TGLBoundingBox.cxx

Go to the documentation of this file.

// @(#)root/gl:$Id: TGLBoundingBox.cxx 37397 2010-12-08 13:54:23Z matevz $
// Author:  Richard Maunder  25/05/2005

/*************************************************************************
 * 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 "TGLBoundingBox.h"
#include "TGLIncludes.h"
#include "TMathBase.h"

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TGLBoundingBox                                                       //
//                                                                      //
// Concrete class describing an orientated (free) or axis aligned box   //
// of 8 verticies. Supports methods for setting aligned or orientated   //
// boxes, find volume, axes, extents, centers, face planes etc.         //
// Also tests for overlap testing of planes and other bounding boxes,   //
// with fast sphere approximation.                                      //
//////////////////////////////////////////////////////////////////////////

ClassImp(TGLBoundingBox)

//______________________________________________________________________________
TGLBoundingBox::TGLBoundingBox()
{
   // Construct an empty bounding box
   SetEmpty();
}

//______________________________________________________________________________
TGLBoundingBox::TGLBoundingBox(const TGLVertex3 vertex[8])
{
   // Construct a bounding box from provided 8 vertices
   Set(vertex);
}

//______________________________________________________________________________
TGLBoundingBox::TGLBoundingBox(const Double_t vertex[8][3])
{
   // Construct a bounding box from provided 8 vertices
   Set(vertex);
}

//______________________________________________________________________________
TGLBoundingBox::TGLBoundingBox(const TGLVertex3 & lowVertex, const TGLVertex3 & highVertex)
{
   // Construct an global axis ALIGNED bounding box from provided low/high vertex pair
   SetAligned(lowVertex, highVertex);
}

//______________________________________________________________________________
TGLBoundingBox::TGLBoundingBox(const TGLBoundingBox & other)
{
   // Construct a bounding box as copy of existing one
   Set(other);
}

//______________________________________________________________________________
TGLBoundingBox::~TGLBoundingBox()
{
  // Destroy bounding box
}

//______________________________________________________________________________
void TGLBoundingBox::UpdateCache()
{
   // Update the internally cached volume and axes vectors - these are retained
   // for efficiency - many more reads than modifications

   //    y
   //    |
   //    |
   //    |________x
   //   /  3-------2
   //  /  /|      /|
   // z  7-------6 |
   //    | 0-----|-1
   //    |/      |/
   //    4-------5
   //

   // Do axes first so Extents() is correct
   fAxes[0].Set(fVertex[1] - fVertex[0]);
   fAxes[1].Set(fVertex[3] - fVertex[0]);
   fAxes[2].Set(fVertex[4] - fVertex[0]);

   // Sometimes have zero volume BB due to single zero magnitude
   // axis record and try to fix below
   Bool_t fixZeroMagAxis = kFALSE;
   Int_t zeroMagAxisInd = -1;
   for (UInt_t i = 0; i<3; i++) {
      fAxesNorm[i] = fAxes[i];
      Double_t mag = fAxesNorm[i].Mag();
      if (mag > 0.0) {
         fAxesNorm[i] /= mag;
      } else {
         if (!fixZeroMagAxis && zeroMagAxisInd == -1) {
            zeroMagAxisInd = i;
            fixZeroMagAxis = kTRUE;
         } else if (fixZeroMagAxis) {
            fixZeroMagAxis = kFALSE;
         }
      }
   }

   // Try to cope with a zero volume bounding box where one
   // axis is zero by using cross product of other two
   if (fixZeroMagAxis) {
      fAxesNorm[zeroMagAxisInd] = Cross(fAxesNorm[(zeroMagAxisInd+1)%3],
                                        fAxesNorm[(zeroMagAxisInd+2)%3]);
   }

   TGLVector3 extents = Extents();
   fVolume   = TMath::Abs(extents.X() * extents.Y() * extents.Z());
   fDiagonal = extents.Mag();
}

