"""Geometry of the SimurgArray mark on its dot grid (no dependencies beyond the standard library).

A frontal simurg with raised wings (three feathers each), a three-dot crown and three tail plumes: red channel,
gold, green channel, each ending in a peacock eye. Shapes are capsules, circles and an ellipse in grid units; a cell
belongs to the first shape that contains its centre. ``SIMPLE`` and ``MICRO`` are hand-drawn small versions.
"""

from __future__ import annotations

import math
from typing import Any


def _seg(px: float, py: float, a: tuple[float, float], b: tuple[float, float]) -> float:
    dx, dy = b[0] - a[0], b[1] - a[1]
    t = max(0.0, min(1.0, ((px - a[0]) * dx + (py - a[1]) * dy) / ((dx * dx + dy * dy) or 1.0)))
    return math.hypot(px - a[0] - t * dx, py - a[1] - t * dy)


CX = 15.5
_WING = [([(13.6, 9.6), (8, 5.2), (1.8, 1.4)], 1.25), ([(13.4, 11), (7.5, 8.4), (1.2, 6.6)], 1.25),
         ([(13.4, 12.6), (8, 12), (2.6, 11.8)], 1.2)]  # fmt: skip
SHAPES: list[tuple[str, Any, str]] = []
for pts, r in _WING:
    SHAPES.append(("cap", (pts, r), "gold"))
    SHAPES.append(("cap", ([(2 * CX - x, y) for x, y in pts], r), "gold"))
SHAPES += [
    ("circ", (CX, 4.4, 2.3), "gold"), ("cap", ([(CX, 6), (CX, 8)], 1.3), "gold"),  # head, neck
    ("circ", (CX, 1.2, 0.62), "gold"), ("circ", (13.6, 1.9, 0.62), "gold"), ("circ", (17.4, 1.9, 0.62), "gold"),
    ("ell", (CX, 12.5, 2.9, 5.4), "gold"),  # body
    ("cap", ([(14.8, 17), (12.6, 20.5), (10.4, 23.2)], 0.7), "red"), ("circ", (10, 24.3, 1.6), "red"),
    ("cap", ([(CX, 17.5), (CX, 23.2)], 0.7), "gold"), ("circ", (CX, 24.6, 1.6), "gold"),
    ("cap", ([(16.2, 17), (18.4, 20.5), (20.6, 23.2)], 0.7), "green"), ("circ", (21, 24.3, 1.6), "green"),
]  # fmt: skip
DETAILED_SIZE = (31, 27)
SIMPLE = """
X.........X
XX.......XX
.XX..X..XX.
..XXXXXXX..
XXXXXXXXXXX
...XXXXX...
....XXX....
...R.X.G...
..R..X..G..
.RR.XXX.GG.
"""
MICRO = """
X.....X
XX.X.XX
.XXXXX.
..XXX..
...X...
.R.X.G.
R..X..G
"""
Grid = dict[tuple[int, int], str]


def _inside(x: float, y: float, kind: str, p: Any) -> bool:
    if kind == "circ":
        return math.hypot(x - p[0], y - p[1]) <= p[2]
    if kind == "cap":
        pts, r = p
        return min(_seg(x, y, pts[i], pts[i + 1]) for i in range(len(pts) - 1)) <= r
    cx, cy, rx, ry = p
    return ((x - cx) / rx) ** 2 + ((y - cy) / ry) ** 2 <= 1


def detailed() -> tuple[Grid, int, int]:
    cols, rows = DETAILED_SIZE
    g: Grid = {}
    for r in range(rows):
        for c in range(cols):
            for kind, p, layer in SHAPES:
                if _inside(c + 0.5, r + 0.5, kind, p):
                    g[(c, r)] = layer
                    break
    return g, cols, rows


def art(s: str) -> tuple[Grid, int, int]:
    lines = s.strip().splitlines()
    g = {(c, r): {"X": "gold", "R": "red", "G": "green"}[ch] for r, ln in enumerate(lines) for c, ch in enumerate(ln)
         if ch != "."}  # fmt: skip
    return g, len(lines[0]), len(lines)