TGeoParaboloid.cxx

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// @(#)root/geom:$Id$
// Author: Mihaela Gheata   20/06/04
 
/*************************************************************************
 * 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 TGeoParaboloid
\ingroup Shapes_classes
 
A paraboloid is defined by the revolution surface generated by a
parabola and is bounded by two planes perpendicular to Z axis. The
parabola equation is taken in the form: `z = a·r2 + b`, where:
`r2 = x2 + y2`. Note the missing linear term (parabola symmetric with
respect to Z axis).
 
The coefficients a and b are computed from the input values which are
the radii of the circular sections cut by the planes at `+/-dz`:
 
  - `-dz = a*r2low  + b`
  - ` dz = a*r2high + b`
 
~~~{.cpp}
TGeoParaboloid(Double_t rlo,Double_t rhi,Double_t dz);
~~~
 
Begin_Macro
{
   new TGeoManager("parab", "paraboloid");
   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->MakeParaboloid("PARAB",med,0, 40, 50);
   TGeoParaboloid *par = (TGeoParaboloid*)vol->GetShape();
   top->AddNode(vol,1);
   gGeoManager->CloseGeometry();
   gGeoManager->SetNsegments(80);
   top->Draw();
   TView *view = gPad->GetView();
   view->ShowAxis();
}
End_Macro
*/
 
#include <iostream>
#include "TGeoManager.h"
#include "TGeoVolume.h"
#include "TVirtualGeoPainter.h"
#include "TGeoParaboloid.h"
#include "TBuffer3D.h"
#include "TBuffer3DTypes.h"
#include "TMath.h"
 
ClassImp(TGeoParaboloid);
 
////////////////////////////////////////////////////////////////////////////////
/// Dummy constructor
 
TGeoParaboloid::TGeoParaboloid()
{
   fRlo = 0;
   fRhi = 0;
   fDz = 0;
   fA = 0;
   fB = 0;
   SetShapeBit(TGeoShape::kGeoParaboloid);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying X and Y semiaxis length
 
TGeoParaboloid::TGeoParaboloid(Double_t rlo, Double_t rhi, Double_t dz) : TGeoBBox(0, 0, 0)
{
   fRlo = 0;
   fRhi = 0;
   fDz = 0;
   fA = 0;
   fB = 0;
   SetShapeBit(TGeoShape::kGeoParaboloid);
   SetParaboloidDimensions(rlo, rhi, dz);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying X and Y semiaxis length
 
TGeoParaboloid::TGeoParaboloid(const char *name, Double_t rlo, Double_t rhi, Double_t dz) : TGeoBBox(name, 0, 0, 0)
{
   fRlo = 0;
   fRhi = 0;
   fDz = 0;
   fA = 0;
   fB = 0;
   SetShapeBit(TGeoShape::kGeoParaboloid);
   SetParaboloidDimensions(rlo, rhi, dz);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
///  - param[0] =  rlo
///  - param[1] =  rhi
///  - param[2] = dz
 
TGeoParaboloid::TGeoParaboloid(Double_t *param)
{
   SetShapeBit(TGeoShape::kGeoParaboloid);
   SetDimensions(param);
   ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TGeoParaboloid::~TGeoParaboloid() {}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoParaboloid::Capacity() const
{
   Double_t capacity = TMath::Pi() * fDz * (fRlo * fRlo + fRhi * fRhi);
   return capacity;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute bounding box of the tube
 