//______________________________________________________________________________
void TGLBoundingBox::Set(const TGLVertex3 vertex[8])
{
   // Set a bounding box from provided 8 vertices
   for (UInt_t v = 0; v < 8; v++) {
      fVertex[v] = vertex[v];
   }
   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
void TGLBoundingBox::Set(const Double_t vertex[8][3])
{
   // Set a bounding box from provided 8 vertices
   for (UInt_t v = 0; v < 8; v++) {
      for (UInt_t a = 0; a < 3; a++) {
         fVertex[v][a] = vertex[v][a];
      }
   }
   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
void TGLBoundingBox::Set(const TGLBoundingBox & other)
{
   // Set a bounding box from vertices of other
   for (UInt_t v = 0; v < 8; v++) {
      fVertex[v].Set(other.fVertex[v]);
   }
   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
void TGLBoundingBox::SetEmpty()
{
   // Set bounding box empty - all vertices at (0,0,0)
   for (UInt_t v = 0; v < 8; v++) {
      fVertex[v].Fill(0.0);
   }
   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
void TGLBoundingBox::SetAligned(const TGLVertex3 & lowVertex, const TGLVertex3 & highVertex)
{
   // Set ALIGNED box from two low/high vertices. Box axes are aligned with
   // global frame axes that vertices are specified in.

   // lowVertex = vertex[0]
   // highVertex = vertex[6]
   //
   //    y
   //    |
   //    |
   //    |________x
   //   /  3-------2
   //  /  /|      /|
   // z  7-------6 |
   //    | 0-----|-1
   //    |/      |/
   //    4-------5
   //

   TGLVector3 diff = highVertex - lowVertex;
   if (diff.X() < 0.0 || diff.Y() < 0.0 || diff.Z() < 0.0) {
      Error("TGLBoundingBox::SetAligned", "low/high vertex range error");
   }
   fVertex[0] = lowVertex;
   fVertex[1] = lowVertex;  fVertex[1].X() += diff.X();
   fVertex[2] = lowVertex;  fVertex[2].X() += diff.X(); fVertex[2].Y() += diff.Y();
   fVertex[3] = lowVertex;  fVertex[3].Y() += diff.Y();
   fVertex[4] = highVertex; fVertex[4].X() -= diff.X(); fVertex[4].Y() -= diff.Y();
   fVertex[5] = highVertex; fVertex[5].Y() -= diff.Y();
   fVertex[6] = highVertex;
   fVertex[7] = highVertex; fVertex[7].X() -= diff.X();
   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
void TGLBoundingBox::SetAligned(UInt_t nbPnts, const Double_t * pnts)
{
   // Set ALIGNED box from one or more points. Box axes are aligned with
   // global frame axes that points are specified in.
   if (nbPnts < 1 || !pnts) {
      assert(false);
      return;
   }

   // Single point gives a zero volume BB
   TGLVertex3 low(pnts[0], pnts[1], pnts[2]);
   TGLVertex3 high(pnts[0], pnts[1], pnts[2]);

   for (UInt_t p = 1; p < nbPnts; p++) {
      for (UInt_t i = 0; i < 3; i++) {
         if (pnts[3*p + i] < low[i]) {
            low[i] = pnts[3*p + i] ;
         }
         if (pnts[3*p + i] > high[i]) {
            high[i] = pnts[3*p + i] ;
         }
      }
   }

   SetAligned(low, high);
}

//______________________________________________________________________________
void TGLBoundingBox::MergeAligned(const TGLBoundingBox & other)
{
   // Expand current bbox so that it includes other's bbox.
   // This make the bbox axis-aligned.

   if (other.IsEmpty()) return;
   if (IsEmpty())
   {
      Set(other);
   }
   else
   {
      TGLVertex3 low (other.MinAAVertex());
      TGLVertex3 high(other.MaxAAVertex());

      low .Minimum(MinAAVertex());
      high.Maximum(MaxAAVertex());
      SetAligned(low, high);
   }
}

//______________________________________________________________________________
void TGLBoundingBox::ExpandAligned(const TGLVertex3 & point)
{
   // Expand current bbox so that it includes the point.
   // This make the bbox axis-aligned.

   TGLVertex3 low (MinAAVertex());
   TGLVertex3 high(MaxAAVertex());

   low .Minimum(point);
   high.Maximum(point);

   SetAligned(low, high);
}

//______________________________________________________________________________
void TGLBoundingBox::Scale(Double_t factor)
{
   // Isotropically scale bounding box along it's LOCAL axes, preserving center
   Scale(factor, factor, factor);
   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
void TGLBoundingBox::Scale(Double_t xFactor, Double_t yFactor, Double_t zFactor)
{
   // Asymetrically scale box along it's LOCAL x,y,z axes, preserving center

   // Get x,y,z edges (non-normalised axis) and scale
   // them by factors
   const TGLVector3 xOffset = Axis(0, kFALSE)*(xFactor - 1.0) / 2.0;
   const TGLVector3 yOffset = Axis(1, kFALSE)*(yFactor - 1.0) / 2.0;
   const TGLVector3 zOffset = Axis(2, kFALSE)*(zFactor - 1.0) / 2.0;

