TGeoXtru.cxx

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// @(#)root/geom:$Id$
// Author: Mihaela Gheata   24/01/04

/*************************************************************************
 * 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.             *
 *************************************************************************/

/** \class  TGeoXtru
\ingroup Geometry_classes
  An extrusion with fixed outline shape in x-y and a sequence
of z extents (segments).  The overall scale of the outline scales
linearly between z points and the center can have an x-y offset.

Based on the initial implementation of R. Hatcher

### Creation of TGeoXtru shape

A TGeoXtru represents a polygonal extrusion. It is defined by the:
1. 'Blueprint' of the arbitrary polygon representing any Z section. This
   is an arbitrary polygon (convex or not) defined by the X/Y positions of
   its vertices.
1. A sequence of Z sections ordered on the Z axis. Each section defines the
  'actual' parameters of the polygon at a given Z. The sections may be
   translated with respect to the blueprint and/or scaled. The TGeoXtru
  segment in between 2 Z sections is a solid represented by the linear
  extrusion between the 2 polygons. Two consecutive sections may be defined
  at same Z position.

1. `TGeoXtru *xtru = TGeoXtru(Int_t nz);`

   where nz=number of Z planes

2. `Double_t x[nvertices]; // array of X positions of blueprint polygon vertices`

   `Double_t y[nvertices]; // array of Y positions of blueprint polygon vertices`

3. `xtru->DefinePolygon(nvertices,x,y);`

4. `DefineSection(0, z0, x0, y0, scale0); // Z position, offset and scale for first section`

   `DefineSection(1, z1, x1, y1, scale1); // -''- second section`
   `....`
   `DefineSection(nz-1, zn, xn, yn, scalen); // parameters for last section`

#### NOTES
Currently navigation functionality not fully implemented (only Contains()).
Decomposition in concave polygons not implemented - drawing in solid mode
within x3d produces incorrect end-faces
*/

#include "TGeoXtru.h"

#include "Riostream.h"
#include "TVirtualPad.h"
#include "TThread.h"
#include "TBuffer3D.h"
#include "TBuffer3DTypes.h"
#include "TClass.h"
#include "TMath.h"

#include "TVirtualGeoPainter.h"
#include "TGeoManager.h"
#include "TGeoVolume.h"
#include "TGeoPolygon.h"

ClassImp(TGeoXtru)

////////////////////////////////////////////////////////////////////////////////
/// Constructor.

TGeoXtru::ThreadData_t::ThreadData_t() :
   fSeg(0), fIz(0), fXc(0), fYc(0), fPoly(0)
{
}

////////////////////////////////////////////////////////////////////////////////
/// Destructor.

TGeoXtru::ThreadData_t::~ThreadData_t()
{
   delete [] fXc;
   delete [] fYc;
   delete fPoly;
}

////////////////////////////////////////////////////////////////////////////////

TGeoXtru::ThreadData_t& TGeoXtru::GetThreadData() const
{
   if (!fThreadSize) ((TGeoXtru*)this)->CreateThreadData(1);
   Int_t tid = TGeoManager::ThreadId();
/*
   TThread::Lock();
   if (tid >= fThreadSize) {
      Error("GetThreadData", "Thread id=%d bigger than maximum declared thread number %d. \nUse TGeoManager::SetMaxThreads properly !!!",
             tid, fThreadSize);
   }
   if (tid >= fThreadSize)
   {
      fThreadData.resize(tid + 1);
      fThreadSize = tid + 1;
   }
   if (fThreadData[tid] == 0)
   {
      fThreadData[tid] = new ThreadData_t;
      ThreadData_t &td = *fThreadData[tid];

      td.fXc = new Double_t [fNvert];
      td.fYc = new Double_t [fNvert];
      memcpy(td.fXc, fX, fNvert*sizeof(Double_t));
      memcpy(td.fYc, fY, fNvert*sizeof(Double_t));
      td.fPoly = new TGeoPolygon(fNvert);
      td.fPoly->SetXY(td.fXc, td.fYc); // initialize with current coordinates
      td.fPoly->FinishPolygon();
      if (tid == 0 && td.fPoly->IsIllegalCheck()) {
         Error("DefinePolygon", "Shape %s of type XTRU has an illegal polygon.", GetName());
      }
   }
   TThread::UnLock();
*/
   return *fThreadData[tid];
}

////////////////////////////////////////////////////////////////////////////////

void TGeoXtru::ClearThreadData() const
{
   std::vector<ThreadData_t*>::iterator i = fThreadData.begin();
   while (i != fThreadData.end())
   {
      delete *i;
      ++i;
   }
   fThreadData.clear();
   fThreadSize = 0;
}

////////////////////////////////////////////////////////////////////////////////
/// Create thread data for n threads max.

void TGeoXtru::CreateThreadData(Int_t nthreads)
{
   TThread::Lock();
   fThreadData.resize(nthreads);
   fThreadSize = nthreads;
   for (Int_t tid=0; tid<nthreads; tid++) {
      if (fThreadData[tid] == 0) {
         fThreadData[tid] = new ThreadData_t;
         ThreadData_t &td = *fThreadData[tid];
         td.fXc = new Double_t [fNvert];
         td.fYc = new Double_t [fNvert];
         memcpy(td.fXc, fX, fNvert*sizeof(Double_t));
         memcpy(td.fYc, fY, fNvert*sizeof(Double_t));
         td.fPoly = new TGeoPolygon(fNvert);
         td.fPoly->SetXY(td.fXc, td.fYc); // initialize with current coordinates
         td.fPoly->FinishPolygon();
         if (tid == 0 && td.fPoly->IsIllegalCheck()) {
            Error("DefinePolygon", "Shape %s of type XTRU has an illegal polygon.", GetName());
         }
      }
   }
   TThread::UnLock();
}

////////////////////////////////////////////////////////////////////////////////
/// Set current z-plane.

void TGeoXtru::SetIz(Int_t iz)
{
   GetThreadData().fIz = iz;
}
////////////////////////////////////////////////////////////////////////////////
/// Set current segment.

void TGeoXtru::SetSeg(Int_t iseg)
{
   GetThreadData().fSeg = iseg;
}

////////////////////////////////////////////////////////////////////////////////
/// dummy ctor

TGeoXtru::TGeoXtru()
         :TGeoBBox(),
          fNvert(0),
          fNz(0),
          fZcurrent(0.),
          fX(0),
          fY(0),
          fZ(0),
          fScale(0),
          fX0(0),
          fY0(0),
          fThreadData(0),
          fThreadSize(0)
{
   SetShapeBit(TGeoShape::kGeoXtru);
}