void TGeoParaboloid::ComputeBBox()
{
   fDX = TMath::Max(fRlo, fRhi);
   fDY = fDX;
   fDZ = fDz;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoParaboloid::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm)
{
   norm[0] = norm[1] = 0.0;
   if (TMath::Abs(point[2]) > fDz) {
      norm[2] = TMath::Sign(1., dir[2]);
      return;
   }
   Double_t safz = fDz - TMath::Abs(point[2]);
   Double_t r = TMath::Sqrt(point[0] * point[0] + point[1] * point[1]);
   Double_t safr = TMath::Abs(r - TMath::Sqrt((point[2] - fB) / fA));
   if (safz < safr) {
      norm[2] = TMath::Sign(1., dir[2]);
      return;
   }
   Double_t talf = -2. * fA * r;
   Double_t calf = 1. / TMath::Sqrt(1. + talf * talf);
   Double_t salf = talf * calf;
   Double_t phi = TMath::ATan2(point[1], point[0]);
 
   norm[0] = salf * TMath::Cos(phi);
   norm[1] = salf * TMath::Sin(phi);
   norm[2] = calf;
   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 the elliptical tube
 
Bool_t TGeoParaboloid::Contains(const Double_t *point) const
{
   if (TMath::Abs(point[2]) > fDz)
      return kFALSE;
   Double_t aa = fA * (point[2] - fB);
   if (aa < 0)
      return kFALSE;
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   if (aa < fA * fA * rsq)
      return kFALSE;
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute closest distance from point px,py to each vertex
 
Int_t TGeoParaboloid::DistancetoPrimitive(Int_t px, Int_t py)
{
   Int_t n = gGeoManager->GetNsegments();
   const Int_t numPoints = n * (n + 1) + 2;
   return ShapeDistancetoPrimitive(numPoints, px, py);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute distance from a point to the parabola given by:
///  `z = a*rsq + b;   rsq = x*x+y*y`
 
Double_t TGeoParaboloid::DistToParaboloid(const Double_t *point, const Double_t *dir, Bool_t in) const
{
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t a = fA * (dir[0] * dir[0] + dir[1] * dir[1]);
   Double_t b = 2. * fA * (point[0] * dir[0] + point[1] * dir[1]) - dir[2];
   Double_t c = fA * rsq + fB - point[2];
   Double_t dist = TGeoShape::Big();
   if (TMath::Abs(a) < TGeoShape::Tolerance()) {
      if (TMath::Abs(b) < TGeoShape::Tolerance())
         return dist; // big
      dist = -c / b;
      if (dist < 0)
         return TGeoShape::Big();
      return dist; // OK
   }
   Double_t ainv = 1. / a;
   Double_t sum = -b * ainv;
   Double_t prod = c * ainv;
   Double_t delta = sum * sum - 4. * prod;
   if (delta < 0)
      return dist; // big
   delta = TMath::Sqrt(delta);
   Double_t sone = TMath::Sign(1., ainv);
   Int_t i = -1;
   while (i < 2) {
      dist = 0.5 * (sum + i * sone * delta);
      i += 2;
      if (dist < 0)
         continue;
      if (dist < 1.E-8) {
         Double_t talf = -2. * fA * TMath::Sqrt(rsq);
         Double_t phi = TMath::ATan2(point[1], point[0]);
         Double_t ndotd = talf * (TMath::Cos(phi) * dir[0] + TMath::Sin(phi) * dir[1]) + dir[2];
         if (!in)
            ndotd *= -1;
         if (ndotd < 0)
            return dist;
      } else
         return dist;
   }
   return TGeoShape::Big();
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from inside point to surface of the paraboloid
 
Double_t TGeoParaboloid::DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step,
                                        Double_t *safe) const
{
   if (iact < 3 && safe) {
      // compute safe distance
      *safe = Safety(point, kTRUE);
      if (iact == 0)
         return TGeoShape::Big();
      if (iact == 1 && step < *safe)
         return TGeoShape::Big();
   }
 
   Double_t dz = TGeoShape::Big();
   if (dir[2] < 0) {
      dz = -(point[2] + fDz) / dir[2];
   } else if (dir[2] > 0) {
      dz = (fDz - point[2]) / dir[2];
   }
   Double_t dpara = DistToParaboloid(point, dir, kTRUE);
   return TMath::Min(dz, dpara);
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from outside point to surface of the paraboloid and safe distance
 