   //    y
   //    |
   //    |
   //    |________x
   //   /  3-------2
   //  /  /|      /|
   // z  7-------6 |
   //    | 0-----|-1
   //    |/      |/
   //    4-------5
   //
   fVertex[0] += -xOffset - yOffset - zOffset;
   fVertex[1] +=  xOffset - yOffset - zOffset;
   fVertex[2] +=  xOffset + yOffset - zOffset;
   fVertex[3] += -xOffset + yOffset - zOffset;

   fVertex[4] += -xOffset - yOffset + zOffset;
   fVertex[5] +=  xOffset - yOffset + zOffset;
   fVertex[6] +=  xOffset + yOffset + zOffset;
   fVertex[7] += -xOffset + yOffset + zOffset;

   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
void TGLBoundingBox::Translate(const TGLVector3 & offset)
{
   // Translate all vertices by offset
   for (UInt_t v = 0; v < 8; v++) {
      fVertex[v] = fVertex[v] + offset;
   }

   // No cache change - volume and axes vectors remain same
}

//______________________________________________________________________________
void TGLBoundingBox::Transform(const TGLMatrix & matrix)
{
   // Transform all vertices with matrix.

   for (UInt_t v = 0; v < 8; v++) {
      matrix.TransformVertex(fVertex[v]);
   }

   // Could change cached volume/axes
   UpdateCache();
}

//______________________________________________________________________________
const std::vector<UInt_t> & TGLBoundingBox::FaceVertices(EFace face) const
{
   //return a vector of face vertices
   //    y
   //    |
   //    |
   //    |________x
   //   /  3-------2
   //  /  /|      /|
   // z  7-------6 |
   //    | 0-----|-1
   //    |/      |/
   //    4-------5
   //
   static Bool_t init = kFALSE;
   static std::vector<UInt_t> faceIndexes[kFaceCount];
   if (!init) {
      // Low X - 7403
      faceIndexes[kFaceLowX].push_back(7);
      faceIndexes[kFaceLowX].push_back(4);
      faceIndexes[kFaceLowX].push_back(0);
      faceIndexes[kFaceLowX].push_back(3);
      // High X - 2156
      faceIndexes[kFaceHighX].push_back(2);
      faceIndexes[kFaceHighX].push_back(1);
      faceIndexes[kFaceHighX].push_back(5);
      faceIndexes[kFaceHighX].push_back(6);
      // Low Y - 5104
      faceIndexes[kFaceLowY].push_back(5);
      faceIndexes[kFaceLowY].push_back(1);
      faceIndexes[kFaceLowY].push_back(0);
      faceIndexes[kFaceLowY].push_back(4);
      // High Y - 2673
      faceIndexes[kFaceHighY].push_back(2);
      faceIndexes[kFaceHighY].push_back(6);
      faceIndexes[kFaceHighY].push_back(7);
      faceIndexes[kFaceHighY].push_back(3);
      // Low Z - 3012
      faceIndexes[kFaceLowZ].push_back(3);
      faceIndexes[kFaceLowZ].push_back(0);
      faceIndexes[kFaceLowZ].push_back(1);
      faceIndexes[kFaceLowZ].push_back(2);
      // High Z - 6547
      faceIndexes[kFaceHighZ].push_back(6);
      faceIndexes[kFaceHighZ].push_back(5);
      faceIndexes[kFaceHighZ].push_back(4);
      faceIndexes[kFaceHighZ].push_back(7);
      init= kTRUE;
   }
   return faceIndexes[face];
}

//______________________________________________________________________________
void TGLBoundingBox::PlaneSet(TGLPlaneSet_t & planeSet) const
{
   // Fill out supplied plane set vector with TGLPlane objects
   // representing six faces of box
   assert(planeSet.empty());

   //    y
   //    |
   //    |
   //    |________x
   //   /  3-------2
   //  /  /|      /|
   // z  7-------6 |
   //    | 0-----|-1
   //    |/      |/
   //    4-------5
   //
   // Construct plane set using axis + vertices
   planeSet.push_back(TGLPlane( fAxesNorm[2], fVertex[4])); // Near
   planeSet.push_back(TGLPlane(-fAxesNorm[2], fVertex[0])); // Far
   planeSet.push_back(TGLPlane(-fAxesNorm[0], fVertex[0])); // Left
   planeSet.push_back(TGLPlane( fAxesNorm[0], fVertex[1])); // Right
   planeSet.push_back(TGLPlane(-fAxesNorm[1], fVertex[0])); // Bottom
   planeSet.push_back(TGLPlane( fAxesNorm[1], fVertex[3])); // Top
}

//______________________________________________________________________________
TGLPlane TGLBoundingBox::GetNearPlane() const
{
   // Return the near-plane.

   return TGLPlane(fAxesNorm[2], fVertex[4]);
}

//______________________________________________________________________________
EOverlap TGLBoundingBox::Overlap(const TGLPlane & plane) const
{
   // Find overlap (Inside, Outside, Partial) of plane c.f. bounding box.

