// Shared utilities for mq_editor

// Evaluate interpolating curve at time t via Lagrange interpolation.
// The curve passes through all 4 control points at their stored time positions.
// Knot positions: u_k = (t_k - t0) / (t3 - t0), k=0..3.
// TODO: support arbitrary number of inner control points
function evalBezier(curve, t) {
  const dt = curve.t3 - curve.t0;
  if (dt <= 0) return curve.v0;
  let u = (t - curve.t0) / dt;
  u = Math.max(0, Math.min(1, u));
  const u1 = (curve.t1 - curve.t0) / dt;
  const u2 = (curve.t2 - curve.t0) / dt;
  const d0 = (-u1) * (-u2) * (-1);
  const d1 = u1 * (u1 - u2) * (u1 - 1);
  const d2 = u2 * (u2 - u1) * (u2 - 1);
  const d3 = (1 - u1) * (1 - u2);
  if (Math.abs(d0) < 1e-9 || Math.abs(d1) < 1e-9 || Math.abs(d2) < 1e-9 || Math.abs(d3) < 1e-9)
    return curve.v0 + (curve.v3 - curve.v0) * u;
  const l0 = (u - u1) * (u - u2) * (u - 1) / d0;
  const l1 = u * (u - u2) * (u - 1) / d1;
  const l2 = u * (u - u1) * (u - 1) / d2;
  const l3 = u * (u - u1) * (u - u2) / d3;
  return l0 * curve.v0 + l1 * curve.v1 + l2 * curve.v2 + l3 * curve.v3;
}

// Evaluate amplitude component of interpolating curve at time t
function evalBezierAmp(curve, t) {
  const dt = curve.t3 - curve.t0;
  if (dt <= 0) return curve.a0;
  let u = (t - curve.t0) / dt;
  u = Math.max(0, Math.min(1, u));
  const u1 = (curve.t1 - curve.t0) / dt;
  const u2 = (curve.t2 - curve.t0) / dt;
  const d0 = (-u1) * (-u2) * (-1);
  const d1 = u1 * (u1 - u2) * (u1 - 1);
  const d2 = u2 * (u2 - u1) * (u2 - 1);
  const d3 = (1 - u1) * (1 - u2);
  if (Math.abs(d0) < 1e-9 || Math.abs(d1) < 1e-9 || Math.abs(d2) < 1e-9 || Math.abs(d3) < 1e-9)
    return curve.a0 + (curve.a3 - curve.a0) * u;
  const l0 = (u - u1) * (u - u2) * (u - 1) / d0;
  const l1 = u * (u - u2) * (u - 1) / d1;
  const l2 = u * (u - u1) * (u - 1) / d2;
  const l3 = u * (u - u1) * (u - u2) / d3;
  return l0 * curve.a0 + l1 * curve.a1 + l2 * curve.a2 + l3 * curve.a3;
}

// Get canvas-relative {x, y} from a mouse event
function getCanvasCoords(e, canvas) {
  const rect = canvas.getBoundingClientRect();
  return { x: e.clientX - rect.left, y: e.clientY - rect.top };
}

// Build upper/lower band point arrays for a frequency curve.
// factorAbove/factorBelow are fractional offsets (e.g. 0.02 = ±2%).
// Returns { upper: [[x,y],...], lower: [[x,y],...] }
function buildBandPoints(viewer, curve, factorAbove, factorBelow) {
  const STEPS = 60;
  const upper = [], lower = [];
  for (let i = 0; i <= STEPS; ++i) {
    const t = curve.t0 + (curve.t3 - curve.t0) * i / STEPS;
    if (t < viewer.t_view_min - 0.01 || t > viewer.t_view_max + 0.01) continue;
    const f = evalBezier(curve, t);
    upper.push([viewer.timeToX(t), viewer.freqToY(f * (1 + factorAbove))]);
    lower.push([viewer.timeToX(t), viewer.freqToY(f * (1 - factorBelow))]);
  }
  return { upper, lower };
}