Double_t TGeoParaboloid::DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step,
                                         Double_t *safe) const
{
   if (iact < 3 && safe) {
      // compute safe distance
      *safe = Safety(point, kFALSE);
      if (iact == 0)
         return TGeoShape::Big();
      if (iact == 1 && step < *safe)
         return TGeoShape::Big();
   }
   Double_t xnew, ynew, znew;
   if (point[2] <= -fDz) {
      if (dir[2] <= 0)
         return TGeoShape::Big();
      Double_t snxt = -(fDz + point[2]) / dir[2];
      // find extrapolated X and Y
      xnew = point[0] + snxt * dir[0];
      ynew = point[1] + snxt * dir[1];
      if ((xnew * xnew + ynew * ynew) <= fRlo * fRlo)
         return snxt;
   } else if (point[2] >= fDz) {
      if (dir[2] >= 0)
         return TGeoShape::Big();
      Double_t snxt = (fDz - point[2]) / dir[2];
      // find extrapolated X and Y
      xnew = point[0] + snxt * dir[0];
      ynew = point[1] + snxt * dir[1];
      if ((xnew * xnew + ynew * ynew) <= fRhi * fRhi)
         return snxt;
   }
   Double_t snxt = DistToParaboloid(point, dir, kFALSE);
   if (snxt > 1E20)
      return snxt;
   znew = point[2] + snxt * dir[2];
   if (TMath::Abs(znew) <= fDz)
      return snxt;
   return TGeoShape::Big();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Divide the paraboloid along one axis.
 
TGeoVolume *TGeoParaboloid::Divide(TGeoVolume * /*voldiv*/, const char * /*divname*/, Int_t /*iaxis*/, Int_t /*ndiv*/,
                                   Double_t /*start*/, Double_t /*step*/)
{
   Error("Divide", "Paraboloid divisions not implemented");
   return nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill vector param[4] with the bounding cylinder parameters. The order
/// is the following : Rmin, Rmax, Phi1, Phi2
 
void TGeoParaboloid::GetBoundingCylinder(Double_t *param) const
{
   param[0] = 0.;  // Rmin
   param[1] = fDX; // Rmax
   param[1] *= param[1];
   param[2] = 0.;   // Phi1
   param[3] = 360.; // Phi2
}
 
////////////////////////////////////////////////////////////////////////////////
/// in case shape has some negative parameters, these has to be computed
/// in order to fit the mother
 
TGeoShape *TGeoParaboloid::GetMakeRuntimeShape(TGeoShape *, TGeoMatrix *) const
{
   return nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
/// print shape parameters
 
void TGeoParaboloid::InspectShape() const
{
   printf("*** Shape %s: TGeoParaboloid ***\n", GetName());
   printf("    rlo    = %11.5f\n", fRlo);
   printf("    rhi    = %11.5f\n", fRhi);
   printf("    dz     = %11.5f\n", fDz);
   printf(" Bounding box:\n");
   TGeoBBox::InspectShape();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Creates a TBuffer3D describing *this* shape.
/// Coordinates are in local reference frame.
 
TBuffer3D *TGeoParaboloid::MakeBuffer3D() const
{
   Int_t n = gGeoManager->GetNsegments();
   Int_t nbPnts = n * (n + 1) + 2;
   Int_t nbSegs = n * (2 * n + 3);
   Int_t nbPols = n * (n + 2);
 
   TBuffer3D *buff =
      new TBuffer3D(TBuffer3DTypes::kGeneric, nbPnts, 3 * nbPnts, nbSegs, 3 * nbSegs, nbPols, 2 * n * 5 + n * n * 6);
 
   if (buff) {
      SetPoints(buff->fPnts);
      SetSegsAndPols(*buff);
   }
 
   return buff;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill TBuffer3D structure for segments and polygons.
 
