    // @(#):$Name:  $:$Id: TGeoBoolNode.cxx,v 1.22 2005/05/25 14:25:16 brun Exp $
    // Author: Andrei Gheata   30/05/02
    // TGeoBoolNode::Contains and parser implemented by Mihaela Gheata

    /*************************************************************************
     * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
     * All rights reserved.                                                  *
     *                                                                       *
     * For the licensing terms see $ROOTSYS/LICENSE.                         *
     * For the list of contributors see $ROOTSYS/README/CREDITS.             *
     *************************************************************************/

    #include "Riostream.h"

    #include "TGeoCompositeShape.h"
    #include "TGeoMatrix.h"
    #include "TGeoManager.h"

    #include "TGeoBoolNode.h"

    #include "TVirtualPad.h"
    #include "TVirtualViewer3D.h"
    #include "TBuffer3D.h"
    #include "TBuffer3DTypes.h"

    // statics and globals

    ClassImp(TGeoBoolNode)

    //-----------------------------------------------------------------------------
    TGeoBoolNode::TGeoBoolNode()
    {
    // Default constructor
       fLeft     = 0;
       fRight    = 0;
       fLeftMat  = 0;
       fRightMat = 0;
       fSelected = 0;
    }
    //-----------------------------------------------------------------------------
    TGeoBoolNode::TGeoBoolNode(const char *expr1, const char *expr2)
    {
    // constructor
       fLeft     = 0;
       fRight    = 0;
       fLeftMat  = 0;
       fRightMat = 0;
       fSelected = 0;
       if (!MakeBranch(expr1, kTRUE)) {
          return;
       }
       if (!MakeBranch(expr2, kFALSE)) {
          return;
       }
    }

    //-----------------------------------------------------------------------------
    TGeoBoolNode::TGeoBoolNode(TGeoShape *left, TGeoShape *right, TGeoMatrix *lmat, TGeoMatrix *rmat)
    {
       fSelected = 0;
       fLeft = left;
       fRight = right;
       fLeftMat = lmat;
       if (!fLeftMat) fLeftMat = gGeoIdentity;
       else fLeftMat->RegisterYourself();
       fRightMat = rmat;
       if (!fRightMat) fRightMat = gGeoIdentity;
       else fRightMat->RegisterYourself();
       if (!fLeft) {
          Error("ctor", "left shape is NULL");
          return;
       }
       if (!fRight) {
          Error("ctor", "right shape is NULL");
          return;
       }
    }

    //-----------------------------------------------------------------------------
    TGeoBoolNode::~TGeoBoolNode()
    {
    // Destructor
    // --- deletion of components handled by TGeoManager class.
    }
    //-----------------------------------------------------------------------------
    Bool_t TGeoBoolNode::MakeBranch(const char *expr, Bool_t left)
    {
    // Expands the boolean expression either on left or right branch, creating
    // component elements (composite shapes and boolean nodes). Returns true on success.
       TString sleft, sright, stransf;
       Int_t boolop = TGeoManager::Parse(expr, sleft, sright, stransf);
       if (boolop<0) {
          Error("MakeBranch", "invalid expresion");
          return kFALSE;
       }
       TGeoShape *shape = 0;
       TGeoMatrix *mat;
       TString newshape;

       if (stransf.Length() == 0) {
          mat = gGeoIdentity;
       } else {
          mat = (TGeoMatrix*)gGeoManager->GetListOfMatrices()->FindObject(stransf.Data());
       }
       if (!mat) {
          Error("MakeBranch", "transformation %s not found", stransf.Data());
          return kFALSE;
       }
       switch (boolop) {
          case 0:
             // elementary shape
             shape = (TGeoShape*)gGeoManager->GetListOfShapes()->FindObject(sleft.Data());
             if (!shape) {
                Error("MakeBranch", "shape %s not found", sleft.Data());
                return kFALSE;
             }
             break;
          case 1:
             // composite shape - union
             newshape = sleft;
             newshape += "+";
             newshape += sright;
             shape = new TGeoCompositeShape(newshape.Data());
             break;
          case 2:
             // composite shape - difference
             newshape = sleft;
             newshape += "-";
             newshape += sright;
             shape = new TGeoCompositeShape(newshape.Data());
             break;
          case 3:
             // composite shape - intersection
             newshape = sleft;
             newshape += "*";
             newshape += sright;
             shape = new TGeoCompositeShape(newshape.Data());
             break;
       }
       if (boolop && !shape->IsValid()) {
          Error("MakeBranch", "Shape %s not valid", newshape.Data());
          delete shape;
          return kFALSE;
       }
       if (left) {
          fLeft = shape;
          fLeftMat = mat;
       } else {
          fRight = shape;
          fRightMat = mat;
       }
       return kTRUE;
    }
    //-----------------------------------------------------------------------------
    void TGeoBoolNode::Paint(Option_t * option)
    {
       TVirtualViewer3D * viewer = gPad->GetViewer3D();
       if (!viewer) return;

       // Components of composite shape hierarchies for local frame viewers are painted
       // in coordinate frame of the top level composite shape. So we force
       // conversion to this.  See TGeoPainter::PaintNode for loading of GLMatrix.
       Bool_t localFrame = kFALSE; //viewer->PreferLocalFrame();

       TGeoHMatrix *glmat = gGeoManager->GetGLMatrix();
       TGeoHMatrix mat;
       mat = glmat; // keep a copy

       // Now perform fetch and add of the two components buffers.
       // Note we assume that composite shapes are always completely added
       // so don't bother to get addDaughters flag from viewer->AddObject()

       // Setup matrix and fetch/add the left component buffer
       glmat->Multiply(fLeftMat);
       //fLeft->Paint(option);
       if (TGeoCompositeShape *left = dynamic_cast<TGeoCompositeShape *>(fLeft)) left->PaintComposite(option);
       else {
          const TBuffer3D & leftBuffer = fLeft->GetBuffer3D(TBuffer3D::kAll, localFrame);
          viewer->AddObject(leftBuffer);
       }

