private static void renderHull(PtEntry pt) {
    Inf inf = Inf.create();
    int count = 30;
    PtEntry ptStart = pt;
    do {
      inf.update();
      if (pt.prev(true) != null) {
        boolean valley = false;

        valley =
            (pt.prev(true).source() == pt.source() && pt.prev(true).orig().next(true) != pt.orig());

        V.pushColor(MyColor.cBLUE);
        V.pushStroke(valley ? STRK_RUBBERBAND : STRK_THICK);
        V.drawLine(pt.prev(true), pt);
        V.pop(2);
      }
      V.pushColor(MyColor.cDARKGREEN);
      V.mark(pt, MARK_DISC, .6);
      V.pop();
      if (Editor.withLabels(true)) {
        StringBuilder sb = new StringBuilder();
        sb.append(" #" + pt.id());
        if (pt.source() != null) sb.append(" <" + pt.source() + ">");

        V.pushScale(.6);
        V.draw(sb.toString(), MyMath.ptOnCircle(pt, MyMath.radians(30), 3), TX_FRAME | TX_BGND);
        V.pop();
      }
      pt = pt.next(true);
      if (count-- == 0) V.draw("too many points rendering!", 50, 50, TX_CLAMP);
    } while (pt != ptStart && count > 0);
  }
  /**
   * Calculate possible hull of a pair of polygons
   *
   * @param a
   * @param b
   * @return possible hull
   */
  private static EdPolygon calcPHull(EdPolygon aPoly, EdPolygon bPoly) {
    final boolean db = true;

    if (db && T.update())
      T.msg(
          "calc possible hull of two polygons"
              + T.show(aPoly, MyColor.cBLUE, STRK_THICK, -1)
              + T.show(bPoly, MyColor.cDARKGREEN, STRK_THICK, -1));
    PtEntry a = PtEntry.buildFrom(aPoly);
    PtEntry b = PtEntry.buildFrom(bPoly);

    PtEntry aHull = PtEntry.convexHull(a);
    PtEntry bHull = PtEntry.convexHull(b);

    inf = Inf.create();

    if (db && T.update()) {
      T.msg(
          "convex hulls"
              + T.show(aHull.toPolygon(), MyColor.cBLUE, STRK_THICK, -1)
              + T.show(bHull.toPolygon(), MyColor.cDARKGREEN, STRK_THICK, -1));
    }

    PtEntry ph = hullOfPolygons(a, b, aHull, bHull);
    traceHullPt = ph;

    insertValleys(ph, a.source(), b.source());

    expandHull(ph, aHull, bHull, true);
    expandHull(ph, aHull, bHull, false);

    return ph.toPolygon();
  }
  /**
   * Determine convex hull of two polygons, using rotating calipers method
   *
   * @param pa first polygon
   * @param pb second polygon
   * @return convex hull structure
   */
  private static PtEntry hullOfPolygons(PtEntry pa, PtEntry pb, PtEntry aHull, PtEntry bHull) {

    boolean db = C.vb(DB_INITIALHULL);

    if (db && T.update())
      T.msg(
          "construct convex hull of polygons"
              + T.show(pa, MyColor.cBLUE, STRK_THICK, -1)
              + T.show(pb, MyColor.cDARKGREEN, STRK_THICK, -1));

    PtEntry hullVertex = null;

    // A hull vertex and index
    PtEntry av = rightMostVertex(aHull);

    // B hull vertex and index
    PtEntry bv = rightMostVertex(bHull);

    double theta = Math.PI / 2;

    LineEqn aLine = new LineEqn(av, theta);

    int bSide = aLine.sideOfLine(bv);
    boolean bActive = (bSide == 0) ? (bv.y > av.y) : bSide < 0;

    if (db && T.update()) T.msg("rightmost vertices" + T.show(av) + T.show(bv));

    // construct initial vertex of hull
    hullVertex = new PtEntry(!bActive ? av : bv);

    //    if (db && T.update())
    //      T.msg("constructed initial hull vertex: " + hullVertex);

    PtEntry.join(hullVertex, hullVertex);
    PtEntry firstEnt = hullVertex;

    while (true) {
      Inf.update(inf);

      PtEntry av2 = av.next(true);
      PtEntry bv2 = bv.next(true);

      // next vertex is either A advance, B advance, or bridge
      double anga = MyMath.polarAngle(av, av2);
      double angb = MyMath.polarAngle(bv, bv2);

      double angBridge = bActive ? MyMath.polarAngle(bv, av) : MyMath.polarAngle(av, bv);

      double ta = MyMath.normalizeAnglePositive(anga - theta);
      double tb = MyMath.normalizeAnglePositive(angb - theta);
      double tc = MyMath.normalizeAnglePositive(angBridge - theta);

      // precision problem: if A and B tangent lines are parallel, both can
      // reach near zero simultaneously

      final double MAX = Math.PI * 2 - 1e-3;
      if (ta >= MAX) ta = 0;
      if (tb >= MAX) tb = 0;
      if (tc >= MAX) tc = 0;

      theta += Math.min(ta, Math.min(tb, tc));

      if (db && T.update())
        T.msg("caliper" + T.show(hullVertex) + tr(hullVertex, theta) + tp(av) + tp(bv));

      PtEntry newPoint = null;

      if (ta <= tb && ta <= tc) {
        if (db && T.update()) T.msg("A vertex is nearest" + tl(av, av2));
        // ai++;
        av = av2;
        if (!bActive) newPoint = av;
      } else if (tb <= ta && tb <= tc) {
        if (db && T.update()) T.msg("B vertex is nearest" + tl(bv, bv2));
        // bi++;
        bv = bv2;
        if (bActive) newPoint = bv;
      } else {
        if (db && T.update())
          T.msg("Bridge vertex is nearest" + tl(bActive ? bv : av, bActive ? av : bv));
        bActive ^= true;
        newPoint = bActive ? bv : av;
      }

      if (newPoint != null) {
        if (PtEntry.samePoint(newPoint, firstEnt)) {
          break;
        }

        // construct new vertex for hull of the two;
        // remember, use original vertex, not the convex hull
        hullVertex = hullVertex.insert(new PtEntry(newPoint), true);
        if (db && T.update()) T.msg("adding new caliper vertex " + T.show(hullVertex));
      }
    }
    return hullVertex;
  }