   // First : cheap square approxiamtion test. If distance of our
   // center to plane > our half extent length we are outside plane
   if (plane.DistanceTo(Center()) + (Extents().Mag()/2.0) < 0.0) {
      return kOutside;
   }

   // Second : test all 8 box vertices against plane
   Int_t verticesInsidePlane = 8;
   for (UInt_t v = 0; v < 8; v++) {
      if (plane.DistanceTo(fVertex[v]) < 0.0) {
         verticesInsidePlane--;
      }
   }

   if ( verticesInsidePlane == 0 ) {
      return kOutside;
   } else if ( verticesInsidePlane == 8 ) {
      return kInside;
   } else {
      return kPartial;
   }
}

//______________________________________________________________________________
EOverlap TGLBoundingBox::Overlap(const TGLBoundingBox & other) const
{
   // Find overlap (Inside, Outside, Partial) of other bounding box c.f. us.

   // Simplify code with refs
   const TGLBoundingBox & a = *this;
   const TGLBoundingBox & b = other;

   TGLVector3 aHL = a.Extents() / 2.0; // Half length extents
   TGLVector3 bHL = b.Extents() / 2.0; // Half length extents

   // Following tests are greatly simplified
   // if we convert into our local frame

   // Find translation in parent frame
   TGLVector3 parentT = b.Center() - a.Center();

   // First: Do a simple & cheap sphere approximation containment test.
   // In many uses b will be completely contained by a and very much smaller
   // these cases short circuited here

   // We need the inner sphere for the container (box a) - radius = shortest box half length
   Double_t aSphereRadius = aHL[0] < aHL[1] ? aHL[0] : aHL[1];
   if (aHL[2] < aSphereRadius) {
      aSphereRadius = aHL[2];
   }
   // and the outer sphere for containee (box b) - radius = box diagonal
   Double_t bSphereRadius = bHL.Mag();

   // If b sphere radius + translation mag is smaller than b sphere radius
   // b is complete contained by a
   if (bSphereRadius + parentT.Mag() < aSphereRadius) {
      return kInside;
   }

   // Second: Perform more expensive 15 seperating axes test

   // Find translation in A's frame
   TGLVector3 aT(Dot(parentT, a.Axis(0)), Dot(parentT, a.Axis(1)), Dot(parentT, a.Axis(2)));

   // Find B's basis with respect to A's local frame
   // Get rotation matrix
   Double_t   roaT[3][3];
   UInt_t     i, k;
   for (i=0 ; i<3 ; i++) {
      for (k=0; k<3; k++) {
         roaT[i][k] = Dot(a.Axis(i), b.Axis(k));
         // Force very small components to zero to avoid rounding errors
         if (fabs(roaT[i][k]) < 1e-14) {
            roaT[i][k] = 0.0;
         }
      }
      // Normalise columns to avoid rounding errors
      Double_t norm = sqrt(roaT[i][0]*roaT[i][0] + roaT[i][1]*roaT[i][1] + roaT[i][2]*roaT[i][2]);
      roaT[i][0] /= norm; roaT[i][1] /= norm; roaT[i][2] /= norm;
   }

   // Perform separating axis test for all 15 potential
   // axes. If no separating axes found, the two boxes overlap.
   Double_t ra, rb, t;

   // A's 3 basis vectors
   for (i=0; i<3; i++) {
      ra = aHL[i];
      rb = bHL[0]*fabs(roaT[i][0]) + bHL[1]*fabs(roaT[i][1]) + bHL[2]*fabs(roaT[i][2]);
      t = fabs(aT[i]);
      if (t > ra + rb)
         return kOutside;
      else if (ra < t + rb)
         return kPartial;
   }

