Пример #1
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();
  }
Пример #2
0
  /**
   * Calc possible hull from a set of polygons
   *
   * @param polySet set of polygons
   * @param first first polygon to include
   * @param last last polygon to include
   * @return polygon containing possible hull
   */
  private static EdPolygon calcPHullRange(EdPolygon[] polySet, int first, int last) {
    final boolean db = true;
    int len = last + 1 - first;
    if (len == 1) return polySet[first];
    if (len > 2) {
      if (db && T.update()) {
        DArray a = new DArray();
        for (int i = first; i <= last; i++) a.add(polySet[i]);
        T.msg("calc possible hull of multiple polygons" + T.show(a, MyColor.cRED, STRK_THICK, -1));
      }

      int n = len / 2;
      return calcPHull(
          calcPHullRange(polySet, first, first + n - 1), calcPHullRange(polySet, first + n, last));
    }

    return calcPHull(polySet[first], polySet[first + 1]);
  }
Пример #3
0
  private void construct(EdDisc a, EdDisc b) {
    this.discA = a;
    this.discB = b;

    if (EdDisc.partiallyDisjoint(a, b)) {

      // if (!UHullMain.oldBitanMethod())
      {
        final boolean db = false;

        if (a.getRadius() == b.getRadius()) {
          FPoint2 oa = a.getOrigin(), ob = b.getOrigin();

          FPoint2 n = new FPoint2(-(ob.y - oa.y), ob.x - oa.x);
          n.normalize();
          n.x *= a.getRadius();
          n.y *= a.getRadius();
          seg = new DirSeg(FPoint2.add(oa, n, null), FPoint2.add(ob, n, null));
          return;
        }

        boolean swap = a.getRadius() > b.getRadius();

        if (swap) {
          b = (EdDisc) discA;
          a = (EdDisc) discB;
        }

        if (db && T.update())
          T.msg(
              "BiTangent construct, arad="
                  + Tools.f(a.getRadius())
                  + " brad="
                  + Tools.f(b.getRadius())
                  + " swap="
                  + swap
                  + " origin.a="
                  + T.show(a.getOrigin()));

        FPoint2 oa = a.getOrigin();
        FPoint2 ob = b.getOrigin();

        double U = ob.x, V = ob.y;
        double A = oa.x - U, B = oa.y - V;
        double R1 = a.getRadius();
        double R2 = b.getRadius();
        double S = R2 - R1;

        double x1, y1, x2, y2;
        x1 = A;
        y1 = B;

        boolean secondRoot;
        boolean altSlope = Math.abs(B) < Math.abs(A);
        if (!altSlope) {

          double C1 = S * S / B, C2 = -A / B;
          double qA = 1 + C2 * C2, qB = 2 * C1 * C2, qC = C1 * C1 - S * S;
          double root = Math.sqrt(qB * qB - 4 * qA * qC);
          x2 = (-qB - root) / (2 * qA);
          y2 = C1 + C2 * x2;

          secondRoot = MyMath.sideOfLine(x2, y2, A, B, 0, 0) < 0;

          if (swap ^ secondRoot) {
            x2 = (-qB + root) / (2 * qA);
            y2 = C1 + C2 * x2;
          }
        } else {

          double C1 = S * S / A, C2 = -B / A;
          double qA = 1 + C2 * C2, qB = 2 * C1 * C2, qC = C1 * C1 - S * S;
          double root = Math.sqrt(qB * qB - 4 * qA * qC);
          y2 = (-qB - root) / (2 * qA);
          x2 = C1 + C2 * y2;

          secondRoot = MyMath.sideOfLine(x2, y2, A, B, 0, 0) < 0;

          if (swap ^ secondRoot) {
            y2 = (-qB + root) / (2 * qA);
            x2 = C1 + C2 * y2;
          }
        }
        // now grow both discs back to r1, r2

        double tx = U;
        double ty = V;

        //        if (S == 0) {
        //          FPoint2 unit = new FPoint2(-A, -B);
        //          if (swap) {
        //            unit.x = -unit.x;
        //            unit.y = -unit.y;
        //          }
        //          unit.normalize();
        //          tx += -unit.y * R1;
        //          ty += unit.x * R1;
        //        } else
        {
          double F = R1 / S;
          tx += x2 * F;
          ty += y2 * F;
        }

        if (db && T.update())
          T.msg("adding offset to both points: " + tx + ", " + ty + T.show(new FPoint2(tx, ty)));
        x1 += tx;
        y1 += ty;
        x2 += tx;
        y2 += ty;
        FPoint2 p1 = new FPoint2(x1, y1);
        FPoint2 p2 = new FPoint2(x2, y2);
        if (swap) {
          FPoint2 tmp = p1;
          p1 = p2;
          p2 = tmp;
        }

