TGeoPara.cxx

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// @(#)root/geom:$Id$
// Author: Andrei Gheata   31/01/02
// TGeoPara::Contains() implemented by Mihaela Gheata
 
/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
/** \class TGeoPara
\ingroup Shapes_classes
\brief Parallelepiped class.
 
A parallelepiped is a shape having 3 pairs of parallel faces out of
which one is parallel with the XY plane (Z faces). All faces are
parallelograms in the general case. The Z faces have 2 edges parallel
with the X-axis.
 
The shape has the center in the origin and it is defined by:
 
  - `dX, dY, dZ:` half-lengths of the projections of the edges on X, Y
    and Z. The lower Z face is positioned at `-dZ`, while the upper at `+dZ`.
  - `alpha:` angle between the segment defined by the centers of the
    X-parallel edges and Y axis `[-90,90]` in degrees
  -   `theta:` theta angle of the segment defined by the centers of the Z faces;
  - `phi:` phi angle of the same segment
 
~~~ {.cpp}
TGeoPara(dX,dY,dZ,alpha,theta,phi);
~~~
 
A box is a particular parallelepiped having the parameters:
`(dX,dY,dZ,0.,0.,0.)`.
 
Begin_Macro
{
   TCanvas *c = new TCanvas("c", "c",0,0,600,600);
   new TGeoManager("para", "poza1");
   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->MakePara("PARA",med, 20,30,40,30,15,30);
   vol->SetLineWidth(2);
   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 "TGeoMatrix.h"
#include "TGeoVolume.h"
#include "TGeoPara.h"
#include "TMath.h"
 
ClassImp(TGeoPara);
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor
 
TGeoPara::TGeoPara()
{
   SetShapeBit(TGeoShape::kGeoPara);
   fX = fY = fZ = 0;
   fAlpha = 0;
   fTheta = 0;
   fPhi = 0;
   fTxy = 0;
   fTxz = 0;
   fTyz = 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
 
TGeoPara::TGeoPara(Double_t dx, Double_t dy, Double_t dz, Double_t alpha, Double_t theta, Double_t phi)
   : TGeoBBox(0, 0, 0)
{
   SetShapeBit(TGeoShape::kGeoPara);
   fX = dx;
   fY = dy;
   fZ = dz;
   fAlpha = alpha;
   fTheta = theta;
   fPhi = phi;
   fTxy = TMath::Tan(alpha * TMath::DegToRad());
   Double_t tth = TMath::Tan(theta * TMath::DegToRad());
   Double_t ph = phi * TMath::DegToRad();
   fTxz = tth * TMath::Cos(ph);
   fTyz = tth * TMath::Sin(ph);
   if ((fX < 0) || (fY < 0) || (fZ < 0)) {
      //      printf("para : %f %f %f\n", fX, fY, fZ);
      SetShapeBit(kGeoRunTimeShape);
   } else
      ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor specifying minimum and maximum radius
 
TGeoPara::TGeoPara(const char *name, Double_t dx, Double_t dy, Double_t dz, Double_t alpha, Double_t theta,
                   Double_t phi)
   : TGeoBBox(name, 0, 0, 0)
{
   SetShapeBit(TGeoShape::kGeoPara);
   fX = dx;
   fY = dy;
   fZ = dz;
   fAlpha = alpha;
   fTheta = theta;
   fPhi = phi;
   fTxy = TMath::Tan(alpha * TMath::DegToRad());
   Double_t tth = TMath::Tan(theta * TMath::DegToRad());
   Double_t ph = phi * TMath::DegToRad();
   fTxz = tth * TMath::Cos(ph);
   fTyz = tth * TMath::Sin(ph);
   if ((fX < 0) || (fY < 0) || (fZ < 0)) {
      //      printf("para : %f %f %f\n", fX, fY, fZ);
      SetShapeBit(kGeoRunTimeShape);
   } else
      ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Default constructor
///  - param[0] = dx
///  - param[1] = dy
///  - param[2] = dz
///  - param[3] = alpha
///  - param[4] = theta
///  - param[5] = phi
 
TGeoPara::TGeoPara(Double_t *param) : TGeoBBox(0, 0, 0)
{
   SetShapeBit(TGeoShape::kGeoPara);
   SetDimensions(param);
   if ((fX < 0) || (fY < 0) || (fZ < 0))
      SetShapeBit(kGeoRunTimeShape);
   else
      ComputeBBox();
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TGeoPara::~TGeoPara() {}
 
