Aislo/E06_StabRock/E06_StabRock_Stereonet.py

"""E06 스테레오넷 투영 좌표 — 하반구 · 등각(Wulff) · 등면적(Schmidt) (PLAN 536-1).

화면(SVG)은 이 좌표를 그리기만 함 — 반지름 1 원 · x = 동 · y = 북(화면은 y 를 뒤집음).
극점 · 대원 · 교선 · 마찰원 · 일광 엔벨로프 · 위험 영역(Markland 부등식과 같은 경계 —
`E06_StabRock_Engine.kinematic`)을 냄. 투영식 = 표준 구면 투영(mplstereonet 등은 대조만).
"""

from __future__ import annotations

import math
from typing import Any

from E06_StabRock.E06_StabRock_Engine import (
    LATERAL_PLANAR_DEG,
    LATERAL_TOPPLING_DEG,
    apparent_dip,
    intersection,
    pole,
)

PROJECTIONS = ("equal_angle", "equal_area")
STEP_DEG = 2.0  # 곡선 표본 간격


def radius(plunge: float, kind: str) -> float:
    """선주각 → 중심에서 거리(0 = 연직 · 1 = 수평)."""
    half = math.radians(90.0 - plunge) / 2.0
    return math.tan(half) if kind == "equal_angle" else math.sqrt(2.0) * math.sin(half)


def project(trend: float, plunge: float, kind: str) -> list[float]:
    r = radius(plunge, kind)
    t = math.radians(trend)
    return [round(r * math.sin(t), 5), round(r * math.cos(t), 5)]


def inverse(x: float, y: float, kind: str) -> tuple[float, float]:
    """투영 좌표 → (추향 · 선주각) — 왕복 시험 · 화면 마우스 자리 읽기."""
    r = math.hypot(x, y)
    half = math.atan(r) if kind == "equal_angle" else math.asin(min(1.0, r / math.sqrt(2.0)))
    return math.degrees(math.atan2(x, y)) % 360.0, 90.0 - math.degrees(2.0 * half)


def _samples(lo: float, hi: float) -> list[float]:
    n = max(2, int(math.ceil((hi - lo) / STEP_DEG)) + 1)
    return [lo + (hi - lo) * k / (n - 1) for k in range(n)]


def great_circle(dip_dir: float, dip: float, kind: str) -> list[list[float]]:
    """면의 대원 — 주향 한끝 → 경사 방향 → 다른 끝."""
    return [
        project(dip_dir + b, max(0.0, apparent_dip(dip, dip_dir, dip_dir + b)), kind)
        for b in _samples(-90.0, 90.0)
    ]


def _zone(trend_lo, trend_hi, plunge_lo, plunge_hi, kind) -> list[list[float]] | None:
    """(추향 · 선주각) 띠 → 닫힌 다각형 — plunge_lo/hi 는 추향의 함수 · 비면 None."""
    ts = _samples(trend_lo, trend_hi)
    lows = [plunge_lo(t) for t in ts]
    highs = [plunge_hi(t) for t in ts]
    keep = [k for k in range(len(ts)) if highs[k] > lows[k]]
    if len(keep) < 2:
        return None
    outer = [project(ts[k], lows[k], kind) for k in keep]
    inner = [project(ts[k], highs[k], kind) for k in reversed(keep)]
    return outer + inner


def stereonet(
    slope: dict,
    joints: list[dict],
    phi: float,
    kind: str = "equal_angle",
    lateral_planar: float = LATERAL_PLANAR_DEG,
    lateral_toppling: float = LATERAL_TOPPLING_DEG,
) -> dict[str, Any]:
    """slope = {dip_direction, dip} · joints = [{id, dip_direction, dip}] · phi = 영역 마찰각."""
    af, pf = float(slope["dip_direction"]), float(slope["dip"])

    def face_app(t: float) -> float:
        return apparent_dip(pf, af, t)

    planes = []
    for j in joints:
        tr, pl = pole(j["dip_direction"], j["dip"])
        planes.append(
            {
                "id": j["id"],
                "pole": project(tr, pl, kind),
                "great_circle": great_circle(j["dip_direction"], j["dip"], kind),
            }
        )
    lines = []
    for i, a in enumerate(joints):
        for b in joints[i + 1 :]:
            line = intersection(a, b)
            if line is not None:
                lines.append({"ids": [a["id"], b["id"]], "point": project(*line, kind)})
    # 일광 엔벨로프(극점 꼴) = 사면 겉보기 경사로 기운 면들의 극점
    envelope = [
        project(af + b + 180.0, 90.0 - face_app(af + b), kind) for b in _samples(-90.0, 90.0)
    ]
    zones = {
        # 평면(극점) — 극점 추향 αf + 180 ± 측방 · 선주각 90 − ψapp ~ 90 − φ
        "planar": _zone(
            af + 180.0 - lateral_planar,
            af + 180.0 + lateral_planar,
            lambda t: 90.0 - face_app(t - 180.0),
            lambda t: 90.0 - phi,
            kind,
        ),
        # 쐐기(교선) — 추향 αf ± 90 · 선주각 φ ~ ψapp
        "wedge": _zone(af - 90.0, af + 90.0, lambda t: phi, face_app, kind),
        # 전도(극점) — 극점 추향 αf ± 측방 · 선주각 0 ~ ψf − φ
        "toppling": _zone(
            af - lateral_toppling,
            af + lateral_toppling,
            lambda t: 0.0,
            lambda t: pf - phi,
            kind,
        ),
    }
    return {
        "projection": kind,
        "slope": {
            "pole": project(*pole(af, pf), kind),
            "great_circle": great_circle(af, pf, kind),
        },
        "planes": planes,
        "intersections": lines,
        # 마찰원 — 극점 꼴 = 중심에서 φ(선주각 90 − φ) · 교선 꼴 = 선주각 φ
        "friction_pole_r": round(radius(90.0 - phi, kind), 5),
        "friction_line_r": round(radius(phi, kind), 5),
        "daylight_envelope": envelope,
        "zones": zones,
    }