////////////////////////////////////////////////////////////////////////////////
/// Default constructor

TGeoXtru::TGeoXtru(Int_t nz)
         :TGeoBBox(0, 0, 0),
          fNvert(0),
          fNz(nz),
          fZcurrent(0.),
          fX(0),
          fY(0),
          fZ(new Double_t[nz]),
          fScale(new Double_t[nz]),
          fX0(new Double_t[nz]),
          fY0(new Double_t[nz]),
          fThreadData(0),
          fThreadSize(0)
{
   SetShapeBit(TGeoShape::kGeoXtru);
   if (nz<2) {
      Error("ctor", "Cannot create TGeoXtru %s with less than 2 Z planes", GetName());
      SetShapeBit(TGeoShape::kGeoBad);
      return;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Default constructor in GEANT3 style
///  - param[0] = nz  // number of z planes
///
///  - param[1] = z1  // Z position of first plane
///  - param[2] = x1  // X position of first plane
///  - param[3] = y1  // Y position of first plane
///  - param[4] = scale1  // scale factor for first plane
/// ...
///  - param[4*(nz-1]+1] = zn
///  - param[4*(nz-1)+2] = xn
///  - param[4*(nz-1)+3] = yn
///  - param[4*(nz-1)+4] = scalen

TGeoXtru::TGeoXtru(Double_t *param)
         :TGeoBBox(0, 0, 0),
          fNvert(0),
          fNz(0),
          fZcurrent(0.),
          fX(0),
          fY(0),
          fZ(0),
          fScale(0),
          fX0(0),
          fY0(0),
          fThreadData(0),
          fThreadSize(0)
{
   SetShapeBit(TGeoShape::kGeoXtru);
   SetDimensions(param);
}

////////////////////////////////////////////////////////////////////////////////
///copy constructor

TGeoXtru::TGeoXtru(const TGeoXtru& xt) :
  TGeoBBox(xt),
  fNvert(0),
  fNz(0),
  fZcurrent(0),
  fX(0),
  fY(0),
  fZ(0),
  fScale(0),
  fX0(0),
  fY0(0),
  fThreadData(0),
  fThreadSize(0)
{
}

////////////////////////////////////////////////////////////////////////////////
///assignment operator

TGeoXtru& TGeoXtru::operator=(const TGeoXtru& xt)
{
   if(this!=&xt) {
      TGeoBBox::operator=(xt);
      fNvert=0;
      fNz=0;
      fZcurrent=0;
      fX=0;
      fY=0;
      fZ=0;
      fScale=0;
      fX0=0;
      fY0=0;
      fThreadSize=0;
   }
   return *this;
}

////////////////////////////////////////////////////////////////////////////////
/// destructor

TGeoXtru::~TGeoXtru()
{
   if (fX)  {delete[] fX; fX = 0;}
   if (fY)  {delete[] fY; fY = 0;}
   if (fZ)  {delete[] fZ; fZ = 0;}
   if (fScale) {delete[] fScale; fScale = 0;}
   if (fX0)  {delete[] fX0; fX0 = 0;}
   if (fY0)  {delete[] fY0; fY0 = 0;}
   ClearThreadData();
}

////////////////////////////////////////////////////////////////////////////////
/// Compute capacity [length^3] of this shape.

Double_t TGeoXtru::Capacity() const
{
   ThreadData_t& td = GetThreadData();
   Int_t iz;
   Double_t capacity = 0;
   Double_t area, dz, sc1, sc2;
   TGeoXtru *xtru = (TGeoXtru*)this;
   xtru->SetCurrentVertices(0.,0.,1.);
   area = td.fPoly->Area();
   for (iz=0; iz<fNz-1; iz++) {
      dz = fZ[iz+1]-fZ[iz];
      if (TGeoShape::IsSameWithinTolerance(dz,0)) continue;
      sc1 = fScale[iz];
      sc2 = fScale[iz+1];
      capacity += (area*dz/3.)*(sc1*sc1+sc1*sc2+sc2*sc2);
   }
   return capacity;
}

////////////////////////////////////////////////////////////////////////////////
/// compute bounding box of the pcon

void TGeoXtru::ComputeBBox()
{
   ThreadData_t& td = GetThreadData();
   if (!fX || !fZ || !fNvert) {
      Error("ComputeBBox", "In shape %s polygon not defined", GetName());
      SetShapeBit(TGeoShape::kGeoBad);
      return;
   }
   Double_t zmin = fZ[0];
   Double_t zmax = fZ[fNz-1];
   Double_t xmin = TGeoShape::Big();
   Double_t xmax = -TGeoShape::Big();
   Double_t ymin = TGeoShape::Big();
   Double_t ymax = -TGeoShape::Big();
   for (Int_t i=0; i<fNz; i++) {
      SetCurrentVertices(fX0[i], fY0[i], fScale[i]);
      for (Int_t j=0; j<fNvert; j++) {
         if (td.fXc[j]<xmin) xmin=td.fXc[j];
         if (td.fXc[j]>xmax) xmax=td.fXc[j];
         if (td.fYc[j]<ymin) ymin=td.fYc[j];
         if (td.fYc[j]>ymax) ymax=td.fYc[j];
      }
   }
   fOrigin[0] = 0.5*(xmin+xmax);
   fOrigin[1] = 0.5*(ymin+ymax);
   fOrigin[2] = 0.5*(zmin+zmax);
   fDX = 0.5*(xmax-xmin);
   fDY = 0.5*(ymax-ymin);
   fDZ = 0.5*(zmax-zmin);
}

////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.

void TGeoXtru::ComputeNormal(const Double_t * /*point*/, const Double_t *dir, Double_t *norm)
{
   ThreadData_t& td = GetThreadData();
   if (td.fIz<0) {
      memset(norm,0,3*sizeof(Double_t));
      norm[2] = (dir[2]>0)?1:-1;
      return;
   }
   Double_t vert[12];
   GetPlaneVertices(td.fIz, td.fSeg, vert);
   GetPlaneNormal(vert, norm);
   Double_t ndotd = norm[0]*dir[0]+norm[1]*dir[1]+norm[2]*dir[2];
   if (ndotd<0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
      norm[2] = -norm[2];
   }
}

////////////////////////////////////////////////////////////////////////////////
/// test if point is inside this shape