////////////////////////////////////////////////////////////////////////////////
/// Computes capacity of the shape in [length^3]
 
Double_t TGeoPara::Capacity() const
{
   Double_t capacity = 8. * fX * fY * fZ;
   return capacity;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute bounding box
 
void TGeoPara::ComputeBBox()
{
   Double_t dx = fX + fY * TMath::Abs(fTxy) + fZ * TMath::Abs(fTxz);
   Double_t dy = fY + fZ * TMath::Abs(fTyz);
   Double_t dz = fZ;
   TGeoBBox::SetBoxDimensions(dx, dy, dz);
   memset(fOrigin, 0, 3 * sizeof(Double_t));
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute normal to closest surface from POINT.
 
void TGeoPara::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm)
{
   Double_t saf[3];
   // distance from point to higher Z face
   saf[0] = TMath::Abs(fZ - TMath::Abs(point[2])); // Z
 
   Double_t yt = point[1] - fTyz * point[2];
   saf[1] = TMath::Abs(fY - TMath::Abs(yt)); // Y
   // cos of angle YZ
   Double_t cty = 1.0 / TMath::Sqrt(1.0 + fTyz * fTyz);
 
   Double_t xt = point[0] - fTxz * point[2] - fTxy * yt;
   saf[2] = TMath::Abs(fX - TMath::Abs(xt)); // X
   // cos of angle XZ
   Double_t ctx = 1.0 / TMath::Sqrt(1.0 + fTxy * fTxy + fTxz * fTxz);
   saf[2] *= ctx;
   saf[1] *= cty;
   Int_t i = TMath::LocMin(3, saf);
   switch (i) {
   case 0:
      norm[0] = norm[1] = 0;
      norm[2] = TMath::Sign(1., dir[2]);
      return;
   case 1:
      norm[0] = 0;
      norm[1] = cty;
      norm[2] = -fTyz * cty;
      break;
   case 2:
      norm[0] = TMath::Cos(fTheta * TMath::DegToRad()) * TMath::Cos(fAlpha * TMath::DegToRad());
      norm[1] = -TMath::Cos(fTheta * TMath::DegToRad()) * TMath::Sin(fAlpha * TMath::DegToRad());
      norm[2] = -TMath::Sin(fTheta * TMath::DegToRad());
   }
   if (norm[0] * dir[0] + norm[1] * dir[1] + norm[2] * dir[2] < 0) {
      norm[0] = -norm[0];
      norm[1] = -norm[1];
      norm[2] = -norm[2];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// test if point is inside this sphere
/// test Z range
 
Bool_t TGeoPara::Contains(const Double_t *point) const
{
   if (TMath::Abs(point[2]) > fZ)
      return kFALSE;
   // check X and Y
   Double_t yt = point[1] - fTyz * point[2];
   if (TMath::Abs(yt) > fY)
      return kFALSE;
   Double_t xt = point[0] - fTxz * point[2] - fTxy * yt;
   if (TMath::Abs(xt) > fX)
      return kFALSE;
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from inside point to surface of the para
/// Boundary safe algorithm.
 
Double_t
TGeoPara::DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
{
   if (iact < 3 && safe) {
      // compute safety
      *safe = Safety(point, kTRUE);
      if (iact == 0)
         return TGeoShape::Big();
      if (iact == 1 && step < *safe)
         return TGeoShape::Big();
   }
   Double_t saf[2];
   Double_t snxt = TGeoShape::Big();
   Double_t s;
   saf[0] = fZ + point[2];
   saf[1] = fZ - point[2];
   if (!TGeoShape::IsSameWithinTolerance(dir[2], 0)) {
      s = (dir[2] > 0) ? (saf[1] / dir[2]) : (-saf[0] / dir[2]);
      if (s < 0)
         return 0.0;
      if (s < snxt)
         snxt = s;
   }
   // distance from point to center axis on Y
   Double_t yt = point[1] - fTyz * point[2];
   saf[0] = fY + yt;
   saf[1] = fY - yt;
   Double_t dy = dir[1] - fTyz * dir[2];
   if (!TGeoShape::IsSameWithinTolerance(dy, 0)) {
      s = (dy > 0) ? (saf[1] / dy) : (-saf[0] / dy);
      if (s < 0)
         return 0.0;
      if (s < snxt)
         snxt = s;
   }
   // distance from point to center axis on X
   Double_t xt = point[0] - fTxz * point[2] - fTxy * yt;
   saf[0] = fX + xt;
   saf[1] = fX - xt;
   Double_t dx = dir[0] - fTxz * dir[2] - fTxy * dy;
   if (!TGeoShape::IsSameWithinTolerance(dx, 0)) {
      s = (dx > 0) ? (saf[1] / dx) : (-saf[0] / dx);
      if (s < 0)
         return 0.0;
      if (s < snxt)
         snxt = s;
   }
   return snxt;
}
 