       // Setup matrix and fetch/add the right component buffer
       *glmat = &mat;
       glmat->Multiply(fRightMat);
       //fRight->Paint(option);
       if (TGeoCompositeShape *right = dynamic_cast<TGeoCompositeShape *>(fRight)) right->PaintComposite(option);
       else {
          const TBuffer3D & rightBuffer = fRight->GetBuffer3D(TBuffer3D::kAll, localFrame);
          viewer->AddObject(rightBuffer);
       }

       *glmat = &mat;
    }
    //_____________________________________________________________________________
    void TGeoBoolNode::RegisterMatrices()
    {
    // Register all matrices of the boolean node and descendents.
       if (!fLeftMat->IsIdentity()) fLeftMat->RegisterYourself();
       if (!fRightMat->IsIdentity()) fRightMat->RegisterYourself();
       if (fLeft->IsComposite()) ((TGeoCompositeShape*)fLeft)->GetBoolNode()->RegisterMatrices();
       if (fRight->IsComposite()) ((TGeoCompositeShape*)fRight)->GetBoolNode()->RegisterMatrices();
    }
    //_____________________________________________________________________________
    void TGeoBoolNode::SavePrimitive(ofstream &out, Option_t *option)
    {
    // Save a primitive as a C++ statement(s) on output stream "out".
       fLeft->SavePrimitive(out,option);
       fRight->SavePrimitive(out,option);
       if (!fLeftMat->IsIdentity()) {
          fLeftMat->RegisterYourself();
          fLeftMat->SavePrimitive(out,option);
       }
       if (!fRightMat->IsIdentity()) {
          fRightMat->RegisterYourself();
          fRightMat->SavePrimitive(out,option);
       }
    }
    //-----------------------------------------------------------------------------
    void TGeoBoolNode::Sizeof3D() const
    {
    // register size of this 3D object
       fLeft->Sizeof3D();
       fRight->Sizeof3D();
    }
    ClassImp(TGeoUnion)

    //-----------------------------------------------------------------------------
    void TGeoUnion::Paint(Option_t *option)
    {
       TVirtualViewer3D *viewer = gPad->GetViewer3D();

       if (!viewer) {
          Error("Paint", "gPad->GetViewer3D() returned 0, cannot work with composite!\n");
          return;
       }

       viewer->AddCompositeOp(TBuffer3D::kCSUnion);

       TGeoBoolNode::Paint(option);
    }

    //-----------------------------------------------------------------------------
    TGeoUnion::TGeoUnion()
    {
    // Default constructor
    }
    //-----------------------------------------------------------------------------
    TGeoUnion::TGeoUnion(const char *expr1, const char *expr2)
              :TGeoBoolNode(expr1, expr2)
    {
    // Constructor
    }

    //-----------------------------------------------------------------------------
    TGeoUnion::TGeoUnion(TGeoShape *left, TGeoShape *right, TGeoMatrix *lmat, TGeoMatrix *rmat)
              :TGeoBoolNode(left,right,lmat,rmat)
    {
    // Constructor providing pointers to components
       if (left->TestShapeBit(TGeoShape::kGeoHalfSpace) || right->TestShapeBit(TGeoShape::kGeoHalfSpace)) {
          Fatal("TGeoUnion", "Unions with a half-space (%s + %s) not allowed", left->GetName(), right->GetName());
       }
    }

    //-----------------------------------------------------------------------------
    TGeoUnion::~TGeoUnion()
    {
    // Destructor
    // --- deletion of components handled by TGeoManager class.
    }
    //-----------------------------------------------------------------------------
    void TGeoUnion::ComputeBBox(Double_t &dx, Double_t &dy, Double_t &dz, Double_t *origin)
    {
    // Compute bounding box corresponding to a union of two shapes.
       if (((TGeoBBox*)fLeft)->IsNullBox()) fLeft->ComputeBBox();
       if (((TGeoBBox*)fRight)->IsNullBox()) fRight->ComputeBBox();
       Double_t vert[48];
       Double_t pt[3];
       Int_t i;
       Double_t xmin, xmax, ymin, ymax, zmin, zmax;
       xmin = ymin = zmin = TGeoShape::Big();
       xmax = ymax = zmax = -TGeoShape::Big();
       ((TGeoBBox*)fLeft)->SetBoxPoints(&vert[0]);
       ((TGeoBBox*)fRight)->SetBoxPoints(&vert[24]);
       for (i=0; i<8; i++) {
          fLeftMat->LocalToMaster(&vert[3*i], &pt[0]);
          if (pt[0]<xmin) xmin=pt[0];
          if (pt[0]>xmax) xmax=pt[0];
          if (pt[1]<ymin) ymin=pt[1];
          if (pt[1]>ymax) ymax=pt[1];
          if (pt[2]<zmin) zmin=pt[2];
          if (pt[2]>zmax) zmax=pt[2];
       }
       for (i=8; i<16; i++) {
          fRightMat->LocalToMaster(&vert[3*i], &pt[0]);
          if (pt[0]<xmin) xmin=pt[0];
          if (pt[0]>xmax) xmax=pt[0];
          if (pt[1]<ymin) ymin=pt[1];
          if (pt[1]>ymax) ymax=pt[1];
          if (pt[2]<zmin) zmin=pt[2];
          if (pt[2]>zmax) zmax=pt[2];
       }
       dx = 0.5*(xmax-xmin);
       origin[0] = 0.5*(xmin+xmax);
       dy = 0.5*(ymax-ymin);
       origin[1] = 0.5*(ymin+ymax);
       dz = 0.5*(zmax-zmin);
       origin[2] = 0.5*(zmin+zmax);
    }
    //-----------------------------------------------------------------------------
    Bool_t TGeoUnion::Contains(Double_t *point) const
    {
    // Find if a union of two shapes contains a given point
       Double_t local[3];
       fLeftMat->MasterToLocal(point, &local[0]);
       Bool_t inside = fLeft->Contains(&local[0]);
       if (inside) return kTRUE;
       fRightMat->MasterToLocal(point, &local[0]);
       inside = fRight->Contains(&local[0]);
       return inside;
    }