void TGeoParaboloid::SetSegsAndPols(TBuffer3D &buff) const
{
   Int_t indx, i, j;
   Int_t n = gGeoManager->GetNsegments();
 
   Int_t c = GetBasicColor();
 
   Int_t nn1 = (n + 1) * n + 1;
   indx = 0;
   // Lower end-cap (n radial segments)
   for (j = 0; j < n; j++) {
      buff.fSegs[indx++] = c + 2;
      buff.fSegs[indx++] = 0;
      buff.fSegs[indx++] = j + 1;
   }
   // Sectors (n)
   for (i = 0; i < n + 1; i++) {
      // lateral (circles) segments (n)
      for (j = 0; j < n; j++) {
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = n * i + 1 + j;
         buff.fSegs[indx++] = n * i + 1 + ((j + 1) % n);
      }
      if (i == n)
         break; // skip i=n for generators
      // generator segments (n)
      for (j = 0; j < n; j++) {
         buff.fSegs[indx++] = c;
         buff.fSegs[indx++] = n * i + 1 + j;
         buff.fSegs[indx++] = n * (i + 1) + 1 + j;
      }
   }
   // Upper end-cap
   for (j = 0; j < n; j++) {
      buff.fSegs[indx++] = c + 1;
      buff.fSegs[indx++] = n * n + 1 + j;
      buff.fSegs[indx++] = nn1;
   }
 
   indx = 0;
 
   // lower end-cap (n polygons)
   for (j = 0; j < n; j++) {
      buff.fPols[indx++] = c + 2;
      buff.fPols[indx++] = 3;
      buff.fPols[indx++] = n + j;
      buff.fPols[indx++] = (j + 1) % n;
      buff.fPols[indx++] = j;
   }
   // Sectors (n)
   for (i = 0; i < n; i++) {
      // lateral faces (n)
      for (j = 0; j < n; j++) {
         buff.fPols[indx++] = c;
         buff.fPols[indx++] = 4;
         buff.fPols[indx++] = (2 * i + 1) * n + j;
         buff.fPols[indx++] = 2 * (i + 1) * n + j;
         buff.fPols[indx++] = (2 * i + 3) * n + j;
         buff.fPols[indx++] = 2 * (i + 1) * n + ((j + 1) % n);
      }
   }
   // upper end-cap (n polygons)
   for (j = 0; j < n; j++) {
      buff.fPols[indx++] = c + 1;
      buff.fPols[indx++] = 3;
      buff.fPols[indx++] = 2 * n * (n + 1) + j;
      buff.fPols[indx++] = 2 * n * (n + 1) + ((j + 1) % n);
      buff.fPols[indx++] = (2 * n + 1) * n + j;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes the closest distance from given point to this shape.
 
Double_t TGeoParaboloid::Safety(const Double_t *point, Bool_t in) const
{
   Double_t safz = fDz - TMath::Abs(point[2]);
   if (!in)
      safz = -safz;
   Double_t safr;
   Double_t rsq = point[0] * point[0] + point[1] * point[1];
   Double_t z0 = fA * rsq + fB;
   Double_t r0sq = (point[2] - fB) / fA;
   if (r0sq < 0) {
      if (in)
         return 0.;
      return safz;
   }
   Double_t dr = TMath::Sqrt(rsq) - TMath::Sqrt(r0sq);
   if (in) {
      if (dr > -1.E-8)
         return 0.;
      Double_t dz = TMath::Abs(point[2] - z0);
      safr = -dr * dz / TMath::Sqrt(dr * dr + dz * dz);
   } else {
      if (dr < 1.E-8)
         return safz;
      Double_t talf = -2. * fA * TMath::Sqrt(r0sq);
      Double_t salf = talf / TMath::Sqrt(1. + talf * talf);
      safr = TMath::Abs(dr * salf);
   }
   if (in)
      return TMath::Min(safr, safz);
   return TMath::Max(safr, safz);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set paraboloid dimensions.
 
