"""Tortendiagramm-Segmente (Ausbaustufe 13), rein.

Beträge und Anteile bleiben Decimal; nur die Geometrie (Winkel, SVG-
Koordinaten im Einheitskreis) rechnet mit float. Start 12 Uhr, im
Uhrzeigersinn (SVG-y zeigt nach unten). Große Segmente (> 50 %) werden als
zwei Teilbögen durch Mittelpunkt gezogen, um Rundungsfehler zu vermeiden.
"""
import math
from dataclasses import dataclass
from decimal import ROUND_HALF_UP, Decimal

UEBRIGE = "Übrige"
MIN_SHARE = Decimal("0.03")
MAX_NAMED = 8
PCT = Decimal("0.1")


@dataclass(frozen=True)
class Slice:
    label: str
    value: Decimal
    share: Decimal            # Prozent der Tortenbasis, eine Nachkommastelle
    path: str | None          # SVG-d; None = Vollkreis (einziges Segment)
    color: str                # "s1".."s8", "uebrige", "frei"
    merged: bool
    members: tuple[str, ...]
    start: float              # Anteil 0..1
    end: float


def _point(fraction: float) -> tuple[float, float]:
    angle = 2 * math.pi * fraction - math.pi / 2
    return math.cos(angle), math.sin(angle)


def _arc(start: float, end: float) -> str:
    x0, y0 = _point(start)
    x1, y1 = _point(end)
    if end - start > 0.5:
        # Großes Segment: zwei Teilbögen durch Mittelpunkt, um Rundungsfehler zu vermeiden
        mid = (start + end) / 2
        xm, ym = _point(mid)
        return f"M 0 0 L {x0:.4f} {y0:.4f} A 1 1 0 0 1 {xm:.4f} {ym:.4f} A 1 1 0 0 1 {x1:.4f} {y1:.4f} Z"
    else:
        return f"M 0 0 L {x0:.4f} {y0:.4f} A 1 1 0 0 1 {x1:.4f} {y1:.4f} Z"


def pie_slices(values: list[tuple[str, Decimal]], rest: Decimal | None = None,
               rest_label: str = "", min_share: Decimal = MIN_SHARE,
               max_named: int = MAX_NAMED) -> list[Slice]:
    items = sorted(((l, v) for l, v in values if v > 0), key=lambda lv: (-lv[1], lv[0]))
    rest = rest if rest is not None and rest > 0 else None
    total = sum((v for _, v in items), Decimal("0")) + (rest or Decimal("0"))
    if total <= 0:
        return []
    named: list[tuple[str, Decimal]] = []
    small: list[tuple[str, Decimal]] = []
    for label, value in items:
        if len(named) < max_named and value / total >= min_share:
            named.append((label, value))
        else:
            small.append((label, value))
    parts = [(l, v, f"s{i}", False, ()) for i, (l, v) in enumerate(named, 1)]
    if len(small) == 1:
        parts.append((small[0][0], small[0][1], "uebrige", False, ()))
    elif small:
        parts.append((UEBRIGE, sum((v for _, v in small), Decimal("0")), "uebrige",
                      True, tuple(l for l, _ in small)))
    if rest is not None:
        parts.append((rest_label, rest, "frei", False, ()))
    slices: list[Slice] = []
    acc = Decimal("0")
    for label, value, color, merged, members in parts:
        start = float(acc / total)
        acc += value
        end = float(acc / total)
        slices.append(Slice(label, value,
                            (value * 100 / total).quantize(PCT, ROUND_HALF_UP),
                            None if len(parts) == 1 else _arc(start, end),
                            color, merged, members, start, end))
    return slices