    //_____________________________________________________________________________
    void TGeoUnion::ComputeNormal(Double_t *point, Double_t *dir, Double_t *norm)
    {
       norm[0] = norm[1] = 0.;
       norm[2] = 1.;
       Double_t local[3];
       Double_t ldir[3], lnorm[3];
       if (fSelected == 1) {
          fLeftMat->MasterToLocal(point, local);
          fLeftMat->MasterToLocalVect(dir, ldir);
          fLeft->ComputeNormal(local,ldir,lnorm);
          fLeftMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       if (fSelected == 2) {
          fRightMat->MasterToLocal(point, local);
          fRightMat->MasterToLocalVect(dir, ldir);
          fRight->ComputeNormal(local,ldir,lnorm);
          fRightMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       fLeftMat->MasterToLocal(point, local);
       if (fLeft->Contains(local)) {
          fLeftMat->MasterToLocalVect(dir, ldir);
          fLeft->ComputeNormal(local,ldir,lnorm);
          fLeftMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       fRightMat->MasterToLocal(point, local);
       if (fRight->Contains(local)) {
          fRightMat->MasterToLocalVect(dir, ldir);
          fRight->ComputeNormal(local,ldir,lnorm);
          fRightMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       // Propagate forward/backward to see which of the components is intersected first
       local[0] = point[0] + 1E-5*dir[0];
       local[1] = point[1] + 1E-5*dir[1];
       local[2] = point[2] + 1E-5*dir[2];

       if (!Contains(local)) {
          local[0] = point[0] - 1E-5*dir[0];
          local[1] = point[1] - 1E-5*dir[1];
          local[2] = point[2] - 1E-5*dir[2];
          if (!Contains(local)) return;
       }
       ComputeNormal(local,dir,norm);
    }

    //-----------------------------------------------------------------------------
    Int_t TGeoUnion::DistanceToPrimitive(Int_t /*px*/, Int_t /*py*/)
    {
    // Compute minimum distance to shape vertices
       return 9999;
    }
    //-----------------------------------------------------------------------------
    Double_t TGeoUnion::DistFromInside(Double_t *point, Double_t *dir, Int_t iact,
                                  Double_t step, Double_t *safe) const
    {
    // Compute distance from a given point to outside.
    //   printf("Point is : %g, %g, %g\n", point[0], point[1], point[2]);
       if (iact<3 && safe) {
          // compute safe distance
          *safe = Safety(point,kTRUE);
          if (iact==0) return TGeoShape::Big();
          if (iact==1 && step<*safe) return TGeoShape::Big();
       }

       Double_t local[3], master[3], ldir[3], rdir[3];
       memcpy(master, point, 3*sizeof(Double_t));
       Int_t i;
       TGeoBoolNode *node = (TGeoBoolNode*)this;
       Double_t d1=0., d2=0., snxt=0.;
       fLeftMat->MasterToLocalVect(dir, ldir);
       fRightMat->MasterToLocalVect(dir, rdir);
       fLeftMat->MasterToLocal(point, local);
       Bool_t inside1 = fLeft->Contains(local);
       if (inside1) d1 = fLeft->DistFromInside(local, ldir, 3);
       fRightMat->MasterToLocal(point, local);
       Bool_t inside2 = fRight->Contains(local);
       if (inside2) d2 = fRight->DistFromInside(local, rdir, 3);

       while (inside1 || inside2) {
          if (inside1 && inside2) {
             if (d1<d2) {
                snxt += d1;
                node->SetSelected(1);
                // propagate to exit of left shape
                inside1 = kFALSE;
                for (i=0; i<3; i++) master[i] += d1*dir[i];
                // check if propagated point is in right shape
                fRightMat->MasterToLocal(master, local);
                inside2 = fRight->Contains(local);
                if (inside2) d2 = fRight->DistFromInside(local, rdir, 3);
             } else {
                snxt += d2;
                node->SetSelected(2);
                // propagate to exit of right shape
                inside2 = kFALSE;
                for (i=0; i<3; i++) master[i] += d2*dir[i];
                // check if propagated point is in left shape
                fLeftMat->MasterToLocal(master, local);
                inside1 = fLeft->Contains(local);
                if (inside1) d1 = fLeft->DistFromInside(local, ldir, 3);
             }
          }
          if (inside1) {
             snxt += d1;
             node->SetSelected(1);
             // propagate to exit of left shape
             inside1 = kFALSE;
             for (i=0; i<3; i++) master[i] += d1*dir[i];
             // check if propagated point is in right shape
             fRightMat->MasterToLocal(master, local);
             inside2 = fRight->Contains(local);
             if (inside2) d2 = fRight->DistFromInside(local, rdir, 3);
          }
          if (inside2) {
             snxt += d2;
             node->SetSelected(2);
             // propagate to exit of right shape
             inside2 = kFALSE;
             for (i=0; i<3; i++) master[i] += d2*dir[i];
             // check if propagated point is in left shape
             fLeftMat->MasterToLocal(master, local);
             inside1 = fLeft->Contains(local);
             if (inside1) d1 = fLeft->DistFromInside(local, ldir, 3);
          }
       }
       return snxt;
    }
    //-----------------------------------------------------------------------------
    Double_t TGeoUnion::DistFromOutside(Double_t *point, Double_t *dir, Int_t iact,
                                  Double_t step, Double_t *safe) const
    {
    // Compute distance from a given point to inside.
       if (iact<3 && safe) {
          // compute safe distance
          *safe = Safety(point,kFALSE);
          if (iact==0) return TGeoShape::Big();
          if (iact==1 && step<*safe) return TGeoShape::Big();
       }
       TGeoBoolNode *node = (TGeoBoolNode*)this;
       Double_t local[3], ldir[3], rdir[3];
       Double_t d1, d2, snxt;
       fLeftMat->MasterToLocal(point, &local[0]);
       fLeftMat->MasterToLocalVect(dir, &ldir[0]);
       fRightMat->MasterToLocalVect(dir, &rdir[0]);
       d1 = fLeft->DistFromOutside(&local[0], &ldir[0], iact, step, safe);
       fRightMat->MasterToLocal(point, &local[0]);
       d2 = fRight->DistFromOutside(&local[0], &rdir[0], iact, step, safe);
       if (d1<d2) {
          snxt = d1;
          node->SetSelected(1);
       } else {
          snxt = d2;
          node->SetSelected(2);
       }
       return snxt;
    }
    //-----------------------------------------------------------------------------
    Int_t TGeoUnion::GetNpoints() const
    {
    // Returns number of vertices for the composite shape described by this union.
       return 0;
    }
    //-----------------------------------------------------------------------------
    void TGeoUnion::SetPoints(Double_t * /*points*/) const
    {
    // Fill buffer with shape vertices.
    }

