feat: Engine pie – Tortensegmente mit Übrige-Regel und SVG-Pfaden (A13-T3)

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

finance/app/engine/pie.py

@@ -0,0 +1,75 @@
+"""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).
+"""
+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)
+    large = 1 if end - start > 0.5 else 0
+    return f"M 0 0 L {x0:.4f} {y0:.4f} A 1 1 0 {large} 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