feat: unified 0 and 90 degree PDF envelope and category descriptors

app/src/lib/bilinear-interp.ts

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+/**
+ * Interpolação bilinear 2D conforme plano técnico (sec. 3.2).
+ *
+ * Dados quatro pontos Q₁₁(x₁,y₁), Q₁₂(x₁,y₂), Q₂₁(x₂,y₁), Q₂₂(x₂,y₂),
+ * estima f(x,y) por:
+ *   f ≈ ((x₂-x)(y₂-y)·f₁₁ + (x-x₁)(y₂-y)·f₂₁ + (x₂-x)(y-y₁)·f₁₂ + (x-x₁)(y-y₁)·f₂₂) /
+ *       ((x₂-x₁)(y₂-y₁))
+ *
+ * Aceita x fora do intervalo por extrapolação linear (clamp opcional).
+ */
+
+export type Grid2D = {
+  xs: readonly number[];
+  ys: readonly number[];
+  values: readonly (readonly number[])[];
+};
+
+function findBracket(xs: readonly number[], x: number): [number, number, boolean] {
+  const clamped = Math.max(xs[0], Math.min(x, xs[xs.length - 1]));
+  const extrapolated = clamped !== x;
+  if (xs.length === 1) return [0, 0, extrapolated];
+  if (clamped >= xs[xs.length - 1]) {
+    return [xs.length - 2, xs.length - 1, extrapolated];
+  }
+  for (let i = 0; i < xs.length - 1; i++) {
+    const a = xs[i];
+    const b = xs[i + 1];
+    if (clamped >= a && clamped <= b) {
+      return [i, i + 1, extrapolated];
+    }
+  }
+  return [0, xs.length - 1, extrapolated];
+}
+
+export function bilinearInterp(grid: Grid2D, x: number, y: number): number {
+  const { xs, ys, values } = grid;
+
+  const [ix0, ix1] = findBracket(xs, x);
+  const [iy0, iy1] = findBracket(ys, y);
+
+  const x1 = xs[ix0];
+  const x2 = xs[ix1];
+  const y1 = ys[iy0];
+  const y2 = ys[iy1];
+
+  const f11 = values[iy0][ix0];
+  const f21 = values[iy0][ix1];
+  const f12 = values[iy1][ix0];
+  const f22 = values[iy1][ix1];
+
+  const dx = x2 - x1;
+  const dy = y2 - y1;
+  if (dx === 0 || dy === 0) return f11;
+
+  const denom = dx * dy;
+  const num =
+    (x2 - x) * (y2 - y) * f11 +
+    (x - x1) * (y2 - y) * f21 +
+    (x2 - x) * (y - y1) * f12 +
+    (x - x1) * (y - y1) * f22;
+
+  return num / denom;
+}