    //-----------------------------------------------------------------------------
    Double_t TGeoUnion::Safety(Double_t *point, Bool_t) const
    {
    // Compute safety distance for a union node;
       Double_t local1[3], local2[3];
       fLeftMat->MasterToLocal(point,local1);
       Bool_t in1 = fLeft->Contains(local1);
       fRightMat->MasterToLocal(point,local2);
       Bool_t in2 = fRight->Contains(local2);
       Double_t saf1 = fLeft->Safety(local1, in1);
       Double_t saf2 = fRight->Safety(local2, in2);
       if (in1 && in2) return TMath::Min(saf1, saf2);
       if (in1)        return saf1;
       if (in2)        return saf2;
       return TMath::Min(saf1,saf2);
    }

    //_____________________________________________________________________________
    void TGeoUnion::SavePrimitive(ofstream &out, Option_t *option)
    {
    // Save a primitive as a C++ statement(s) on output stream "out".
       TGeoBoolNode::SavePrimitive(out,option);
       out << "   pBoolNode = new TGeoUnion(";
       out << fLeft->GetPointerName() << ",";
       out << fRight->GetPointerName() << ",";
       if (!fLeftMat->IsIdentity()) out << fLeftMat->GetPointerName() << ",";
       else                         out << "0,";
       if (!fRightMat->IsIdentity()) out << fRightMat->GetPointerName() << ");" << endl;
       else                         out << "0);" << endl;
    }

    //-----------------------------------------------------------------------------
    void TGeoUnion::SetPoints(Float_t * /*points*/) const
    {
    // Fill buffer with shape vertices.
    }
    //-----------------------------------------------------------------------------
    void TGeoUnion::Sizeof3D() const
    {
    // Register 3D size of this shape.
       TGeoBoolNode::Sizeof3D();
    }

    ClassImp(TGeoSubtraction)

    //-----------------------------------------------------------------------------
    void TGeoSubtraction::Paint(Option_t *option)
    {
       TVirtualViewer3D *viewer = gPad->GetViewer3D();

       if (!viewer) {
          Error("Paint", "gPad->GetViewer3D() returned 0, cannot work with composite!\n");
          return;
       }

       viewer->AddCompositeOp(TBuffer3D::kCSDifference);

       TGeoBoolNode::Paint(option);
    }

    //-----------------------------------------------------------------------------
    TGeoSubtraction::TGeoSubtraction()
    {
    // Default constructor
    }

    //-----------------------------------------------------------------------------
    TGeoSubtraction::TGeoSubtraction(const char *expr1, const char *expr2)
              :TGeoBoolNode(expr1, expr2)
    {
    // Constructor
    }

    //-----------------------------------------------------------------------------
    TGeoSubtraction::TGeoSubtraction(TGeoShape *left, TGeoShape *right, TGeoMatrix *lmat, TGeoMatrix *rmat)
                    :TGeoBoolNode(left,right,lmat,rmat)
    {
    // Constructor providing pointers to components
       if (left->TestShapeBit(TGeoShape::kGeoHalfSpace)) {
          Fatal("TGeoSubstraction", "Substractions from a half-space (%s) not allowed", left->GetName());
       }
    }

    //-----------------------------------------------------------------------------
    TGeoSubtraction::~TGeoSubtraction()
    {
    // Destructor
    // --- deletion of components handled by TGeoManager class.
    }

    //-----------------------------------------------------------------------------
    void TGeoSubtraction::ComputeBBox(Double_t &dx, Double_t &dy, Double_t &dz, Double_t *origin)
    {
    // Compute bounding box corresponding to a subtraction of two shapes.
       TGeoBBox *box = (TGeoBBox*)fLeft;
       if (box->IsNullBox()) fLeft->ComputeBBox();
       Double_t vert[24];
       Double_t pt[3];
       Int_t i;
       Double_t xmin, xmax, ymin, ymax, zmin, zmax;
       xmin = ymin = zmin = TGeoShape::Big();
       xmax = ymax = zmax = -TGeoShape::Big();
       box->SetBoxPoints(&vert[0]);
       for (i=0; i<8; i++) {
          fLeftMat->LocalToMaster(&vert[3*i], &pt[0]);
          if (pt[0]<xmin) xmin=pt[0];
          if (pt[0]>xmax) xmax=pt[0];
          if (pt[1]<ymin) ymin=pt[1];
          if (pt[1]>ymax) ymax=pt[1];
          if (pt[2]<zmin) zmin=pt[2];
          if (pt[2]>zmax) zmax=pt[2];
       }
       dx = 0.5*(xmax-xmin);
       origin[0] = 0.5*(xmin+xmax);
       dy = 0.5*(ymax-ymin);
       origin[1] = 0.5*(ymin+ymax);
       dz = 0.5*(zmax-zmin);
       origin[2] = 0.5*(zmin+zmax);
    }