        seg = new DirSeg(p1, p2);

        if (db && T.update())
          T.msg(
              "swap="
                  + swap
                  + " altSlope="
                  + altSlope
                  + " secondRoot="
                  + secondRoot
                  + " dirseg="
                  + EdSegment.showDirected(p1, p2));
      }
      //      else {
      //
      //        double th = calcTheta(a, b);
      //        LineEqn eqn = new LineEqn(a.polarPoint(th + Math.PI / 2), th);
      //        double ta = eqn.parameterFor(a.getOrigin());
      //        double tb = eqn.parameterFor(b.getOrigin());
      //        seg = new DirSeg(eqn.pt(ta), eqn.pt(tb));
      //
      //      }
    }
  }
Пример #4
0
  private static void OLDexpandHull(
      PtEntry convHullEntry, PtEntry aHull, PtEntry bHull, boolean ccw) {
    boolean db__OLD = C.vb(DB_HULLEXPAND);
    if (db__OLD && T.update()) T.msg("expandHull" + T.show(convHullEntry) + " ccw=" + ccw);

    PtEntry[] opp = new PtEntry[2];
    opp[0] = aHull;
    opp[1] = bHull;

    PtEntry old____hEnt = convHullEntry;
    boolean advanced = false;
    do {
      if (old____hEnt != convHullEntry) advanced = true;
      inf.update();
      if (old____hEnt.source() == null) {
        if (db__OLD && T.update())
          T.msg("expandHull, source unknown, guaranteed not convex" + T.show(old____hEnt));
        old____hEnt = old____hEnt.next(ccw);
        continue;
      }

      int w = (old____hEnt.source() == opp[0].source()) ? 1 : 0;
      PtEntry oppEnt = opp[w];

      boolean isTangent =
          !COper3.right(old____hEnt, oppEnt, oppEnt.next(true), ccw)
              && !COper3.right(old____hEnt, oppEnt, oppEnt.prev(true), ccw);

      if (!isTangent) {
        if (db__OLD && T.update())
          T.msg(
              "expandHull, advance tangent line"
                  + T.show(oppEnt.toPolygon(), MyColor.cDARKGRAY, -1, MARK_X)
                  + T.show(old____hEnt)
                  + tl(old____hEnt, oppEnt));
        opp[w] = oppEnt.next(ccw);
        continue;
      }

      if (COper3.left(old____hEnt, oppEnt, old____hEnt.next(ccw), ccw)
          && COper3.left(old____hEnt, oppEnt, old____hEnt.prev(ccw), ccw)) {
        DArray dispPts = new DArray();

        // delete points until cross tangent line
        PtEntry next = old____hEnt.next(ccw);
        while (true) {
          PtEntry prev = next;
          dispPts.add(prev);
          next = prev.delete(ccw);

          inf.update();
          if (COper3.right(old____hEnt, oppEnt, next, ccw)) {
            FPoint2 cross = MyMath.linesIntersection(old____hEnt, oppEnt, prev, next, null);
            old____hEnt = old____hEnt.insert(new PtEntry(cross), ccw);
            if (db__OLD && T.update())
              T.msg(
                  "expandHull, clipped to shadow region"
                      + tl(old____hEnt, oppEnt)
                      + T.show(old____hEnt)
                      + T.show(dispPts));
            break;
          }
        }
      } else {
        if (db__OLD && T.update())
          T.msg(
              "expandHull, not dipping into shadow region"
                  + T.show(old____hEnt.next(ccw))
                  + tl(old____hEnt, oppEnt));
      }
      old____hEnt = old____hEnt.next(ccw);
    } while (!advanced || old____hEnt != convHullEntry);
  }
Пример #5
0
  /**
   * 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;
  }
Пример #6
0
  private static void insertValleys(
      PtEntry hullPt, Object aSrc, Object bSrc) { // pa, MyPolygon pb) {
    boolean db = C.vb(DB_INSERTVALLEY);
    PtEntry ent = hullPt;

    if (db && T.update()) T.msg("insertValleys");
    do {
      PtEntry next = ent.next(true);

      if (ent.source() == next.source()) {
        PtEntry orig = ent.orig();

        if (orig.next(true) != next.orig()) {

          PtEntry vPeak0 = ent;
          PtEntry vPeak1 = next;

          EdPolygon opp = (EdPolygon) (vPeak0.source() == aSrc ? bSrc : aSrc);

          FPoint2 kernelPt = opp.getPointMod(C.vi(KERNELVERT));

