"""Distance certificates for Q2; does not change Q1's angular polygon model."""

from math import cos, sin, radians, isfinite
from .localization import Measurement


def first_bearing_candidate_disk(measurement: Measurement,
                                 max_range_m: float = 1500,
                                 guaranteed_range_m: float = 1000) -> dict:
    """Enclose the entire truncated first-bearing sector, then erode its disk.

    For half-angle <=45 degrees the sector MEC has center distance and radius
    a=R/(2*cos(delta)). Intersecting with Omega only shrinks the source set.
    A missing sufficient disk is NOT proof that Q is empty. The certificate
    guarantees distance only: directional transmitters may still be invisible.
    """
    if any(isinstance(v, bool) or not isinstance(v, (int, float)) or not isfinite(v)
           or v <= 0 for v in (max_range_m, guaranteed_range_m)):
        raise ValueError("接收半径必须为有限正数")
    if measurement.half_angle_deg > 45:
        raise ValueError("此窄角域证书仅支持半角不超过45度；题设为1度")
    delta, theta = radians(measurement.half_angle_deg), radians(measurement.bearing_deg % 360)
    a = max_range_m/(2*cos(delta))
    center = [measurement.x+a*cos(theta), measurement.y+a*sin(theta)]
    available = guaranteed_range_m-a
    return {"source_model": "first_bearing_sector_with_range_upper_bound",
            "sector_enclosing_circle": {"center": center, "radius_m": a},
            "sufficient_candidate_disk": {"center": center, "radius_m": available}
                if available >= 0 else None,
            "candidate_nonempty_certified": available >= 0,
            "distance_only": True,
            "max_range_m": max_range_m, "guaranteed_range_m": guaranteed_range_m}