    //_____________________________________________________________________________
    void TGeoSubtraction::ComputeNormal(Double_t *point, Double_t *dir, Double_t *norm)
    {
       norm[0] = norm[1] = 0.;
       norm[2] = 1.;
       Double_t local[3], ldir[3], lnorm[3];
       if (fSelected == 1) {
          fLeftMat->MasterToLocal(point, local);
          fLeftMat->MasterToLocalVect(dir, ldir);
          fLeft->ComputeNormal(local,ldir,lnorm);
          fLeftMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       if (fSelected == 2) {
          fRightMat->MasterToLocal(point, local);
          fRightMat->MasterToLocalVect(dir, ldir);
          fRight->ComputeNormal(local,ldir,lnorm);
          fRightMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       fRightMat->MasterToLocal(point,local);
       if (fRight->Contains(local)) {
          fRightMat->MasterToLocalVect(dir,ldir);
          fRight->ComputeNormal(local,ldir, lnorm);
          fRightMat->LocalToMasterVect(lnorm,norm);
          return;
       }
       fLeftMat->MasterToLocal(point,local);
       if (!fLeft->Contains(local)) {
          fLeftMat->MasterToLocalVect(dir,ldir);
          fLeft->ComputeNormal(local,ldir, lnorm);
          fLeftMat->LocalToMasterVect(lnorm,norm);
          return;
       }
       // point is inside left shape, but not inside the right
       local[0] = point[0]+1E-5*dir[0];
       local[1] = point[1]+1E-5*dir[1];
       local[2] = point[2]+1E-5*dir[2];
       if (Contains(local)) {
          local[0] = point[0]-1E-5*dir[0];
          local[1] = point[1]-1E-5*dir[1];
          local[2] = point[2]-1E-5*dir[2];
          if (Contains(local)) return;
       }
       ComputeNormal(local,dir,norm);
    }

    //-----------------------------------------------------------------------------
    Bool_t TGeoSubtraction::Contains(Double_t *point) const
    {
    // Find if a subtraction of two shapes contains a given point
       Double_t local[3];
       fLeftMat->MasterToLocal(point, &local[0]);
       Bool_t inside = fLeft->Contains(&local[0]);
       if (!inside) return kFALSE;
       fRightMat->MasterToLocal(point, &local[0]);
       inside = !fRight->Contains(&local[0]);
       return inside;
    }
    //-----------------------------------------------------------------------------
    Int_t TGeoSubtraction::DistanceToPrimitive(Int_t /*px*/, Int_t /*py*/)
    {
    // Compute minimum distance to shape vertices
       return 9999;
    }
    //-----------------------------------------------------------------------------
    Double_t TGeoSubtraction::DistFromInside(Double_t *point, Double_t *dir, Int_t iact,
                                  Double_t step, Double_t *safe) const
    {
    // Compute distance from a given point to outside.
       if (iact<3 && safe) {
          // compute safe distance
          *safe = Safety(point,kTRUE);
          if (iact==0) return TGeoShape::Big();
          if (iact==1 && step<*safe) return TGeoShape::Big();
       }
       TGeoBoolNode *node = (TGeoBoolNode*)this;
       Double_t local[3], ldir[3], rdir[3];
       Double_t d1, d2, snxt=0.;
       fLeftMat->MasterToLocal(point, &local[0]);
       fLeftMat->MasterToLocalVect(dir, &ldir[0]);
       fRightMat->MasterToLocalVect(dir, &rdir[0]);
       d1 = fLeft->DistFromInside(&local[0], &ldir[0], iact, step, safe);
       fRightMat->MasterToLocal(point, &local[0]);
       d2 = fRight->DistFromOutside(&local[0], &rdir[0], iact, step, safe);
       if (d1<d2) {
          snxt = d1;
          node->SetSelected(1);
       } else {
          snxt = d2;
          node->SetSelected(2);
       }
       return snxt;
    }
    //-----------------------------------------------------------------------------
    Double_t TGeoSubtraction::DistFromOutside(Double_t *point, Double_t *dir, Int_t iact,
                                  Double_t step, Double_t *safe) const
    {
    // Compute distance from a given point to inside.
       if (iact<3 && safe) {
          // compute safe distance
          *safe = Safety(point,kFALSE);
          if (iact==0) return TGeoShape::Big();
          if (iact==1 && step<*safe) return TGeoShape::Big();
       }
       TGeoBoolNode *node = (TGeoBoolNode*)this;
       Double_t local[3], master[3], ldir[3], rdir[3];
       memcpy(&master[0], point, 3*sizeof(Double_t));
       Int_t i;
       Double_t d1, d2, snxt=0.;
       fRightMat->MasterToLocal(point, &local[0]);
       fLeftMat->MasterToLocalVect(dir, &ldir[0]);
       fRightMat->MasterToLocalVect(dir, &rdir[0]);
       // check if inside '-'
       Bool_t inside = fRight->Contains(&local[0]);
       Double_t epsil = 0.;
       while (1) {
          if (inside) {
             // propagate to outside of '-'
             d1 = fRight->DistFromInside(&local[0], &rdir[0], iact, step, safe);
             snxt += d1+epsil;
             for (i=0; i<3; i++) master[i] += (d1+1E-8)*dir[i];
             epsil = 1.E-8;
             // now master outside '-'; check if inside '+'
             fLeftMat->MasterToLocal(&master[0], &local[0]);
             if (fLeft->Contains(&local[0])) {
                node->SetSelected(2);
                return snxt;
             }
          }
          // master outside '-' and outside '+' ;  find distances to both
          fLeftMat->MasterToLocal(&master[0], &local[0]);
          d2 = fLeft->DistFromOutside(&local[0], &ldir[0], iact, step, safe);
          if (d2>1E20) {
             node->SetSelected(0);
             return TGeoShape::Big();
          }
          fRightMat->MasterToLocal(&master[0], &local[0]);
          d1 = fRight->DistFromOutside(&local[0], &rdir[0], iact, step, safe);
          if (d2<d1) {
             node->SetSelected(1);
             snxt += d2+epsil;
             return snxt;
          }
          // propagate to '-'
          snxt += d1+epsil;
          for (i=0; i<3; i++) master[i] += (d1+1E-8)*dir[i];
          epsil = 1.E-8;
          // now inside '-' and not inside '+'
          fRightMat->MasterToLocal(&master[0], &local[0]);
          inside = kTRUE;
       }
    }
    //-----------------------------------------------------------------------------
    Int_t TGeoSubtraction::GetNpoints() const
    {
    // Returns number of vertices for the composite shape described by this subtraction.
       return 0;
    }
    //-----------------------------------------------------------------------------
    Double_t TGeoSubtraction::Safety(Double_t *point, Bool_t) const
    {
    // Compute safety distance for a union node;
       Double_t local1[3], local2[3];
       fLeftMat->MasterToLocal(point,local1);
       Bool_t in1 = fLeft->Contains(local1);
       fRightMat->MasterToLocal(point,local2);
       Bool_t in2 = fRight->Contains(local2);
       Double_t saf1 = fLeft->Safety(local1, in1);
       Double_t saf2 = fRight->Safety(local2, in2);
       if (in1 && in2) return saf2;
       if (in1)        return TMath::Min(saf1,saf2);
       if (in2)        return TMath::Max(saf1,saf2);
       return saf1;
    }
    //_____________________________________________________________________________
    void TGeoSubtraction::SavePrimitive(ofstream &out, Option_t *option)
    {
    // Save a primitive as a C++ statement(s) on output stream "out".
       TGeoBoolNode::SavePrimitive(out,option);
       out << "   pBoolNode = new TGeoSubtraction(";
       out << fLeft->GetPointerName() << ",";
       out << fRight->GetPointerName() << ",";
       if (!fLeftMat->IsIdentity()) out << fLeftMat->GetPointerName() << ",";
       else                         out << "0,";
       if (!fRightMat->IsIdentity()) out << fRightMat->GetPointerName() << ");" << endl;
       else                         out << "0);" << endl;
    }
    //-----------------------------------------------------------------------------
    void TGeoSubtraction::SetPoints(Double_t * /*points*/) const
    {
    // Fill buffer with shape vertices.
    }
    //-----------------------------------------------------------------------------
    void TGeoSubtraction::SetPoints(Float_t * /*points*/) const
    {
    // Fill buffer with shape vertices.
    }
    //-----------------------------------------------------------------------------
    void TGeoSubtraction::Sizeof3D() const
    {
    // Register 3D size of this shape.
       TGeoBoolNode::Sizeof3D();
    }