Bool_t TGeoXtru::Contains(const Double_t *point) const
{
   ThreadData_t& td = GetThreadData();
   // Check Z range
   TGeoXtru *xtru = (TGeoXtru*)this;
   if (point[2]<fZ[0]) return kFALSE;
   if (point[2]>fZ[fNz-1]) return kFALSE;
   Int_t iz = TMath::BinarySearch(fNz, fZ, point[2]);
   if (iz<0 || iz==fNz-1) return kFALSE;
   if (TGeoShape::IsSameWithinTolerance(point[2],fZ[iz])) {
      xtru->SetIz(-1);
      xtru->SetCurrentVertices(fX0[iz],fY0[iz], fScale[iz]);
      if (td.fPoly->Contains(point)) return kTRUE;
      if (iz>1 && TGeoShape::IsSameWithinTolerance(fZ[iz],fZ[iz-1])) {
         xtru->SetCurrentVertices(fX0[iz-1],fY0[iz-1], fScale[iz-1]);
         return td.fPoly->Contains(point);
      } else if (iz<fNz-2 && TGeoShape::IsSameWithinTolerance(fZ[iz],fZ[iz+1])) {
         xtru->SetCurrentVertices(fX0[iz+1],fY0[iz+1], fScale[iz+1]);
         return td.fPoly->Contains(point);
      }
   }
   xtru->SetCurrentZ(point[2], iz);
   if (TMath::Abs(point[2]-fZ[iz])<TGeoShape::Tolerance() ||
       TMath::Abs(fZ[iz+1]-point[2])<TGeoShape::Tolerance())  xtru->SetIz(-1);
   // Now td.fXc,fYc represent the vertices of the section at point[2]
   return td.fPoly->Contains(point);
}

////////////////////////////////////////////////////////////////////////////////
/// compute closest distance from point px,py to each corner

Int_t TGeoXtru::DistancetoPrimitive(Int_t px, Int_t py)
{
   const Int_t numPoints = fNvert*fNz;
   return ShapeDistancetoPrimitive(numPoints, px, py);
}

////////////////////////////////////////////////////////////////////////////////
/// Draw the section polygon.

void TGeoXtru::DrawPolygon(Option_t *option)
 {
   ThreadData_t& td = GetThreadData();
   if (td.fPoly) td.fPoly->Draw(option);
}

////////////////////////////////////////////////////////////////////////////////
/// Compute distance to a Xtru lateral surface.

Double_t TGeoXtru::DistToPlane(const Double_t *point, const Double_t *dir, Int_t iz, Int_t ivert, Double_t stepmax, Bool_t in) const
{
   ThreadData_t& td = GetThreadData();
   Double_t snext;
   Double_t vert[12];
   Double_t norm[3];
   Double_t znew;
   Double_t pt[3];
   Double_t safe;
   if (TGeoShape::IsSameWithinTolerance(fZ[iz],fZ[iz+1]) && !in) {
      TGeoXtru *xtru = (TGeoXtru*)this;
      snext = (fZ[iz]-point[2])/dir[2];
      if (snext<0) return TGeoShape::Big();
      pt[0] = point[0]+snext*dir[0];
      pt[1] = point[1]+snext*dir[1];
      pt[2] = point[2]+snext*dir[2];
      if (dir[2] < 0.) xtru->SetCurrentVertices(fX0[iz], fY0[iz], fScale[iz]);
      else             xtru->SetCurrentVertices(fX0[iz+1], fY0[iz+1], fScale[iz+1]);
      if (!td.fPoly->Contains(pt)) return TGeoShape::Big();
      return snext;
   }
   GetPlaneVertices(iz, ivert, vert);
   GetPlaneNormal(vert, norm);
   Double_t ndotd = norm[0]*dir[0]+norm[1]*dir[1]+norm[2]*dir[2];
   if (in) {
      if (ndotd<=0) return TGeoShape::Big();
      safe = (vert[0]-point[0])*norm[0]+
             (vert[1]-point[1])*norm[1]+
             (vert[2]-point[2])*norm[2];
      if (safe<-1.E-8) return TGeoShape::Big(); // direction outwards plane
   } else {
      ndotd = -ndotd;
      if (ndotd<=0) return TGeoShape::Big();
      safe = (point[0]-vert[0])*norm[0]+
             (point[1]-vert[1])*norm[1]+
             (point[2]-vert[2])*norm[2];
      if (safe<-1.E-8) return TGeoShape::Big(); // direction outwards plane
   }
   snext = safe/ndotd;
   if (snext>stepmax) return TGeoShape::Big();
   if (fZ[iz]<fZ[iz+1]) {
      znew = point[2] + snext*dir[2];
      if (znew<fZ[iz]) return TGeoShape::Big();
      if (znew>fZ[iz+1]) return TGeoShape::Big();
   }
   pt[0] = point[0]+snext*dir[0];
   pt[1] = point[1]+snext*dir[1];
   pt[2] = point[2]+snext*dir[2];
   if (!IsPointInsidePlane(pt, vert, norm)) return TGeoShape::Big();
   return TMath::Max(snext, 0.);
}

////////////////////////////////////////////////////////////////////////////////
/// compute distance from inside point to surface of the polycone
/// locate Z segment

Double_t TGeoXtru::DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
{
   ThreadData_t& td = GetThreadData();
   if (iact<3 && safe) {
      *safe = Safety(point, kTRUE);
      if (iact==0) return TGeoShape::Big();
      if (iact==1 && step<*safe) return TGeoShape::Big();
   }
   TGeoXtru *xtru = (TGeoXtru*)this;
   Int_t iz = TMath::BinarySearch(fNz, fZ, point[2]);
   if (iz < 0) {
      if (dir[2]<=0) {
         xtru->SetIz(-1);
         return 0.;
      }
      iz = 0;
   }
   if (iz==fNz-1) {
      if (dir[2]>=0) {
         xtru->SetIz(-1);
         return 0.;
      }
      iz--;
   } else {
      if (iz>0) {
         if (TGeoShape::IsSameWithinTolerance(point[2],fZ[iz])) {
            if (TGeoShape::IsSameWithinTolerance(fZ[iz],fZ[iz+1]) && dir[2]<0) iz++;
            else if (TGeoShape::IsSameWithinTolerance(fZ[iz],fZ[iz-1]) && dir[2]>0) iz--;
         }
      }
   }
   Bool_t convex = td.fPoly->IsConvex();
//   Double_t stepmax = step;
//   if (stepmax>TGeoShape::Big()) stepmax = TGeoShape::Big();
   Double_t snext = TGeoShape::Big();
   Double_t dist, sz;
   Double_t pt[3];
   Int_t iv, ipl, inext;
   // we treat the special case when dir[2]=0
   if (TGeoShape::IsSameWithinTolerance(dir[2],0)) {
      for (iv=0; iv<fNvert; iv++) {
         xtru->SetIz(-1);
         dist = DistToPlane(point,dir,iz,iv,TGeoShape::Big(),kTRUE);
         if (dist<snext) {
            snext = dist;
            xtru->SetSeg(iv);
            if (convex) return snext;
         }
      }
      if (snext < 1.E10) return snext;
      return TGeoShape::Tolerance();
   }