          // construct a chain from the vertices of the valley
          PtEntry handle = new PtEntry(vPeak0);
          PtEntry hNext = handle;
          PtEntry e = vPeak0.orig();
          while (e != vPeak1.orig()) {
            inf.update();
            e = e.next(true);
            hNext = hNext.insert(new PtEntry(e), true);
          }

          if (C.vb(SKIPCONTOUR)) {
            PtEntry h0 = handle.next(true);
            PtEntry h1 = hNext.prev(true);
            PtEntry.join(vPeak0, h0);
            PtEntry.join(h1, vPeak1);
            if (db && T.update())
              T.msg("inserted unmodified valley" + T.show(vPeak0) + T.show(vPeak1));

          } else {
            if (!C.vb(DB_CONTOUR)) T.disable();
            PtEntry hull = COper3.buildHullForChain(handle, kernelPt);
            if (!C.vb(DB_CONTOUR)) T.enable();
            // find entries corresponding to start, end of hull
            PtEntry peak0 = null, peak1 = null;
            {
              PtEntry hEnt = hull;
              while (peak0 == null || peak1 == null) {
                inf.update();
                if (hEnt.orig() == vPeak0.orig()) peak0 = hEnt;
                if (hEnt.orig() == vPeak1.orig()) peak1 = hEnt;
                hEnt = hEnt.next(true);
              }
            }
            PtEntry.join(vPeak0, peak0.next(true));
            PtEntry.join(peak1.prev(true), vPeak1);
            if (db && T.update())
              T.msg("inserted monotonic valley" + T.show(vPeak0) + T.show(vPeak1));
          }
        }
      }
      ent = next;
    } while (ent != hullPt);
  }
Пример #7
0
  /**
   * Apply hull expansion procedure
   *
   * @param convHullEntry an entry of the hull (should be on the convex hull, so it is not deleted
   *     or replaced and is still valid for subsequent calls)
   * @param aHull entry on convex hull of polygon A
   * @param bHull entry on convex hull of polygon B
   * @param ccw true to move in ccw direction, else cw
   */
  private static void expandHull(PtEntry convHullEntry, PtEntry aHull, PtEntry bHull, boolean ccw) {
    if (C.vb(OLDMETHOD)) {
      OLDexpandHull(convHullEntry, aHull, bHull, ccw);
      return;
    }
    boolean db = C.vb(DB_HULLEXPAND);

    if (db && T.update()) T.msg("expandHull" + T.show(convHullEntry) + " ccw=" + ccw);

    // tangent points for A, B
    PtEntry[] tangentPoints = new PtEntry[2];
    tangentPoints[0] = aHull;
    tangentPoints[1] = bHull;

    PtEntry hEnt = convHullEntry;
    do {
      inf.update();

      // calculate tangent ray R
      PtEntry tangentPt = null;
      while (true) {
        int tanIndex = (hEnt.source() == tangentPoints[0].source()) ? 1 : 0;
        tangentPt = tangentPoints[tanIndex];

        if (!COper3.right(hEnt, tangentPt, tangentPt.next(true), ccw)
            && !COper3.right(hEnt, tangentPt, tangentPt.prev(true), ccw)) break;

        tangentPt = tangentPt.next(ccw);

        if (db && T.update())
          T.msg(
              "expandHull, advance tangent line"
                  + T.show(tangentPt.toPolygon(), MyColor.cDARKGRAY, -1, MARK_DISC)
                  + T.show(hEnt)
                  + tl(hEnt, tangentPt));
        tangentPoints[tanIndex] = tangentPt;
      }

      if (COper3.left(hEnt, tangentPt, hEnt.next(ccw), ccw)) {
        DArray dispPts = new DArray();

        // delete points until cross tangent line
        PtEntry next = hEnt.next(ccw);
        while (true) {
          PtEntry prev = next;
          dispPts.add(prev);
          next = prev.delete(ccw);
          if (COper3.right(hEnt, tangentPt, next, ccw)) {
            FPoint2 cross = MyMath.linesIntersection(hEnt, tangentPt, prev, next, null);
            hEnt = hEnt.insert(new PtEntry(cross), ccw);
            if (db && T.update())
              T.msg(
                  "expandHull, clipped to shadow region"
                      + tl(hEnt, tangentPt)
                      + T.show(hEnt)
                      + T.show(dispPts));
            break;
          }
        }
      } else {
        if (db && T.update())
          T.msg(
              "expandHull, not dipping into shadow region"
                  + T.show(hEnt.next(ccw))
                  + tl(hEnt, tangentPt));
      }
      while (true) {
        hEnt = hEnt.next(ccw);
        if (COper3.left(hEnt.prev(ccw), hEnt, hEnt.next(ccw), ccw)) break;
        if (db && T.update()) T.msg("skipping reflex vertex" + T.show(hEnt));
      }
    } while (hEnt != convHullEntry);
  }