38 lines
1.6 KiB
Python
38 lines
1.6 KiB
Python
"""问题二算例：随机首次示向度（全向源）。"""
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from __future__ import annotations
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import math
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import random
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from mcm26b.config import ProblemConfig
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def random_case(seed: int, config: ProblemConfig | None = None) -> dict:
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"""随机检测点 s 与示向度 θ：默认让真源与读数一致（误差 ±1° 内）。"""
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config = config or ProblemConfig()
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rng = random.Random(seed)
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radius = config.field.omega_radius_m
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# 检测点可在目标域内或域外；这里取域内，符合题目常规场景
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angle_s = rng.uniform(0, 2 * math.pi)
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distance_s = radius * math.sqrt(rng.random()) * 0.9
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station = (distance_s * math.cos(angle_s), distance_s * math.sin(angle_s))
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# 真源与检测点距离落在 [60, 1500) 且仍在 Ω 内
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while True:
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bearing_true = rng.uniform(0, 2 * math.pi)
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source_distance = rng.uniform(60, config.field.r_eff_max_m - 1)
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target = (station[0] + source_distance * math.cos(bearing_true),
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station[1] + source_distance * math.sin(bearing_true))
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if math.hypot(*target) <= radius:
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break
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error = math.radians(rng.uniform(-0.95, 0.95))
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bearing_deg = math.degrees(bearing_true + error) % 360.0
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return {"id": f"q2-{seed}", "station": [round(station[0], 2), round(station[1], 2)],
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"bearing_deg": round(bearing_deg, 2), "half_angle_deg": 1.0,
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"true_source": [round(target[0], 2), round(target[1], 2)]}
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def random_cases(count: int, base_seed: int = 4200,
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config: ProblemConfig | None = None) -> list[dict]:
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return [random_case(base_seed + index, config) for index in range(count)]
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