   // normal case
   Int_t incseg = (dir[2]>0)?1:-1;
   Int_t iznext = iz;
   Bool_t zexit = kFALSE;
   while (iz>=0 && iz<fNz-1) {
      // find the distance  to current segment end Z surface
      ipl = iz+((incseg+1)>>1); // next plane
      inext = ipl+incseg; // next next plane
      sz = (fZ[ipl]-point[2])/dir[2];
      if (sz<snext) {
         iznext += incseg;
         // we cross the next Z section before stepmax
         pt[0] = point[0]+sz*dir[0];
         pt[1] = point[1]+sz*dir[1];
         xtru->SetCurrentVertices(fX0[ipl],fY0[ipl],fScale[ipl]);
         if (td.fPoly->Contains(pt)) {
            // ray gets through next polygon - is it the last one?
            if (ipl==0 || ipl==fNz-1) {
               xtru->SetIz(-1);
               if (convex) return sz;
               zexit = kTRUE;
               snext = sz;
            }
            // maybe a Z discontinuity - check this
            if (!zexit && TGeoShape::IsSameWithinTolerance(fZ[ipl],fZ[inext])) {
               xtru->SetCurrentVertices(fX0[inext],fY0[inext],fScale[inext]);
               // if we do not cross the next polygone, we are out
               if (!td.fPoly->Contains(pt)) {
                  xtru->SetIz(-1);
                  if (convex) return sz;
                  zexit = kTRUE;
                  snext = sz;
               } else {
                  iznext = inext;
               }
            }
         }
      } else {
         iznext = fNz-1;   // stop
      }
      // ray may cross the lateral surfaces of section iz
      for (iv=0; iv<fNvert; iv++) {
         dist = DistToPlane(point,dir,iz,iv,TGeoShape::Big(),kTRUE);
         if (dist<snext) {
            xtru->SetIz(iz);
            xtru->SetSeg(iv);
            snext = dist;
            if (convex) return snext;
            zexit = kTRUE;
         }
      }
      if (zexit) return snext;
      iz = iznext;
   }
   return TGeoShape::Tolerance();
}

////////////////////////////////////////////////////////////////////////////////
/// compute distance from outside point to surface of the tube
///   Warning("DistFromOutside", "not implemented");

Double_t TGeoXtru::DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
{
   ThreadData_t& td = GetThreadData();
   if (iact<3 && safe) {
      *safe = Safety(point, kTRUE);
      if (iact==0) return TGeoShape::Big();
      if (iact==1 && step<*safe) return TGeoShape::Big();
   }
// Check if the bounding box is crossed within the requested distance
   Double_t sdist = TGeoBBox::DistFromOutside(point,dir, fDX, fDY, fDZ, fOrigin, step);
   if (sdist>=step) return TGeoShape::Big();
   Double_t stepmax = step;
   if (stepmax>TGeoShape::Big()) stepmax = TGeoShape::Big();
   Double_t snext = 0.;
   Double_t dist = TGeoShape::Big();
   Int_t i, iv;
   Double_t pt[3];
   memcpy(pt,point,3*sizeof(Double_t));
   TGeoXtru *xtru = (TGeoXtru*)this;
   // We might get out easy with Z checks
   Int_t iz = TMath::BinarySearch(fNz, fZ, point[2]);
   if (iz<0) {
      if (dir[2]<=0) return TGeoShape::Big();
      // propagate to first Z plane
      snext = (fZ[0] - point[2])/dir[2];
      if (snext>stepmax) return TGeoShape::Big();
      for (i=0; i<3; i++) pt[i] = point[i] + snext*dir[i];
      xtru->SetCurrentVertices(fX0[0],fY0[0],fScale[0]);
      if (td.fPoly->Contains(pt)) {
         xtru->SetIz(-1);
         return snext;
      }
      iz=0; // valid starting value = first segment
      stepmax -= snext;
   } else {
      if (iz==fNz-1) {
         if (dir[2]>=0) return TGeoShape::Big();
         // propagate to last Z plane
         snext = (fZ[fNz-1] - point[2])/dir[2];
         if (snext>stepmax) return TGeoShape::Big();
         for (i=0; i<3; i++) pt[i] = point[i] + snext*dir[i];
         xtru->SetCurrentVertices(fX0[fNz-1],fY0[fNz-1],fScale[fNz-1]);
         if (td.fPoly->Contains(pt)) {
            xtru->SetIz(-1);
            return snext;
         }
         iz = fNz-2; // valid value = last segment
         stepmax -= snext;
      }
   }
   // Check if the bounding box is missed by the track
   if (!TGeoBBox::Contains(pt)) {
      dist = TGeoBBox::DistFromOutside(pt,dir,3);
      if (dist>stepmax) return TGeoShape::Big();
      if (dist>1E-6) dist-=1E-6; // decrease snext to make sure we do not cross the xtru
      else dist = 0;
      for (i=0; i<3; i++) pt[i] += dist*dir[i]; // we are now closer
      iz = TMath::BinarySearch(fNz, fZ, pt[2]);
      if (iz<0) iz=0;
      else if (iz==fNz-1) iz = fNz-2;
      snext += dist;
      stepmax -= dist;
   }
   // not the case - we have to do some work...
   // Start tracking from current iz
   // - first solve particular case dir[2]=0
   Bool_t convex = td.fPoly->IsConvex();
   Bool_t hit = kFALSE;
   if (TGeoShape::IsSameWithinTolerance(dir[2],0)) {
      // loop lateral planes to see if we cross something
      xtru->SetIz(iz);
      for (iv=0; iv<fNvert; iv++) {
         dist = DistToPlane(pt,dir,iz,iv,stepmax,kFALSE);
         if (dist<stepmax) {
            xtru->SetSeg(iv);
            if (convex) return (snext+dist);
            stepmax = dist;
            hit = kTRUE;
         }
      }
      if (hit) return (snext+stepmax);
      return TGeoShape::Big();
   }
   // general case
   Int_t incseg = (dir[2]>0)?1:-1;
   while (iz>=0 && iz<fNz-1) {
      // compute distance to lateral planes
      xtru->SetIz(iz);
      if (TGeoShape::IsSameWithinTolerance(fZ[iz],fZ[iz+1])) xtru->SetIz(-1);
      for (iv=0; iv<fNvert; iv++) {
         dist = DistToPlane(pt,dir,iz,iv,stepmax,kFALSE);
         if (dist<stepmax) {
            // HIT
            xtru->SetSeg(iv);
            if (convex) return (snext+dist);
            stepmax = dist;
            hit = kTRUE;
         }
      }
      if (hit) return (snext+stepmax);
      iz += incseg;
   }
   return TGeoShape::Big();
}