////////////////////////////////////////////////////////////////////////////////
/// compute distance from inside point to surface of the para
 
Double_t
TGeoPara::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();
   }
   Bool_t in = kTRUE;
   Double_t safz;
   safz = TMath::Abs(point[2]) - fZ;
   if (safz > 0) {
      // outside Z
      if (point[2] * dir[2] >= 0)
         return TGeoShape::Big();
      in = kFALSE;
   }
   Double_t yt = point[1] - fTyz * point[2];
   Double_t safy = TMath::Abs(yt) - fY;
   Double_t dy = dir[1] - fTyz * dir[2];
   if (safy > 0) {
      if (yt * dy >= 0)
         return TGeoShape::Big();
      in = kFALSE;
   }
   Double_t xt = point[0] - fTxy * yt - fTxz * point[2];
   Double_t safx = TMath::Abs(xt) - fX;
   Double_t dx = dir[0] - fTxy * dy - fTxz * dir[2];
   if (safx > 0) {
      if (xt * dx >= 0)
         return TGeoShape::Big();
      in = kFALSE;
   }
   // protection in case point is actually inside
   if (in) {
      if (safz > safx && safz > safy) {
         if (point[2] * dir[2] > 0)
            return TGeoShape::Big();
         return 0.0;
      }
      if (safx > safy) {
         if (xt * dx > 0)
            return TGeoShape::Big();
         return 0.0;
      }
      if (yt * dy > 0)
         return TGeoShape::Big();
      return 0.0;
   }
   Double_t xnew, ynew, znew;
   if (safz > 0) {
      Double_t snxt = safz / TMath::Abs(dir[2]);
      xnew = point[0] + snxt * dir[0];
      ynew = point[1] + snxt * dir[1];
      znew = (point[2] > 0) ? fZ : (-fZ);
      Double_t ytn = ynew - fTyz * znew;
      if (TMath::Abs(ytn) <= fY) {
         Double_t xtn = xnew - fTxy * ytn - fTxz * znew;
         if (TMath::Abs(xtn) <= fX)
            return snxt;
      }
   }
   if (safy > 0) {
      Double_t snxt = safy / TMath::Abs(dy);
      znew = point[2] + snxt * dir[2];
      if (TMath::Abs(znew) <= fZ) {
         Double_t ytn = (yt > 0) ? fY : (-fY);
         xnew = point[0] + snxt * dir[0];
         Double_t xtn = xnew - fTxy * ytn - fTxz * znew;
         if (TMath::Abs(xtn) <= fX)
            return snxt;
      }
   }
   if (safx > 0) {
      Double_t snxt = safx / TMath::Abs(dx);
      znew = point[2] + snxt * dir[2];
      if (TMath::Abs(znew) <= fZ) {
         ynew = point[1] + snxt * dir[1];
         Double_t ytn = ynew - fTyz * znew;
         if (TMath::Abs(ytn) <= fY)
            return snxt;
      }
   }
   return TGeoShape::Big();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Divide this parallelepiped shape belonging to volume "voldiv" into ndiv equal volumes
/// called divname, from start position with the given step. Returns pointer
/// to created division cell volume. In case a wrong division axis is supplied,
/// returns pointer to volume to be divided.
 