void TGeoParaboloid::SetParaboloidDimensions(Double_t rlo, Double_t rhi, Double_t dz)
{
   if ((rlo < 0) || (rhi < 0) || (dz <= 0) || TMath::Abs(rlo - rhi) < TGeoShape::Tolerance()) {
      SetShapeBit(kGeoRunTimeShape);
      Error("SetParaboloidDimensions", "Dimensions of %s invalid: check (rlo>=0) (rhi>=0) (rlo!=rhi) dz>0", GetName());
      return;
   }
   fRlo = rlo;
   fRhi = rhi;
   fDz = dz;
   Double_t dd = 1. / (fRhi * fRhi - fRlo * fRlo);
   fA = 2. * fDz * dd;
   fB = -fDz * (fRlo * fRlo + fRhi * fRhi) * dd;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set paraboloid dimensions starting from an array.
 
void TGeoParaboloid::SetDimensions(Double_t *param)
{
   Double_t rlo = param[0];
   Double_t rhi = param[1];
   Double_t dz = param[2];
   SetParaboloidDimensions(rlo, rhi, dz);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create paraboloid mesh points.
/// ~~~ {.cpp}
/// Npoints = n*(n+1) + 2
///     ifirst = 0
///     ipoint(i,j) = 1+i*n+j;                              i=[0,n]  j=[0,n-1]
///     ilast = 1+n*(n+1)
/// Nsegments = n*(2*n+3)
///     lower: (0, j+1);                                    j=[0,n-1]
///     circle(i): (n*i+1+j, n*i+1+(j+1)%n);                i=[0,n]  j=[0,n-1]
///     generator(i): (n*i+1+j, n*(i+1)+1+j);               i,j=[0,n-1]
///     upper: (n*n+1+j, (n+1)*n+1)                           j=[0,n-1]
/// Npolygons = n*(n+2)
///     lower: (n+j, (j+1)%n, j)                              j=[0,n-1]
///     lateral(i): ((2*i+1)*n+j, 2*(i+1)*n+j, (2*i+3)*n+j, 2*(i+1)*n+(j+1)%n)
///                                                        i,j = [0,n-1]
///     upper: ((2n+1)*n+j, 2*n*(n+1)+(j+1)%n, 2*n*(n+1)+j)   j=[0,n-1]
/// ~~~
 
void TGeoParaboloid::SetPoints(Double_t *points) const
{
   if (!points)
      return;
   Double_t ttmin, ttmax;
   ttmin = TMath::ATan2(-fDz, fRlo);
   ttmax = TMath::ATan2(fDz, fRhi);
   Int_t n = gGeoManager->GetNsegments();
   Double_t dtt = (ttmax - ttmin) / n;
   Double_t dphi = 360. / n;
   Double_t tt;
   Double_t r, z, delta;
   Double_t phi, sph, cph;
   Int_t indx = 0;
   // center of the lower endcap:
   points[indx++] = 0; // x
   points[indx++] = 0; // y
   points[indx++] = -fDz;
   for (Int_t i = 0; i < n + 1; i++) { // nz planes = n+1
      if (i == 0) {
         r = fRlo;
         z = -fDz;
      } else if (i == n) {
         r = fRhi;
         z = fDz;
      } else {
         tt = TMath::Tan(ttmin + i * dtt);
         delta = tt * tt - 4 * fA * fB; // should be always positive (a*b<0)
         r = 0.5 * (tt + TMath::Sqrt(delta)) / fA;
         z = r * tt;
      }
      for (Int_t j = 0; j < n; j++) {
         phi = j * dphi * TMath::DegToRad();
         sph = TMath::Sin(phi);
         cph = TMath::Cos(phi);
         points[indx++] = r * cph;
         points[indx++] = r * sph;
         points[indx++] = z;
      }
   }
   // center of the upper endcap
   points[indx++] = 0; // x
   points[indx++] = 0; // y
   points[indx++] = fDz;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns numbers of vertices, segments and polygons composing the shape mesh.
 
void TGeoParaboloid::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
{
   Int_t n = gGeoManager->GetNsegments();
   nvert = n * (n + 1) + 2;
   nsegs = n * (2 * n + 3);
   npols = n * (n + 2);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Returns number of vertices on the paraboloid mesh.
 
