndarray:
    """Return a (N,) float32 range array. No-hit entries equal ``max_range``.

    ``sheep_xy`` is every sheep (penned or active) in the scene.
    """
    ch, sh = math.cos(dog_heading), math.sin(dog_heading)
    cos_w = ch * _COS - sh * _SIN
    sin_w = sh * _COS + ch * _SIN

    best = _raycast_static(dog_x, dog_y, cos_w, sin_w)

    if sheep_xy:
        sx = np.asarray([p[0] for p in sheep_xy], dtype=np.float64) - dog_x
        sy = np.asarray([p[1] for p in sheep_xy], dtype=np.float64) - dog_y
        t = np.outer(sx, cos_w) + np.outer(sy, sin_w)
        s_dist2 = (sx ** 2 + sy ** 2)[:, None]
        perp2 = s_dist2 - t ** 2
        R2 = SHEEP_RADIUS ** 2
        hit = (perp2 < R2) & (t > 0.0)
        half = np.sqrt(np.clip(R2 - perp2, 0.0, None))
        candidate = np.where(hit, t - half, np.inf)
        nearest = candidate.min(axis=0)
        np.minimum(best, nearest, out=best)

    ranges = np.minimum(best, max_range).astype(np.float32)
    return _add_noise(ranges, noise, rng, max_range)


def _add_noise(ranges: np.ndarray, sigma: float,
               rng: np.random.Generator | None, max_range: float) -> np.ndarray:
    if sigma <= 0.0:
        return ranges
    if rng is None:
        rng = np.random.default_rng()
    hit_mask = ranges < max_range - 1e-3
    n_hit = int(hit_mask.sum())
    if n_hit:
        ranges = ranges.copy()
        ranges[hit_mask] += rng.normal(0.0, sigma, size=n_hit).astype(np.float32)
        np.clip(ranges, 0.0, max_range, out=ranges)
    return ranges