   // B's 3 basis vectors
   for (k=0; k<3; k++) {
      ra = aHL[0]*fabs(roaT[0][k]) + aHL[1]*fabs(roaT[1][k]) + aHL[2]*fabs(roaT[2][k]);
      rb = bHL[k];
      t = fabs(aT[0]*roaT[0][k] + aT[1]*roaT[1][k] + aT[2]*roaT[2][k]);
      if (t > ra + rb)
         return kOutside;
      else if (ra < t + rb)
         return kPartial;
   }

   // Now the 9 cross products

   // A0 x B0
   ra = aHL[1]*fabs(roaT[2][0]) + aHL[2]*fabs(roaT[1][0]);
   rb = bHL[1]*fabs(roaT[0][2]) + bHL[2]*fabs(roaT[0][1]);
   t = fabs(aT[2]*roaT[1][0] - aT[1]*roaT[2][0]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A0 x B1
   ra = aHL[1]*fabs(roaT[2][1]) + aHL[2]*fabs(roaT[1][1]);
   rb = bHL[0]*fabs(roaT[0][2]) + bHL[2]*fabs(roaT[0][0]);
   t = fabs(aT[2]*roaT[1][1] - aT[1]*roaT[2][1]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A0 x B2
   ra = aHL[1]*fabs(roaT[2][2]) + aHL[2]*fabs(roaT[1][2]);
   rb = bHL[0]*fabs(roaT[0][1]) + bHL[1]*fabs(roaT[0][0]);
   t = fabs(aT[2]*roaT[1][2] - aT[1]*roaT[2][2]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A1 x B0
   ra = aHL[0]*fabs(roaT[2][0]) + aHL[2]*fabs(roaT[0][0]);
   rb = bHL[1]*fabs(roaT[1][2]) + bHL[2]*fabs(roaT[1][1]);
   t = fabs(aT[0]*roaT[2][0] - aT[2]*roaT[0][0]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A1 x B1
   ra = aHL[0]*fabs(roaT[2][1]) + aHL[2]*fabs(roaT[0][1]);
   rb = bHL[0]*fabs(roaT[1][2]) + bHL[2]*fabs(roaT[1][0]);
   t = fabs(aT[0]*roaT[2][1] - aT[2]*roaT[0][1]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A1 x B2
   ra = aHL[0]*fabs(roaT[2][2]) + aHL[2]*fabs(roaT[0][2]);
   rb = bHL[0]*fabs(roaT[1][1]) + bHL[1]*fabs(roaT[1][0]);
   t = fabs(aT[0]*roaT[2][2] - aT[2]*roaT[0][2]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A2 x B0
   ra = aHL[0]*fabs(roaT[1][0]) + aHL[1]*fabs(roaT[0][0]);
   rb = bHL[1]*fabs(roaT[2][2]) + bHL[2]*fabs(roaT[2][1]);
   t = fabs(aT[1]*roaT[0][0] - aT[0]*roaT[1][0]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A2 x B1
   ra = aHL[0]*fabs(roaT[1][1]) + aHL[1]*fabs(roaT[0][1]);
   rb = bHL[0]*fabs(roaT[2][2]) + bHL[2]*fabs(roaT[2][0]);
   t = fabs(aT[1]*roaT[0][1] - aT[0]*roaT[1][1]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // A2 x B2
   ra = aHL[0]*fabs(roaT[1][2]) + aHL[1]*fabs(roaT[0][2]);
   rb = bHL[0]*fabs(roaT[2][1]) + bHL[1]*fabs(roaT[2][0]);
   t = fabs(aT[1]*roaT[0][2] - aT[0]*roaT[1][2]);
   if (t > ra + rb)
      return kOutside;
   else if (ra < t + rb)
      return kPartial;

   // No separating axis - b is inside a
   return kInside;
}

//______________________________________________________________________________
void TGLBoundingBox::Draw(Bool_t solid) const
{
   // Draw the bounding box as either wireframe (default) of solid
   // using current GL color.