////////////////////////////////////////////////////////////////////////////////
/// Creates the polygon representing the blueprint of any Xtru section.
///  - nvert     = number of vertices >2
///  - xv[nvert] = array of X vertex positions
///  - yv[nvert] = array of Y vertex positions
///
/// *NOTE* should be called before DefineSection or ctor with 'param'

Bool_t TGeoXtru::DefinePolygon(Int_t nvert, const Double_t *xv, const Double_t *yv)
{
   if (nvert<3) {
      Error("DefinePolygon","In shape %s cannot create polygon with less than 3 vertices", GetName());
      SetShapeBit(TGeoShape::kGeoBad);
      return kFALSE;
   }
   for (Int_t i=0; i<nvert-1; i++) {
      for (Int_t j=i+1; j<nvert; j++) {
         if (TMath::Abs(xv[i]-xv[j])<TGeoShape::Tolerance() &&
             TMath::Abs(yv[i]-yv[j])<TGeoShape::Tolerance()) {
             Error("DefinePolygon","In shape %s 2 vertices cannot be identical",GetName());
             SetShapeBit(TGeoShape::kGeoBad);
//             return kFALSE;
          }
      }
   }
   fNvert = nvert;
   if (fX) delete [] fX;
   fX = new Double_t[nvert];
   if (fY) delete [] fY;
   fY = new Double_t[nvert];
   memcpy(fX,xv,nvert*sizeof(Double_t));
   memcpy(fY,yv,nvert*sizeof(Double_t));

   ClearThreadData();

   return kTRUE;
}

////////////////////////////////////////////////////////////////////////////////
/// defines z position of a section plane, rmin and rmax at this z.

void TGeoXtru::DefineSection(Int_t snum, Double_t z, Double_t x0, Double_t y0, Double_t scale)
{
   if ((snum<0) || (snum>=fNz)) return;
   fZ[snum]  = z;
   fX0[snum] = x0;
   fY0[snum] = y0;
   fScale[snum] = scale;
   if (snum) {
      if (fZ[snum]<fZ[snum-1]) {
         Warning("DefineSection", "In shape: %s, Z position of section "
                 "%i, z=%e, not in increasing order, %i, z=%e",
                 GetName(),snum,fZ[snum],snum-1,fZ[snum-1]);
         return;
      }
   }
   if (snum==(fNz-1)) {
      ComputeBBox();
      if (TestShapeBit(TGeoShape::kGeoBad)) InspectShape();
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Return the Z coordinate for segment ipl.

Double_t TGeoXtru::GetZ(Int_t ipl) const
{
   if (ipl<0 || ipl>(fNz-1)) {
      Error("GetZ","In shape %s, ipl=%i out of range (0,%i)",GetName(),ipl,fNz-1);
      return 0.;
   }
   return fZ[ipl];
}
////////////////////////////////////////////////////////////////////////////////
/// Returns normal vector to the planar quadrilateral defined by vector VERT.
/// The normal points outwards the xtru.

void TGeoXtru::GetPlaneNormal(const Double_t *vert, Double_t *norm) const
{
   Double_t cross = 0.;
   Double_t v1[3], v2[3];
   v1[0] = vert[9]-vert[0];
   v1[1] = vert[10]-vert[1];
   v1[2] = vert[11]-vert[2];
   v2[0] = vert[3]-vert[0];
   v2[1] = vert[4]-vert[1];
   v2[2] = vert[5]-vert[2];
   norm[0] = v1[1]*v2[2]-v1[2]*v2[1];
   cross += norm[0]*norm[0];
   norm[1] = v1[2]*v2[0]-v1[0]*v2[2];
   cross += norm[1]*norm[1];
   norm[2] = v1[0]*v2[1]-v1[1]*v2[0];
   cross += norm[2]*norm[2];
   if (cross < TGeoShape::Tolerance()) return;
   cross = 1./TMath::Sqrt(cross);
   for (Int_t i=0; i<3; i++) norm[i] *= cross;
}

////////////////////////////////////////////////////////////////////////////////
/// Returns (x,y,z) of 3 vertices of the surface defined by Z sections (iz, iz+1)
/// and polygon vertices (ivert, ivert+1). No range check.

void TGeoXtru::GetPlaneVertices(Int_t iz, Int_t ivert, Double_t *vert) const
{
   ThreadData_t& td = GetThreadData();
   Double_t x,y,z1,z2;
   Int_t iv1 = (ivert+1)%fNvert;
   Int_t icrt = 0;
   z1 = fZ[iz];
   z2 = fZ[iz+1];
   if (td.fPoly->IsClockwise()) {
      x = fX[ivert]*fScale[iz]+fX0[iz];
      y = fY[ivert]*fScale[iz]+fY0[iz];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z1;
      x = fX[iv1]*fScale[iz]+fX0[iz];
      y = fY[iv1]*fScale[iz]+fY0[iz];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z1;
      x = fX[iv1]*fScale[iz+1]+fX0[iz+1];
      y = fY[iv1]*fScale[iz+1]+fY0[iz+1];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z2;
      x = fX[ivert]*fScale[iz+1]+fX0[iz+1];
      y = fY[ivert]*fScale[iz+1]+fY0[iz+1];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z2;
   } else {
      x = fX[iv1]*fScale[iz]+fX0[iz];
      y = fY[iv1]*fScale[iz]+fY0[iz];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z1;
      x = fX[ivert]*fScale[iz]+fX0[iz];
      y = fY[ivert]*fScale[iz]+fY0[iz];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z1;
      x = fX[ivert]*fScale[iz+1]+fX0[iz+1];
      y = fY[ivert]*fScale[iz+1]+fY0[iz+1];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z2;
      x = fX[iv1]*fScale[iz+1]+fX0[iz+1];
      y = fY[iv1]*fScale[iz+1]+fY0[iz+1];
      vert[icrt++] = x;
      vert[icrt++] = y;
      vert[icrt++] = z2;
   }
}
////////////////////////////////////////////////////////////////////////////////
/// Check if the quadrilateral defined by VERT contains a coplanar POINT.