TGeoVolume *
TGeoPara::Divide(TGeoVolume *voldiv, const char *divname, Int_t iaxis, Int_t ndiv, Double_t start, Double_t step)
{
   TGeoShape *shape;          //--- shape to be created
   TGeoVolume *vol;           //--- division volume to be created
   TGeoVolumeMulti *vmulti;   //--- generic divided volume
   TGeoPatternFinder *finder; //--- finder to be attached
   TString opt = "";          //--- option to be attached
   Double_t end = start + ndiv * step;
   switch (iaxis) {
   case 1: //--- divide on X
      shape = new TGeoPara(step / 2, fY, fZ, fAlpha, fTheta, fPhi);
      finder = new TGeoPatternParaX(voldiv, ndiv, start, end);
      opt = "X";
      break;
   case 2: //--- divide on Y
      shape = new TGeoPara(fX, step / 2, fZ, fAlpha, fTheta, fPhi);
      finder = new TGeoPatternParaY(voldiv, ndiv, start, end);
      opt = "Y";
      break;
   case 3: //--- divide on Z
      shape = new TGeoPara(fX, fY, step / 2, fAlpha, fTheta, fPhi);
      finder = new TGeoPatternParaZ(voldiv, ndiv, start, end);
      opt = "Z";
      break;
   default: Error("Divide", "Wrong axis type for division"); return nullptr;
   }
   vol = new TGeoVolume(divname, shape, voldiv->GetMedium());
   vmulti = gGeoManager->MakeVolumeMulti(divname, voldiv->GetMedium());
   vmulti->AddVolume(vol);
   voldiv->SetFinder(finder);
   finder->SetDivIndex(voldiv->GetNdaughters());
   for (Int_t ic = 0; ic < ndiv; ic++) {
      voldiv->AddNodeOffset(vol, ic, start + step / 2. + ic * step, opt.Data());
      ((TGeoNodeOffset *)voldiv->GetNodes()->At(voldiv->GetNdaughters() - 1))->SetFinder(finder);
   }
   return vmulti;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Get range of shape for a given axis.
 
Double_t TGeoPara::GetAxisRange(Int_t iaxis, Double_t &xlo, Double_t &xhi) const
{
   xlo = 0;
   xhi = 0;
   Double_t dx = 0;
   switch (iaxis) {
   case 1:
      xlo = -fX;
      xhi = fX;
      dx = xhi - xlo;
      return dx;
   case 2:
      xlo = -fY;
      xhi = fY;
      dx = xhi - xlo;
      return dx;
   case 3:
      xlo = -fZ;
      xhi = fZ;
      dx = xhi - xlo;
      return dx;
   }
   return dx;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill vector param[4] with the bounding cylinder parameters. The order
/// is the following : Rmin, Rmax, Phi1, Phi2
 
void TGeoPara::GetBoundingCylinder(Double_t *param) const
{
   TGeoBBox::GetBoundingCylinder(param);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fills real parameters of a positioned box inside this. Returns 0 if successful.
 
Int_t TGeoPara::GetFittingBox(const TGeoBBox *parambox, TGeoMatrix *mat, Double_t &dx, Double_t &dy, Double_t &dz) const
{
   dx = dy = dz = 0;
   if (mat->IsRotation()) {
      Error("GetFittingBox", "cannot handle parametrized rotated volumes");
      return 1; // ### rotation not accepted ###
   }
   //--> translate the origin of the parametrized box to the frame of this box.
   Double_t origin[3];
   mat->LocalToMaster(parambox->GetOrigin(), origin);
   if (!Contains(origin)) {
      Error("GetFittingBox", "wrong matrix - parametrized box is outside this");
      return 1; // ### wrong matrix ###
   }
   //--> now we have to get the valid range for all parametrized axis
   Double_t dd[3];
   dd[0] = parambox->GetDX();
   dd[1] = parambox->GetDY();
   dd[2] = parambox->GetDZ();
   //-> check if Z range is fixed
   if (dd[2] < 0) {
      dd[2] = TMath::Min(origin[2] + fZ, fZ - origin[2]);
      if (dd[2] < 0) {
         Error("GetFittingBox", "wrong matrix");
         return 1;
      }
   }
   if (dd[0] >= 0 && dd[1] >= 0) {
      dx = dd[0];
      dy = dd[1];
      dz = dd[2];
      return 0;
   }
   //-> check now range at Z = origin[2] +/- dd[2]
   Double_t upper[8];
   Double_t lower[8];
   Double_t z = origin[2] - dd[2];
   lower[0] = z * fTxz - fTxy * fY - fX;
   lower[1] = -fY + z * fTyz;
   lower[2] = z * fTxz + fTxy * fY - fX;
   lower[3] = fY + z * fTyz;
   lower[4] = z * fTxz + fTxy * fY + fX;
   lower[5] = fY + z * fTyz;
   lower[6] = z * fTxz - fTxy * fY + fX;
   lower[7] = -fY + z * fTyz;
   z = origin[2] + dd[2];
   upper[0] = z * fTxz - fTxy * fY - fX;
   upper[1] = -fY + z * fTyz;
   upper[2] = z * fTxz + fTxy * fY - fX;
   upper[3] = fY + z * fTyz;
   upper[4] = z * fTxz + fTxy * fY + fX;
   upper[5] = fY + z * fTyz;
   upper[6] = z * fTxz - fTxy * fY + fX;
   upper[7] = -fY + z * fTyz;
 