   if (!solid) {
      glBegin(GL_LINE_LOOP);
      glVertex3dv(fVertex[0].CArr());
      glVertex3dv(fVertex[1].CArr());
      glVertex3dv(fVertex[2].CArr());
      glVertex3dv(fVertex[3].CArr());
      glVertex3dv(fVertex[7].CArr());
      glVertex3dv(fVertex[6].CArr());
      glVertex3dv(fVertex[5].CArr());
      glVertex3dv(fVertex[4].CArr());
      glEnd();
      glBegin(GL_LINES);
      glVertex3dv(fVertex[1].CArr());
      glVertex3dv(fVertex[5].CArr());
      glVertex3dv(fVertex[2].CArr());
      glVertex3dv(fVertex[6].CArr());
      glVertex3dv(fVertex[0].CArr());
      glVertex3dv(fVertex[3].CArr());
      glVertex3dv(fVertex[4].CArr());
      glVertex3dv(fVertex[7].CArr());
      glEnd();
   } else {
   //    y
   //    |
   //    |
   //    |________x
   //   /  3-------2
   //  /  /|      /|
   // z  7-------6 |
   //    | 0-----|-1
   //    |/      |/
   //    4-------5
      // Clockwise winding
      glBegin(GL_QUADS);
      // Near
      glNormal3d ( fAxesNorm[2].X(),  fAxesNorm[2].Y(),  fAxesNorm[2].Z());
      glVertex3dv(fVertex[4].CArr());
      glVertex3dv(fVertex[7].CArr());
      glVertex3dv(fVertex[6].CArr());
      glVertex3dv(fVertex[5].CArr());
      // Far
      glNormal3d (-fAxesNorm[2].X(), -fAxesNorm[2].Y(), -fAxesNorm[2].Z());
      glVertex3dv(fVertex[0].CArr());
      glVertex3dv(fVertex[1].CArr());
      glVertex3dv(fVertex[2].CArr());
      glVertex3dv(fVertex[3].CArr());
      // Left
      glNormal3d (-fAxesNorm[0].X(), -fAxesNorm[0].Y(), -fAxesNorm[0].Z());
      glVertex3dv(fVertex[0].CArr());
      glVertex3dv(fVertex[3].CArr());
      glVertex3dv(fVertex[7].CArr());
      glVertex3dv(fVertex[4].CArr());
      // Right
      glNormal3d ( fAxesNorm[0].X(),  fAxesNorm[0].Y(),  fAxesNorm[0].Z());
      glVertex3dv(fVertex[6].CArr());
      glVertex3dv(fVertex[2].CArr());
      glVertex3dv(fVertex[1].CArr());
      glVertex3dv(fVertex[5].CArr());
      // Top
      glNormal3d ( fAxesNorm[1].X(),  fAxesNorm[1].Y(),  fAxesNorm[1].Z());
      glVertex3dv(fVertex[3].CArr());
      glVertex3dv(fVertex[2].CArr());
      glVertex3dv(fVertex[6].CArr());
      glVertex3dv(fVertex[7].CArr());
      // Bottom
      glNormal3d (-fAxesNorm[1].X(), -fAxesNorm[1].Y(), -fAxesNorm[1].Z());
      glVertex3dv(fVertex[4].CArr());
      glVertex3dv(fVertex[5].CArr());
      glVertex3dv(fVertex[1].CArr());
      glVertex3dv(fVertex[0].CArr());

      glEnd();
   }

}

//______________________________________________________________________________
Double_t TGLBoundingBox::Min(UInt_t index) const
{
   // Find minimum vertex value for axis of index X(0), Y(1), Z(2)
   Double_t min = fVertex[0][index];
   for (UInt_t v = 1; v < 8; v++) {
      if (fVertex[v][index] < min) {
         min = fVertex[v][index];
      }
   }
   return min;
}

//______________________________________________________________________________
Double_t TGLBoundingBox::Max(UInt_t index) const
{
   // Find maximum vertex value for axis of index X(0), Y(1), Z(2)
   Double_t max = fVertex[0][index];
   for (UInt_t v = 1; v < 8; v++) {
      if (fVertex[v][index] > max) {
         max = fVertex[v][index];
      }
   }
   return max;
}

//______________________________________________________________________________
TGLVertex3 TGLBoundingBox::MinAAVertex() const
{
   // Find minimum vertex values.

   return TGLVertex3(Min(0), Min(1), Min(2));
}

//______________________________________________________________________________
TGLVertex3 TGLBoundingBox::MaxAAVertex() const
{
   // Find maximum vertex values.

   return TGLVertex3(Max(0), Max(1), Max(2));
}

//______________________________________________________________________________
void TGLBoundingBox::Dump() const
{
   // Output to std::cout the vertices, center and volume of box
   for (UInt_t i = 0; i<8; i++) {
      std::cout << "[" << i << "] (" << fVertex[i].X() << "," << fVertex[i].Y() << "," << fVertex[i].Z() << ")" << std::endl;
   }
   std::cout << "Center:  ";   Center().Dump();
   std::cout << "Extents: ";   Extents().Dump();
   std::cout << "Volume:  " << Volume() << std::endl;
}

---