Bool_t TGeoXtru::IsPointInsidePlane(const Double_t *point, Double_t *vert, Double_t *norm) const
{
   Double_t v1[3], v2[3];
   Double_t cross;
   Int_t j,k;
   for (Int_t i=0; i<4; i++) { // loop vertices
      j = 3*i;
      k = 3*((i+1)%4);
      v1[0] = point[0]-vert[j];
      v1[1] = point[1]-vert[j+1];
      v1[2] = point[2]-vert[j+2];
      v2[0] = vert[k]-vert[j];
      v2[1] = vert[k+1]-vert[j+1];
      v2[2] = vert[k+2]-vert[j+2];
      cross = (v1[1]*v2[2]-v1[2]*v2[1])*norm[0]+
              (v1[2]*v2[0]-v1[0]*v2[2])*norm[1]+
              (v1[0]*v2[1]-v1[1]*v2[0])*norm[2];
      if (cross<0) return kFALSE;
   }
   return kTRUE;
}

////////////////////////////////////////////////////////////////////////////////
/// Print actual Xtru parameters.

void TGeoXtru::InspectShape() const
{
   printf("*** Shape %s: TGeoXtru ***\n", GetName());
   printf("    Nz    = %i\n", fNz);
   printf("    List of (x,y) of polygon vertices:\n");
   for (Int_t ivert = 0; ivert<fNvert; ivert++)
      printf("    x = %11.5f  y = %11.5f\n", fX[ivert],fY[ivert]);
   for (Int_t ipl=0; ipl<fNz; ipl++)
      printf("     plane %i: z=%11.5f x0=%11.5f y0=%11.5f scale=%11.5f\n", ipl, fZ[ipl], fX0[ipl], fY0[ipl], fScale[ipl]);
   printf(" Bounding box:\n");
   TGeoBBox::InspectShape();
}

////////////////////////////////////////////////////////////////////////////////
/// Creates a TBuffer3D describing *this* shape.
/// Coordinates are in local reference frame.

TBuffer3D *TGeoXtru::MakeBuffer3D() const
{
   Int_t nz = GetNz();
   Int_t nvert = GetNvert();
   Int_t nbPnts = nz*nvert;
   Int_t nbSegs = nvert*(2*nz-1);
   Int_t nbPols = nvert*(nz-1)+2;

   TBuffer3D* buff = new TBuffer3D(TBuffer3DTypes::kGeneric,
                                   nbPnts, 3*nbPnts, nbSegs, 3*nbSegs, nbPols, 6*(nbPols-2)+2*(2+nvert));
   if (buff)
   {
      SetPoints(buff->fPnts);
      SetSegsAndPols(*buff);
   }

   return buff;
}

////////////////////////////////////////////////////////////////////////////////
/// Fill TBuffer3D structure for segments and polygons.

void TGeoXtru::SetSegsAndPols(TBuffer3D &buff) const
{
   Int_t nz = GetNz();
   Int_t nvert = GetNvert();
   Int_t c = GetBasicColor();

   Int_t i,j;
   Int_t indx, indx2, k;
   indx = indx2 = 0;
   for (i=0; i<nz; i++) {
      // loop Z planes
      indx2 = i*nvert;
      // loop polygon segments
      for (j=0; j<nvert; j++) {
         k = (j+1)%nvert;
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = indx2+j;
         buff.fSegs[indx++] = indx2+k;
      }
   } // total: nz*nvert polygon segments
   for (i=0; i<nz-1; i++) {
      // loop Z planes
      indx2 = i*nvert;
      // loop polygon segments
      for (j=0; j<nvert; j++) {
         k = j + nvert;
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = indx2+j;
         buff.fSegs[indx++] = indx2+k;
      }
   } // total (nz-1)*nvert lateral segments

   indx = 0;

   // fill lateral polygons
   for (i=0; i<nz-1; i++) {
      indx2 = i*nvert;
      for (j=0; j<nvert; j++) {
      k = (j+1)%nvert;
      buff.fPols[indx++] = c+j%3;
      buff.fPols[indx++] = 4;
      buff.fPols[indx++] = indx2+j;
      buff.fPols[indx++] = nz*nvert+indx2+k;
      buff.fPols[indx++] = indx2+nvert+j;
      buff.fPols[indx++] = nz*nvert+indx2+j;
      }
   } // total (nz-1)*nvert polys
   buff.fPols[indx++] = c+2;
   buff.fPols[indx++] = nvert;
   indx2 = 0;
   for (j = nvert - 1; j >= 0; --j) {
      buff.fPols[indx++] = indx2+j;
   }

   buff.fPols[indx++] = c;
   buff.fPols[indx++] = nvert;
   indx2 = (nz-1)*nvert;

   for (j=0; j<nvert; j++) {
      buff.fPols[indx++] = indx2+j;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Compute safety to sector iz, returning also the closest segment index.

Double_t TGeoXtru::SafetyToSector(const Double_t *point, Int_t iz, Double_t safmin, Bool_t in)
{
   ThreadData_t& td = GetThreadData();
   Double_t safz = TGeoShape::Big();
   Double_t saf1, saf2;
   Bool_t in1, in2;
   Int_t iseg;
   Double_t safe = TGeoShape::Big();
   // segment-break case
   if (TGeoShape::IsSameWithinTolerance(fZ[iz],fZ[iz+1])) {
      safz = TMath::Abs(point[2]-fZ[iz]);
      if (safz>safmin) return TGeoShape::Big();
      SetCurrentVertices(fX0[iz], fY0[iz], fScale[iz]);
      saf1 = td.fPoly->Safety(point, iseg);
      in1 = td.fPoly->Contains(point);
//      if (!in1 && saf1>safmin) return TGeoShape::Big();
      SetCurrentVertices(fX0[iz+1], fY0[iz+1], fScale[iz+1]);
      saf2 = td.fPoly->Safety(point, iseg);
      in2 = td.fPoly->Contains(point);
      if ((in1&!in2)|(in2&!in1)) {
         safe = safz;
      } else {
         safe = TMath::Min(saf1,saf2);
         safe = TMath::Max(safe, safz);
      }
      if (safe>safmin) return TGeoShape::Big();
      return safe;
   }
   // normal case
   safz = fZ[iz]-point[2];
   if (safz>safmin) return TGeoShape::Big();
   if (safz<0) {
      saf1 = point[2]-fZ[iz+1];
      if (saf1>safmin) return TGeoShape::Big();
      if (saf1<0) {
         safz = TMath::Max(safz, saf1); // we are in between the 2 Z segments - we ignore safz
      } else {
         safz = saf1;
      }
   }