Int_t TGeoParaboloid::GetNmeshVertices() const
{
   Int_t n = gGeoManager->GetNsegments();
   return (n * (n + 1) + 2);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Save a primitive as a C++ statement(s) on output stream "out".
 
void TGeoParaboloid::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
{
   if (TObject::TestBit(kGeoSavePrimitive))
      return;
   out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
   out << "   rlo = " << fRlo << ";" << std::endl;
   out << "   rhi = " << fRhi << ";" << std::endl;
   out << "   dz  = " << fDZ << ";" << std::endl;
   out << "   TGeoShape *" << GetPointerName() << " = new TGeoParaboloid(\"" << GetName() << "\", rlo,rhi,dz);"
       << std::endl;
   TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create paraboloid mesh points.
 
void TGeoParaboloid::SetPoints(Float_t *points) const
{
   if (!points)
      return;
   Double_t ttmin, ttmax;
   ttmin = TMath::ATan2(-fDz, fRlo);
   ttmax = TMath::ATan2(fDz, fRhi);
   Int_t n = gGeoManager->GetNsegments();
   Double_t dtt = (ttmax - ttmin) / n;
   Double_t dphi = 360. / n;
   Double_t tt;
   Double_t r, z, delta;
   Double_t phi, sph, cph;
   Int_t indx = 0;
   // center of the lower endcap:
   points[indx++] = 0; // x
   points[indx++] = 0; // y
   points[indx++] = -fDz;
   for (Int_t i = 0; i < n + 1; i++) { // nz planes = n+1
      if (i == 0) {
         r = fRlo;
         z = -fDz;
      } else if (i == n) {
         r = fRhi;
         z = fDz;
      } else {
         tt = TMath::Tan(ttmin + i * dtt);
         delta = tt * tt - 4 * fA * fB; // should be always positive (a*b<0)
         r = 0.5 * (tt + TMath::Sqrt(delta)) / fA;
         z = r * tt;
      }
      for (Int_t j = 0; j < n; j++) {
         phi = j * dphi * TMath::DegToRad();
         sph = TMath::Sin(phi);
         cph = TMath::Cos(phi);
         points[indx++] = r * cph;
         points[indx++] = r * sph;
         points[indx++] = z;
      }
   }
   // center of the upper endcap
   points[indx++] = 0; // x
   points[indx++] = 0; // y
   points[indx++] = fDz;
}
 
////////////////////////////////////////////////////////////////////////////////
void TGeoParaboloid::Sizeof3D() const {}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills a static 3D buffer and returns a reference.
 
const TBuffer3D &TGeoParaboloid::GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
{
   static TBuffer3D buffer(TBuffer3DTypes::kGeneric);
   TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);
 
   if (reqSections & TBuffer3D::kRawSizes) {
      Int_t n = gGeoManager->GetNsegments();
      Int_t nbPnts = n * (n + 1) + 2;
      Int_t nbSegs = n * (2 * n + 3);
      Int_t nbPols = n * (n + 2);
      if (buffer.SetRawSizes(nbPnts, 3 * nbPnts, nbSegs, 3 * nbSegs, nbPols, 2 * n * 5 + n * n * 6)) {
         buffer.SetSectionsValid(TBuffer3D::kRawSizes);
      }
   }
   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 TGeoParaboloid::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 TGeoParaboloid::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 TGeoParaboloid::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 TGeoParaboloid::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 TGeoParaboloid::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]);
}