    ClassImp(TGeoIntersection)

    //-----------------------------------------------------------------------------
     void TGeoIntersection::Paint(Option_t *option)
    {
       TVirtualViewer3D *viewer = gPad->GetViewer3D();

       if (!viewer) {
          Error("Paint", "gPad->GetViewer3D() returned 0, cannot work with composite!\n");
          return;
       }

       viewer->AddCompositeOp(TBuffer3D::kCSIntersection);

       TGeoBoolNode::Paint(option);
    }

    //-----------------------------------------------------------------------------
     TGeoIntersection::TGeoIntersection()
    {
    // Default constructor
    }

    //-----------------------------------------------------------------------------
     TGeoIntersection::TGeoIntersection(const char *expr1, const char *expr2)
              :TGeoBoolNode(expr1, expr2)
    {
    // Constructor
    }

    //-----------------------------------------------------------------------------
     TGeoIntersection::TGeoIntersection(TGeoShape *left, TGeoShape *right, TGeoMatrix *lmat, TGeoMatrix *rmat)
                     :TGeoBoolNode(left,right,lmat,rmat)
    {
    // Constructor providing pointers to components
       Bool_t hs1 = (fLeft->TestShapeBit(TGeoShape::kGeoHalfSpace))?kTRUE:kFALSE;
       Bool_t hs2 = (fRight->TestShapeBit(TGeoShape::kGeoHalfSpace))?kTRUE:kFALSE;
       if (hs1 && hs2) Fatal("ctor", "cannot intersect two half-spaces: %s * %s", left->GetName(), right->GetName());
    }

    //-----------------------------------------------------------------------------
     TGeoIntersection::~TGeoIntersection()
    {
    // Destructor
    // --- deletion of components handled by TGeoManager class.
    }