   // loop segments
   Bool_t found = kFALSE;
   Double_t vert[12];
   Double_t norm[3];
//   printf("plane %d: safz=%f in=%d\n", iz, safz, in);
   for (iseg=0; iseg<fNvert; iseg++) {
      GetPlaneVertices(iz,iseg,vert);
      GetPlaneNormal(vert, norm);
      saf1 = (point[0]-vert[0])*norm[0]+(point[1]-vert[1])*norm[1]+(point[2]-vert[2])*norm[2];
      if (in) saf1 = -saf1;
//      printf("segment %d: (%f,%f)-(%f,%f) norm=(%f,%f,%f): saf1=%f\n", iseg, vert[0],vert[1],vert[3],vert[4],norm[0],norm[1],norm[2],saf1);
      if (saf1<-1.E-8) continue;
      safe = TMath::Max(safz, saf1);
      safe = TMath::Abs(safe);
      if (safe>safmin) continue;
      safmin = safe;
      found = kTRUE;
   }
   if (found) return safmin;
   return TGeoShape::Big();
}

////////////////////////////////////////////////////////////////////////////////
/// computes the closest distance from given point to this shape, according
/// to option. The matching point on the shape is stored in spoint.
///> localize the Z segment

Double_t TGeoXtru::Safety(const Double_t *point, Bool_t in) const
{
   Double_t safmin = TGeoShape::Big();
   Double_t safe;
   Double_t safz = TGeoShape::Big();
   TGeoXtru *xtru = (TGeoXtru*)this;
   Int_t iz;
   if (in) {
      safmin = TMath::Min(point[2]-fZ[0], fZ[fNz-1]-point[2]);
      for (iz=0; iz<fNz-1; iz++) {
         safe = xtru->SafetyToSector(point, iz, safmin, in);
         if (safe<safmin) safmin = safe;
      }
      return safmin;
   }
   // Accurate safety is expensive, use the bounding box
   if (!TGeoBBox::Contains(point)) return TGeoBBox::Safety(point,in);
   iz = TMath::BinarySearch(fNz, fZ, point[2]);
   if (iz<0) {
      iz = 0;
      safz = fZ[0] - point[2];
   } else {
      if (iz==fNz-1) {
         iz = fNz-2;
         safz = point[2] - fZ[fNz-1];
      }
   }
   // loop segments from iz up
   Int_t i;
   for (i=iz; i<fNz-1; i++) {
      safe = xtru->SafetyToSector(point,i,safmin, in);
      if (safe<safmin) safmin=safe;
   }
   // loop segments from iz-1 down
   for (i=iz-1; i>=0; i--) {
      safe = xtru->SafetyToSector(point,i,safmin, in);
      if (safe<safmin) safmin=safe;
   }
   safe = TMath::Min(safmin, safz);
   return safe;
}

////////////////////////////////////////////////////////////////////////////////
/// Save a primitive as a C++ statement(s) on output stream "out".

void TGeoXtru::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
{
   if (TObject::TestBit(kGeoSavePrimitive)) return;
   out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
   out << "   nz       = " << fNz << ";" << std::endl;
   out << "   nvert    = " << fNvert << ";" << std::endl;
   out << "   TGeoXtru *xtru = new TGeoXtru(nz);" << std::endl;
   out << "   xtru->SetName(\"" << GetName() << "\");" << std::endl;
   Int_t i;
   for (i=0; i<fNvert; i++) {
      out << "   xvert[" << i << "] = " << fX[i] << ";   yvert[" << i << "] = " << fY[i] << ";" << std::endl;
   }
   out << "   xtru->DefinePolygon(nvert,xvert,yvert);" << std::endl;
   for (i=0; i<fNz; i++) {
      out << "   zsect  = " << fZ[i] << ";" << std::endl;
      out << "   x0     = " << fX0[i] << ";" << std::endl;
      out << "   y0     = " << fY0[i] << ";" << std::endl;
      out << "   scale0 = " << fScale[i] << ";" << std::endl;
      out << "   xtru->DefineSection(" << i << ",zsect,x0,y0,scale0);" << std::endl;
   }
   out << "   TGeoShape *" << GetPointerName() << " = xtru;" << std::endl;
   TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}

////////////////////////////////////////////////////////////////////////////////
/// Recompute current section vertices for a given Z position within range of section iz.

void TGeoXtru::SetCurrentZ(Double_t z, Int_t iz)
{
   Double_t x0, y0, scale, a, b;
   Int_t ind1, ind2;
   ind1 = iz;
   ind2 = iz+1;
   Double_t invdz = 1./(fZ[ind2]-fZ[ind1]);
   a = (fX0[ind1]*fZ[ind2]-fX0[ind2]*fZ[ind1])*invdz;
   b = (fX0[ind2]-fX0[ind1])*invdz;
   x0 = a+b*z;
   a = (fY0[ind1]*fZ[ind2]-fY0[ind2]*fZ[ind1])*invdz;
   b = (fY0[ind2]-fY0[ind1])*invdz;
   y0 = a+b*z;
   a = (fScale[ind1]*fZ[ind2]-fScale[ind2]*fZ[ind1])*invdz;
   b = (fScale[ind2]-fScale[ind1])*invdz;
   scale = a+b*z;
   SetCurrentVertices(x0,y0,scale);
}

////////////////////////////////////////////////////////////////////////////////
/// Set current vertex coordinates according X0, Y0 and SCALE.

void TGeoXtru::SetCurrentVertices(Double_t x0, Double_t y0, Double_t scale)
{
   ThreadData_t& td = GetThreadData();
   for (Int_t i=0; i<fNvert; i++) {
      td.fXc[i] = scale*fX[i] + x0;
      td.fYc[i] = scale*fY[i] + y0;
   }
}

////////////////////////////////////////////////////////////////////////////////
///  - param[0] = nz  // number of z planes
///
///  - param[1] = z1  // Z position of first plane
///  - param[2] = x1  // X position of first plane
///  - param[3] = y1  // Y position of first plane
///  - param[4] = scale1  // scale factor for first plane
/// ...
///  - param[4*(nz-1]+1] = zn
///  - param[4*(nz-1)+2] = xn
///  - param[4*(nz-1)+3] = yn
///  - param[4*(nz-1)+4] = scalen

void TGeoXtru::SetDimensions(Double_t *param)
{
   fNz = (Int_t)param[0];
   if (fNz<2) {
      Error("SetDimensions","Cannot create TGeoXtru %s with less than 2 Z planes",GetName());
      SetShapeBit(TGeoShape::kGeoBad);
      return;
   }
   if (fZ) delete [] fZ;
   if (fScale) delete [] fScale;
   if (fX0) delete [] fX0;
   if (fY0) delete [] fY0;
   fZ = new Double_t[fNz];
   fScale = new Double_t[fNz];
   fX0 = new Double_t[fNz];
   fY0 = new Double_t[fNz];

   for (Int_t i=0; i<fNz; i++)
      DefineSection(i, param[1+4*i], param[2+4*i], param[3+4*i], param[4+4*i]);
}

