Nested sheets from DXF to toolpaths

const SCALE = { mm: 1, cm: 10, m: 1000, in: 25.4, '': 1 };

/** A closed polyline with bulges → arcs and lines (counter-clockwise when the polyline is). */
export function loopToPrims(pts) {
  const n = pts.length, out = [];
  for (let i = 0; i < n; i++) {
    const a = pts[i], b = pts[(i + 1) % n];
    const s = [a.x, a.y], e = [b.x, b.y];
    const d = Math.hypot(e[0] - s[0], e[1] - s[1]);
    if (d < 1e-9) continue;
    const bu = a.b || 0;
    if (Math.abs(bu) < 1e-12) { out.push(O.line(s, e)); continue; }
    const half = d / 2, r = half * (1 + bu * bu) / (2 * Math.abs(bu));
    const off = half * (1 - bu * bu) / (2 * bu);               // signed distance from the chord's middle to the centre (left of s → e when b > 0)
    const mx = (s[0] + e[0]) / 2, my = (s[1] + e[1]) / 2;
    const nx = -(e[1] - s[1]) / d, ny = (e[0] - s[0]) / d;
    const c = [mx + nx * off, my + ny * off];
    out.push(O.arc(c, r, Math.atan2(s[1] - c[1], s[0] - c[0]), 4 * Math.atan(bu), s, e));
  }
  return out;
}

// a bulged segment can swing outside its end points: sample the arcs for the box
const bboxExact = (loops) => {
  let x0 = Infinity, y0 = Infinity, x1 = -Infinity, y1 = -Infinity;
  for (const l of loops) for (const p of loopToPrims(l)) {
    for (const q of O.samplePrim(p, 0.05)) { x0 = Math.min(x0, q[0]); y0 = Math.min(y0, q[1]); x1 = Math.max(x1, q[0]); y1 = Math.max(y1, q[1]); }
  }
  return { x0, y0, x1, y1 };
};

const move = (l) => l.map((q) => ({ x: (q.x - s.box.x0) * k, y: (q.y - s.box.y0) * k, ...(q.b ? { b: q.b } : {}) }));