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 Shapes_classes
A TGeoXtru shape is represented by the extrusion of an arbitrary
polygon with fixed outline between several Z sections. Each Z section is
a scaled version of the same "blueprint" polygon. Different global XY
translations are allowed from section to section. Corresponding polygon
vertices from consecutive sections are connected.
 
An extruded polygon can be created using the constructor:
 
~~~ {.cpp}
TGeoXtru::TGeoXtru(Int_t nplanes);
~~~
 
  - `nplanes:  `number of Z sections (minimum 2)
 
Begin_Macro
{
   new TGeoManager("xtru", "poza12");
   TGeoMaterial *mat = new TGeoMaterial("Al", 26.98,13,2.7);
   TGeoMedium *med = new TGeoMedium("MED",1,mat);
   TGeoVolume *top = gGeoManager->MakeBox("TOP",med,100,100,100);
   gGeoManager->SetTopVolume(top);
   TGeoVolume *vol = gGeoManager->MakeXtru("XTRU",med,4);
   TGeoXtru *xtru = (TGeoXtru*)vol->GetShape();
   Double_t x[8] = {-30,-30,30,30,15,15,-15,-15};
   Double_t y[8] = {-30,30,30,-30,-30,15,15,-30};
   xtru->DefinePolygon(8,x,y);
   xtru->DefineSection(0,-40, -20., 10., 1.5);
   xtru->DefineSection(1, 10, 0., 0., 0.5);
   xtru->DefineSection(2, 10, 0., 0., 0.7);
   xtru->DefineSection(3, 40, 10., 20., 0.9);
   top->AddNode(vol,1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
   top->Draw();
   if (gPad) {
      TView *view = gPad->GetView();
      if (view) view->ShowAxis();
    }
}
End_Macro
 
The lists of X and Y positions for all vertices have to be provided for
the "blueprint" polygon:
 
~~~{.cpp}
TGeoXtru::DefinePolygon (Int_t nvertices, Double_t *xv,
Double_t *yv);
~~~
 
  - `nvertices:  `number of vertices of the polygon
  - `xv,yv:  `arrays of X and Y coordinates for polygon vertices
 
The method creates an object of the class **`TGeoPolygon`** for which
the convexity is automatically determined . The polygon is decomposed
into convex polygons if needed.
 
Next step is to define the Z positions for each section plane as well as
the XY offset and scaling for the corresponding polygons.
 
~~~{.cpp}
TGeoXtru::DefineSection(Int_t snum,Double_t zsection,Double_t x0,
Double_t y0, Double_t scale);
~~~
 
  - `snum: `Z section index (0, nplanes-1). The section with
    `snum = nplanes-1` must be defined last and triggers the computation
    of the bounding box for the whole shape
  - `zsection: `Z position of section `snum`. Sections must be defined
    in increasing order of Z (e.g. `snum=0` correspond to the minimum Z
    and `snum=nplanes-1` to the maximum one).
  - `x0,y0: `offset of section `snum` with respect to the local shape
    reference frame `T`
  - `scale: `factor that multiplies the X/Y coordinates of each vertex
    of the polygon at section `snum`:
  - `x[ivert] = x0 + scale*xv[ivert]`
  - `y[ivert] = y0 + scale*yv[ivert]`
*/
 
#include "TGeoXtru.h"
 
#include <iostream>
 
#include "TBuffer3D.h"
#include "TBuffer3DTypes.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(nullptr), fYc(nullptr), fPoly(nullptr) {}
 
////////////////////////////////////////////////////////////////////////////////
/// 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();
   return *fThreadData[tid];
}
 
////////////////////////////////////////////////////////////////////////////////
 
void TGeoXtru::ClearThreadData() const
{
   std::lock_guard<std::mutex> guard(fMutex);
   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)
{
   std::lock_guard<std::mutex> guard(fMutex);
   fThreadData.resize(nthreads);
   fThreadSize = nthreads;
   for (Int_t tid = 0; tid < nthreads; tid++) {
      if (fThreadData[tid] == nullptr) {
         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());
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// 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(nullptr),
     fY(nullptr),
     fZ(nullptr),
     fScale(nullptr),
     fX0(nullptr),
     fY0(nullptr),
     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(nullptr),
     fY(nullptr),
     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(nullptr),
     fY(nullptr),
     fZ(nullptr),
     fScale(nullptr),
     fX0(nullptr),
     fY0(nullptr),
     fThreadData(0),
     fThreadSize(0)
{
   SetShapeBit(TGeoShape::kGeoXtru);
   SetDimensions(param);
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TGeoXtru::~TGeoXtru()
{
   if (fX) {
      delete[] fX;
      fX = nullptr;
   }
   if (fY) {
      delete[] fY;
      fY = nullptr;
   }
   if (fZ) {
      delete[] fZ;
      fZ = nullptr;
   }
   if (fScale) {
      delete[] fScale;
      fScale = nullptr;
   }
   if (fX0) {
      delete[] fX0;
      fX0 = nullptr;
   }
   if (fY0) {
      delete[] fY0;
      fY0 = nullptr;
   }
   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) const
{
   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.;
   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)) {
      Double_t 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++) {
         Double_t 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++) {
         Double_t 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 = 0, indx2, k;
   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 saf1, saf2, safz, safe;
   Bool_t in1, in2;
   Int_t iseg;
   // 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 << "   auto " << GetPointerName() << " = new TGeoXtru(" << fNz << ");" << std::endl;
   out << "   " << GetPointerName() << "->SetName(\"" << GetName() << "\");" << std::endl;
   for (Int_t i = 0; i < fNvert; i++) {
      out << "   xvert[" << i << "] = " << fX[i] << ";   yvert[" << i << "] = " << fY[i] << ";" << std::endl;
   }
   out << "   " << GetPointerName() << "->DefinePolygon(" << fNvert << ", xvert, yvert);" << std::endl;
   for (Int_t i = 0; i < fNz; i++)
      out << "   " << GetPointerName() << "->DefineSection(" << i << ", " << fZ[i] << ", " << fX0[i] << ", " << fY0[i]
          << ", " << fScale[i] << ");" << 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]);
}