   for (Int_t iaxis = 0; iaxis < 2; iaxis++) {
      if (dd[iaxis] >= 0)
         continue;
      Double_t ddmin = TGeoShape::Big();
      for (Int_t ivert = 0; ivert < 4; ivert++) {
         ddmin = TMath::Min(ddmin, TMath::Abs(origin[iaxis] - lower[2 * ivert + iaxis]));
         ddmin = TMath::Min(ddmin, TMath::Abs(origin[iaxis] - upper[2 * ivert + iaxis]));
      }
      dd[iaxis] = ddmin;
   }
   dx = dd[0];
   dy = dd[1];
   dz = dd[2];
   return 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// in case shape has some negative parameters, these has to be computed
/// in order to fit the mother
 
TGeoShape *TGeoPara::GetMakeRuntimeShape(TGeoShape *mother, TGeoMatrix * /*mat*/) const
{
   if (!TestShapeBit(kGeoRunTimeShape))
      return nullptr;
   if (!mother->TestShapeBit(kGeoPara)) {
      Error("GetMakeRuntimeShape", "invalid mother");
      return nullptr;
   }
   Double_t dx, dy, dz;
   if (fX < 0)
      dx = ((TGeoPara *)mother)->GetX();
   else
      dx = fX;
   if (fY < 0)
      dy = ((TGeoPara *)mother)->GetY();
   else
      dy = fY;
   if (fZ < 0)
      dz = ((TGeoPara *)mother)->GetZ();
   else
      dz = fZ;
   return (new TGeoPara(dx, dy, dz, fAlpha, fTheta, fPhi));
}
 
////////////////////////////////////////////////////////////////////////////////
/// print shape parameters
 
void TGeoPara::InspectShape() const
{
   printf("*** Shape %s: TGeoPara ***\n", GetName());
   printf("    dX = %11.5f\n", fX);
   printf("    dY = %11.5f\n", fY);
   printf("    dZ = %11.5f\n", fZ);
   printf("    alpha = %11.5f\n", fAlpha);
   printf("    theta = %11.5f\n", fTheta);
   printf("    phi   = %11.5f\n", fPhi);
   printf(" Bounding box:\n");
   TGeoBBox::InspectShape();
}
 
////////////////////////////////////////////////////////////////////////////////
/// computes the closest distance from given point to this shape, according
/// to option. The matching point on the shape is stored in spoint.
 
Double_t TGeoPara::Safety(const Double_t *point, Bool_t in) const
{
   Double_t saf[3];
   // distance from point to higher Z face
   saf[0] = fZ - TMath::Abs(point[2]); // Z
 
   Double_t yt = point[1] - fTyz * point[2];
   saf[1] = fY - TMath::Abs(yt); // Y
   // cos of angle YZ
   Double_t cty = 1.0 / TMath::Sqrt(1.0 + fTyz * fTyz);
 
   Double_t xt = point[0] - fTxz * point[2] - fTxy * yt;
   saf[2] = fX - TMath::Abs(xt); // X
   // cos of angle XZ
   Double_t ctx = 1.0 / TMath::Sqrt(1.0 + fTxy * fTxy + fTxz * fTxz);
   saf[2] *= ctx;
   saf[1] *= cty;
   if (in)
      return saf[TMath::LocMin(3, saf)];
   for (Int_t i = 0; i < 3; i++)
      saf[i] = -saf[i];
   return saf[TMath::LocMax(3, saf)];
}
 