////////////////////////////////////////////////////////////////////////////////
/// create polycone mesh points

void TGeoXtru::SetPoints(Double_t *points) const
{
   ThreadData_t& td = GetThreadData();
   Int_t i, j;
   Int_t indx = 0;
   TGeoXtru *xtru = (TGeoXtru*)this;
   if (points) {
      for (i = 0; i < fNz; i++) {
         xtru->SetCurrentVertices(fX0[i], fY0[i], fScale[i]);
         if (td.fPoly->IsClockwise()) {
            for (j = 0; j < fNvert; j++) {
               points[indx++] = td.fXc[j];
               points[indx++] = td.fYc[j];
               points[indx++] = fZ[i];
            }
         } else {
            for (j = 0; j < fNvert; j++) {
               points[indx++] = td.fXc[fNvert-1-j];
               points[indx++] = td.fYc[fNvert-1-j];
               points[indx++] = fZ[i];
            }
         }
      }
   }
}

////////////////////////////////////////////////////////////////////////////////
/// create polycone mesh points

void TGeoXtru::SetPoints(Float_t *points) const
{
   ThreadData_t& td = GetThreadData();
   Int_t i, j;
   Int_t indx = 0;
   TGeoXtru *xtru = (TGeoXtru*)this;
   if (points) {
      for (i = 0; i < fNz; i++) {
         xtru->SetCurrentVertices(fX0[i], fY0[i], fScale[i]);
         if (td.fPoly->IsClockwise()) {
            for (j = 0; j < fNvert; j++) {
               points[indx++] = td.fXc[j];
               points[indx++] = td.fYc[j];
               points[indx++] = fZ[i];
            }
         } else {
            for (j = 0; j < fNvert; j++) {
               points[indx++] = td.fXc[fNvert-1-j];
               points[indx++] = td.fYc[fNvert-1-j];
               points[indx++] = fZ[i];
            }
         }
      }
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Returns numbers of vertices, segments and polygons composing the shape mesh.

void TGeoXtru::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
   Int_t nz = GetNz();
   Int_t nv = GetNvert();
   nvert = nz*nv;
   nsegs = nv*(2*nz-1);
   npols = nv*(nz-1)+2;
}

////////////////////////////////////////////////////////////////////////////////
/// Return number of vertices of the mesh representation

Int_t TGeoXtru::GetNmeshVertices() const
{
   Int_t numPoints = fNz*fNvert;
   return numPoints;
}

////////////////////////////////////////////////////////////////////////////////
/// fill size of this 3-D object

void TGeoXtru::Sizeof3D() const
{
}

////////////////////////////////////////////////////////////////////////////////
/// Fills a static 3D buffer and returns a reference.

const TBuffer3D & TGeoXtru::GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
{
   static TBuffer3D buffer(TBuffer3DTypes::kGeneric);

   TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);

   if (reqSections & TBuffer3D::kRawSizes) {
      Int_t nz = GetNz();
      Int_t nvert = GetNvert();
      Int_t nbPnts = nz*nvert;
      Int_t nbSegs = nvert*(2*nz-1);
      Int_t nbPols = nvert*(nz-1)+2;
      if (buffer.SetRawSizes(nbPnts, 3*nbPnts, nbSegs, 3*nbSegs, nbPols, 6*(nbPols-2)+2*(2+nvert))) {
         buffer.SetSectionsValid(TBuffer3D::kRawSizes);
      }
   }
   // TODO: Push down to TGeoShape?
   if ((reqSections & TBuffer3D::kRaw) && buffer.SectionsValid(TBuffer3D::kRawSizes)) {
      SetPoints(buffer.fPnts);
      if (!buffer.fLocalFrame) {
         TransformPoints(buffer.fPnts, buffer.NbPnts());
      }

      SetSegsAndPols(buffer);
      buffer.SetSectionsValid(TBuffer3D::kRaw);
   }

   return buffer;
}

////////////////////////////////////////////////////////////////////////////////
/// Check the inside status for each of the points in the array.
/// Input: Array of point coordinates + vector size
/// Output: Array of Booleans for the inside of each point

void TGeoXtru::Contains_v(const Double_t *points, Bool_t *inside, Int_t vecsize) const
{
   for (Int_t i=0; i<vecsize; i++) inside[i] = Contains(&points[3*i]);
}

////////////////////////////////////////////////////////////////////////////////
/// Compute the normal for an array o points so that norm.dot.dir is positive
/// Input: Arrays of point coordinates and directions + vector size
/// Output: Array of normal directions

void TGeoXtru::ComputeNormal_v(const Double_t *points, const Double_t *dirs, Double_t *norms, Int_t vecsize)
{
   for (Int_t i=0; i<vecsize; i++) ComputeNormal(&points[3*i], &dirs[3*i], &norms[3*i]);
}

////////////////////////////////////////////////////////////////////////////////
/// Compute distance from array of input points having directions specified by dirs. Store output in dists

void TGeoXtru::DistFromInside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t* step) const
{
   for (Int_t i=0; i<vecsize; i++) dists[i] = DistFromInside(&points[3*i], &dirs[3*i], 3, step[i]);
}

////////////////////////////////////////////////////////////////////////////////
/// Compute distance from array of input points having directions specified by dirs. Store output in dists

void TGeoXtru::DistFromOutside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t* step) const
{
   for (Int_t i=0; i<vecsize; i++) dists[i] = DistFromOutside(&points[3*i], &dirs[3*i], 3, step[i]);
}

////////////////////////////////////////////////////////////////////////////////
/// Compute safe distance from each of the points in the input array.
/// Input: Array of point coordinates, array of statuses for these points, size of the arrays
/// Output: Safety values

void TGeoXtru::Safety_v(const Double_t *points, const Bool_t *inside, Double_t *safe, Int_t vecsize) const
{
   for (Int_t i=0; i<vecsize; i++) safe[i] = Safety(&points[3*i], inside[i]);
}