    //-----------------------------------------------------------------------------
     void TGeoIntersection::ComputeBBox(Double_t &dx, Double_t &dy, Double_t &dz, Double_t *origin)
    {
    // Compute bounding box corresponding to a intersection of two shapes.
       Bool_t hs1 = (fLeft->TestShapeBit(TGeoShape::kGeoHalfSpace))?kTRUE:kFALSE;
       Bool_t hs2 = (fRight->TestShapeBit(TGeoShape::kGeoHalfSpace))?kTRUE:kFALSE;
       Double_t vert[48];
       Double_t pt[3];
       Int_t i;
       Double_t xmin1, xmax1, ymin1, ymax1, zmin1, zmax1;
       Double_t xmin2, xmax2, ymin2, ymax2, zmin2, zmax2;
       xmin1 = ymin1 = zmin1 = xmin2 = ymin2 = zmin2 = TGeoShape::Big();
       xmax1 = ymax1 = zmax1 = xmax2 = ymax2 = zmax2 =  -TGeoShape::Big();
       if (!hs1) {
          if (((TGeoBBox*)fLeft)->IsNullBox()) fLeft->ComputeBBox();
          ((TGeoBBox*)fLeft)->SetBoxPoints(&vert[0]);
          for (i=0; i<8; i++) {
             fLeftMat->LocalToMaster(&vert[3*i], &pt[0]);
             if (pt[0]<xmin1) xmin1=pt[0];
             if (pt[0]>xmax1) xmax1=pt[0];
             if (pt[1]<ymin1) ymin1=pt[1];
             if (pt[1]>ymax1) ymax1=pt[1];
             if (pt[2]<zmin1) zmin1=pt[2];
             if (pt[2]>zmax1) zmax1=pt[2];
          }
       }
       if (!hs2) {
          if (((TGeoBBox*)fRight)->IsNullBox()) fRight->ComputeBBox();
          ((TGeoBBox*)fRight)->SetBoxPoints(&vert[24]);
          for (i=8; i<16; i++) {
             fRightMat->LocalToMaster(&vert[3*i], &pt[0]);
             if (pt[0]<xmin2) xmin2=pt[0];
             if (pt[0]>xmax2) xmax2=pt[0];
             if (pt[1]<ymin2) ymin2=pt[1];
             if (pt[1]>ymax2) ymax2=pt[1];
             if (pt[2]<zmin2) zmin2=pt[2];
             if (pt[2]>zmax2) zmax2=pt[2];
          }
       }
       if (hs1) {
          dx = 0.5*(xmax2-xmin2);
          origin[0] = 0.5*(xmax2+xmin2);
          dy = 0.5*(ymax2-ymin2);
          origin[1] = 0.5*(ymax2+ymin2);
          dz = 0.5*(zmax2-zmin2);
          origin[2] = 0.5*(zmax2+zmin2);
          return;
       }
       if (hs2) {
          dx = 0.5*(xmax1-xmin1);
          origin[0] = 0.5*(xmax1+xmin1);
          dy = 0.5*(ymax1-ymin1);
          origin[1] = 0.5*(ymax1+ymin1);
          dz = 0.5*(zmax1-zmin1);
          origin[2] = 0.5*(zmax1+zmin1);
          return;
       }
       Double_t sort[4];
       Int_t isort[4];
       sort[0] = xmin1;
       sort[1] = xmax1;
       sort[2] = xmin2;
       sort[3] = xmax2;
       TMath::Sort(4, &sort[0], &isort[0], kFALSE);
       if (isort[1]%2) {
          Warning("ComputeBBox", "shapes %s and %s do not intersect", fLeft->GetName(), fRight->GetName());
          dx = dy = dz = 0;
          memset(origin, 0, 3*sizeof(Double_t));
          return;
       }
       dx = 0.5*(sort[isort[2]]-sort[isort[1]]);
       origin[0] = 0.5*(sort[isort[1]]+sort[isort[2]]);
       sort[0] = ymin1;
       sort[1] = ymax1;
       sort[2] = ymin2;
       sort[3] = ymax2;
       TMath::Sort(4, &sort[0], &isort[0], kFALSE);
       if (isort[1]%2) {
          Warning("ComputeBBox", "shapes %s and %s do not intersect", fLeft->GetName(), fRight->GetName());
          dx = dy = dz = 0;
          memset(origin, 0, 3*sizeof(Double_t));
          return;
       }
       dy = 0.5*(sort[isort[2]]-sort[isort[1]]);
       origin[1] = 0.5*(sort[isort[1]]+sort[isort[2]]);
       sort[0] = zmin1;
       sort[1] = zmax1;
       sort[2] = zmin2;
       sort[3] = zmax2;
       TMath::Sort(4, &sort[0], &isort[0], kFALSE);
       if (isort[1]%2) {
          Warning("ComputeBBox", "shapes %s and %s do not intersect", fLeft->GetName(), fRight->GetName());
          dx = dy = dz = 0;
          memset(origin, 0, 3*sizeof(Double_t));
          return;
       }
       dz = 0.5*(sort[isort[2]]-sort[isort[1]]);
       origin[2] = 0.5*(sort[isort[1]]+sort[isort[2]]);
    }

    //_____________________________________________________________________________
     void TGeoIntersection::ComputeNormal(Double_t *point, Double_t *dir, Double_t *norm)
    {
       Double_t local[3], ldir[3], lnorm[3];
       norm[0] = norm[1] = 0.;
       norm[2] = 1.;
       if (fSelected == 1) {
          fLeftMat->MasterToLocal(point, local);
          fLeftMat->MasterToLocalVect(dir, ldir);
          fLeft->ComputeNormal(local,ldir,lnorm);
          fLeftMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       if (fSelected == 2) {
          fRightMat->MasterToLocal(point, local);
          fRightMat->MasterToLocalVect(dir, ldir);
          fRight->ComputeNormal(local,ldir,lnorm);
          fRightMat->LocalToMasterVect(lnorm, norm);
          return;
       }
       fLeftMat->MasterToLocal(point,local);
       if (!fLeft->Contains(local)) {
          fLeftMat->MasterToLocalVect(dir,ldir);
          fLeft->ComputeNormal(local,ldir,lnorm);
          fLeftMat->LocalToMasterVect(lnorm,norm);
          return;
       }
       fRightMat->MasterToLocal(point,local);
       if (!fRight->Contains(local)) {
          fRightMat->MasterToLocalVect(dir,ldir);
          fRight->ComputeNormal(local,ldir,lnorm);
          fRightMat->LocalToMasterVect(lnorm,norm);
          return;
       }
       // point is inside intersection.
       local[0] = point[0] + 1E-5*dir[0];
       local[1] = point[1] + 1E-5*dir[1];
       local[2] = point[2] + 1E-5*dir[2];
       if (Contains(local)) {
          local[0] = point[0] - 1E-5*dir[0];
          local[1] = point[1] - 1E-5*dir[1];
          local[2] = point[2] - 1E-5*dir[2];
          if (Contains(local)) return;
       }
       ComputeNormal(local,dir,norm);
    }