////////////////////////////////////////////////////////////////////////////////
/// Save a primitive as a C++ statement(s) on output stream "out".
 
void TGeoPara::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
{
   if (TObject::TestBit(kGeoSavePrimitive))
      return;
   out << "   // Shape: " << GetName() << " type: " << ClassName() << std::endl;
   out << "   dx    = " << fX << ";" << std::endl;
   out << "   dy    = " << fY << ";" << std::endl;
   out << "   dz    = " << fZ << ";" << std::endl;
   out << "   alpha = " << fAlpha << ";" << std::endl;
   out << "   theta = " << fTheta << ";" << std::endl;
   out << "   phi   = " << fPhi << ";" << std::endl;
   out << "   TGeoShape *" << GetPointerName() << " = new TGeoPara(\"" << GetName() << "\",dx,dy,dz,alpha,theta,phi);"
       << std::endl;
   TObject::SetBit(TGeoShape::kGeoSavePrimitive);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set dimensions starting from an array.
 
void TGeoPara::SetDimensions(Double_t *param)
{
   fX = param[0];
   fY = param[1];
   fZ = param[2];
   fAlpha = param[3];
   fTheta = param[4];
   fPhi = param[5];
   fTxy = TMath::Tan(param[3] * TMath::DegToRad());
   Double_t tth = TMath::Tan(param[4] * TMath::DegToRad());
   Double_t ph = param[5] * TMath::DegToRad();
   fTxz = tth * TMath::Cos(ph);
   fTyz = tth * TMath::Sin(ph);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create PARA mesh points
 
void TGeoPara::SetPoints(Double_t *points) const
{
   if (!points)
      return;
   Double_t txy = fTxy;
   Double_t txz = fTxz;
   Double_t tyz = fTyz;
   *points++ = -fZ * txz - txy * fY - fX;
   *points++ = -fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = -fZ * txz + txy * fY - fX;
   *points++ = +fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = -fZ * txz + txy * fY + fX;
   *points++ = +fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = -fZ * txz - txy * fY + fX;
   *points++ = -fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = +fZ * txz - txy * fY - fX;
   *points++ = -fY + fZ * tyz;
   *points++ = +fZ;
   *points++ = +fZ * txz + txy * fY - fX;
   *points++ = +fY + fZ * tyz;
   *points++ = +fZ;
   *points++ = +fZ * txz + txy * fY + fX;
   *points++ = +fY + fZ * tyz;
   *points++ = +fZ;
   *points++ = +fZ * txz - txy * fY + fX;
   *points++ = -fY + fZ * tyz;
   *points++ = +fZ;
}
 
////////////////////////////////////////////////////////////////////////////////
/// create sphere mesh points
 
void TGeoPara::SetPoints(Float_t *points) const
{
   if (!points)
      return;
   Double_t txy = fTxy;
   Double_t txz = fTxz;
   Double_t tyz = fTyz;
   *points++ = -fZ * txz - txy * fY - fX;
   *points++ = -fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = -fZ * txz + txy * fY - fX;
   *points++ = +fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = -fZ * txz + txy * fY + fX;
   *points++ = +fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = -fZ * txz - txy * fY + fX;
   *points++ = -fY - fZ * tyz;
   *points++ = -fZ;
   *points++ = +fZ * txz - txy * fY - fX;
   *points++ = -fY + fZ * tyz;
   *points++ = +fZ;
   *points++ = +fZ * txz + txy * fY - fX;
   *points++ = +fY + fZ * tyz;
   *points++ = +fZ;
   *points++ = +fZ * txz + txy * fY + fX;
   *points++ = +fY + fZ * tyz;
   *points++ = +fZ;
   *points++ = +fZ * txz - txy * fY + fX;
   *points++ = -fY + fZ * tyz;
   *points++ = +fZ;
}
 
////////////////////////////////////////////////////////////////////////////////
/// fill size of this 3-D object
 
void TGeoPara::Sizeof3D() const
{
   TGeoBBox::Sizeof3D();
}
 
////////////////////////////////////////////////////////////////////////////////
/// 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 TGeoPara::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 TGeoPara::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 TGeoPara::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 TGeoPara::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 TGeoPara::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]);
}