    //-----------------------------------------------------------------------------
     Bool_t TGeoIntersection::Contains(Double_t *point) const
    {
    // Find if a intersection of two shapes contains a given point
       Double_t local[3];
       fLeftMat->MasterToLocal(point, &local[0]);
       Bool_t inside = fLeft->Contains(&local[0]);
       if (!inside) return kFALSE;
       fRightMat->MasterToLocal(point, &local[0]);
       inside = fRight->Contains(&local[0]);
       return inside;
    }
    //-----------------------------------------------------------------------------
     Int_t TGeoIntersection::DistanceToPrimitive(Int_t /*px*/, Int_t /*py*/)
    {
    // Compute minimum distance to shape vertices
       return 9999;
    }
    //-----------------------------------------------------------------------------
     Double_t TGeoIntersection::DistFromInside(Double_t *point, Double_t *dir, Int_t iact,
                                  Double_t step, Double_t *safe) const
    {
    // Compute distance from a given point to outside.
       if (iact<3 && safe) {
          // compute safe distance
          *safe = Safety(point,kTRUE);
          if (iact==0) return TGeoShape::Big();
          if (iact==1 && step<*safe) return TGeoShape::Big();
       }
       TGeoBoolNode *node = (TGeoBoolNode*)this;
       Double_t local[3], ldir[3], rdir[3];
       Double_t d1, d2, snxt=0.;
       fLeftMat->MasterToLocal(point, &local[0]);
       fLeftMat->MasterToLocalVect(dir, &ldir[0]);
       fRightMat->MasterToLocalVect(dir, &rdir[0]);
       d1 = fLeft->DistFromInside(&local[0], &ldir[0], iact, step, safe);
       fRightMat->MasterToLocal(point, &local[0]);
       d2 = fRight->DistFromInside(&local[0], &rdir[0], iact, step, safe);
       if (d1<d2) {
          snxt = d1;
          node->SetSelected(1);
       } else {
          snxt = d2;
          node->SetSelected(2);
       }
       return snxt;
    }
    //-----------------------------------------------------------------------------
     Double_t TGeoIntersection::DistFromOutside(Double_t *point, Double_t *dir, Int_t iact,
                                  Double_t step, Double_t *safe) const
    {
    // Compute distance from a given point to inside.
       if (iact<3 && safe) {
          // compute safe distance
          *safe = Safety(point,kFALSE);
          if (iact==0) return TGeoShape::Big();
          if (iact==1 && step<*safe) return TGeoShape::Big();
       }
       TGeoBoolNode *node = (TGeoBoolNode*)this;
       Double_t lpt[3], rpt[3], master[3], ldir[3], rdir[3];
       memcpy(master, point, 3*sizeof(Double_t));
       Int_t i;
       Double_t d1 = 0.;
       Double_t d2 = 0.;
       fLeftMat->MasterToLocal(point, lpt);
       fRightMat->MasterToLocal(point, rpt);
       fLeftMat->MasterToLocalVect(dir, ldir);
       fRightMat->MasterToLocalVect(dir, rdir);
       Bool_t inleft = fLeft->Contains(lpt);
       Bool_t inright = fRight->Contains(rpt);
       node->SetSelected(0);
       Double_t snext = 0.0;
       if (inleft && inright) return snext;

       while (1) {
          d1 = d2 = 0.0;
          if (!inleft)  {
             d1 = fLeft->DistFromOutside(lpt,ldir,3);
             if (d1>1E20) return TGeoShape::Big();
          }
          if (!inright) {
             d2 = fRight->DistFromOutside(rpt,rdir,3);
             if (d2>1E20) return TGeoShape::Big();
          }

          if (d1>d2) {
             // propagate to left shape
             snext += d1;
             node->SetSelected(1);
             inleft = kTRUE;
             for (i=0; i<3; i++) master[i] += d1*dir[i];
             fRightMat->MasterToLocal(master,rpt);
             // check if propagated point is inside right shape
             inright = fRight->Contains(rpt);
             if (inright) return snext;
             // here inleft=true, inright=false
          } else {
             // propagate to right shape
             snext += d2;
             node->SetSelected(2);
             inright = kTRUE;
             for (i=0; i<3; i++) master[i] += d2*dir[i];
             fLeftMat->MasterToLocal(master,lpt);
             // check if propagated point is inside left shape
             inleft = fLeft->Contains(lpt);
             if (inleft) return snext;
             // here inleft=false, inright=true
          }
       }
       return snext;
    }

    //-----------------------------------------------------------------------------
     Int_t TGeoIntersection::GetNpoints() const
    {
    // Returns number of vertices for the composite shape described by this intersection.
       return 0;
    }
    //-----------------------------------------------------------------------------
     Double_t TGeoIntersection::Safety(Double_t *point, Bool_t) const
    {
    // Compute safety distance for a union node;
       Double_t local1[3], local2[3];
       fLeftMat->MasterToLocal(point,local1);
       Bool_t in1 = fLeft->Contains(local1);
       fRightMat->MasterToLocal(point,local2);
       Bool_t in2 = fRight->Contains(local2);
       Double_t saf1 = fLeft->Safety(local1, in1);
       Double_t saf2 = fRight->Safety(local2, in2);
       if (in1 && in2) return TMath::Min(saf1, saf2);
       if (in1)        return saf2;
       if (in2)        return saf1;
       return TMath::Max(saf1,saf2);
    }
    //_____________________________________________________________________________
     void TGeoIntersection::SavePrimitive(ofstream &out, Option_t *option)
    {
    // Save a primitive as a C++ statement(s) on output stream "out".
       TGeoBoolNode::SavePrimitive(out,option);
       out << "   pBoolNode = new TGeoIntersection(";
       out << fLeft->GetPointerName() << ",";
       out << fRight->GetPointerName() << ",";
       if (!fLeftMat->IsIdentity()) out << fLeftMat->GetPointerName() << ",";
       else                         out << "0,";
       if (!fRightMat->IsIdentity()) out << fRightMat->GetPointerName() << ");" << endl;
       else                         out << "0);" << endl;
    }
    //-----------------------------------------------------------------------------
     void TGeoIntersection::SetPoints(Double_t * /*points*/) const
    {
    // Fill buffer with shape vertices.
    }
    //-----------------------------------------------------------------------------
     void TGeoIntersection::SetPoints(Float_t * /*points*/) const
    {
    // Fill buffer with shape vertices.
    }
    //-----------------------------------------------------------------------------
     void TGeoIntersection::Sizeof3D() const
    {
    // Register 3D size of this shape.
       TGeoBoolNode::Sizeof3D();
    }