UTrd.cc

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//
// ********************************************************************
// * This Software is part of the AIDA Unified Solids Library package *
// * See: https://aidasoft.web.cern.ch/USolids                        *
// ********************************************************************
//
// $Id:$
//
// --------------------------------------------------------------------
//
// UTrd
//
// 19.10.12 Marek Gayer
//          Created from original implementation in Geant4
// --------------------------------------------------------------------

#include <iostream>
#include <cmath>

#include "UTrd.hh"
#include "UUtils.hh"

//dx1   Half-length along x at the surface positioned at -dz
//dx2   Half-length along x at the surface positioned at +dz
//dy1   Half-length along y at the surface positioned at -dz
//dy2   Half-length along y at the surface positioned at +dz
//dz  Half-length along z axis
//______________________________________________________________________________
UTrd::UTrd(const std::string& pName,
           double pdx1, double pdx2,
           double pdy1, double pdy2,
           double pdz)
  : VUSolid(pName), fCubicVolume(0), fSurfaceArea(0)
{
  CheckAndSetAllParameters (pdx1, pdx2, pdy1, pdy2, pdz);
}

void UTrd::CheckAndSetAllParameters ( double pdx1,  double pdx2,
                                      double pdy1,  double pdy2,
                                      double pdz ) 
{
  if (pdx1 > 0 && pdx2 > 0 && pdy1 > 0 && pdy2 > 0 && pdz > 0)
  {
    fDx1 = pdx1;
    fDx2 = pdx2;
    fDy1 = pdy1;
    fDy2 = pdy2;
    fDz = pdz;
  }
  else
  {
    if (pdx1 >= 0 && pdx2 >= 0 && pdy1 >= 0 && pdy2 >= 0 && pdz >= 0)
    {
      // double  Minimum_length= (1+per_thousand) * VUSolid::fgTolerance/2.;
      // FIX-ME : temporary solution for ZERO or very-small parameters
      //
      double  Minimum_length = fgTolerance;
      fDx1 = std::max(pdx1, Minimum_length);
      fDx2 = std::max(pdx2, Minimum_length);
      fDy1 = std::max(pdy1, Minimum_length);
      fDy2 = std::max(pdy2, Minimum_length);
      fDz = std::max(pdz, Minimum_length);
    }
    else
    {
      std::cout << "ERROR - UTrd()::CheckAndSetAllParameters(): " << GetName()
                << std::endl
                << "        Invalid dimensions, some are < 0 !" << std::endl
                << "          X - " << pdx1 << ", " << pdx2 << std::endl
                << "          Y - " << pdy1 << ", " << pdy2 << std::endl
                << "          Z - " << pdz << std::endl;
      UUtils::Exception("UTrd::CheckAndSetAllParameters()", "InvalidSetup", FatalErrorInArguments, 1, "Invalid parameters.");
    }
  }
}

void UTrd::SetAllParameters ( double pdx1, double pdx2, double pdy1, 
                              double pdy2, double pdz ) 
{
  CheckAndSetAllParameters (pdx1, pdx2, pdy1, pdy2, pdz);
}

double UTrd::SafetyFromInside(const UVector3& p, bool aAccurate) const
{
  if (aAccurate) return SafetyFromInsideAccurate(p);

  double safe, zbase, tanxz, xdist, saf1, tanyz, ydist, saf2;

#ifdef UDEBUG
  if (Inside(p) == kOutside)
  {
    int oldprc = std::cout.precision(16) ;
    std::cout << std::endl ;
    DumpInfo();
    std::cout << "Position:"  << std::endl << std::endl ;
    std::cout << "p.x() = "   << p.x() / mm << " mm" << std::endl ;
    std::cout << "p.y() = "   << p.y() / mm << " mm" << std::endl ;
    std::cout << "p.z() = "   << p.z() / mm << " mm" << std::endl << std::endl ;
    std::cout.precision(oldprc) ;
    UUtils::Exception("G4Trd::DistanceToOut(p)", "Notification", Warning, 1,
                      "Point p is outside !?");
  }
#endif

  safe = fDz - std::fabs(p.z); // z perpendicular Dist

  zbase = fDz + p.z;

  // xdist = distance perpendicular to z axis to closest x plane from p
  //       = (x half width of shape at p.z) - std::abs(p.x)
  //
  tanxz = (fDx2 - fDx1) * 0.5 / fDz; // angle between two parts on trinngle, which reflects proportional part on triangle related to position of point, see it on picture
  xdist = fDx1 + tanxz * zbase - std::fabs(p.x); // distance to closest point on x border on x-axis on which point is located to
  saf1 = xdist / std::sqrt(1.0 + tanxz * tanxz); // x*std::cos(ang_xz) =
  // shortest (perpendicular)
  // distance to plane, see picture
  tanyz = (fDy2 - fDy1) * 0.5 / fDz;
  ydist = fDy1 + tanyz * zbase - std::fabs(p.y);
  saf2 = ydist / std::sqrt(1.0 + tanyz * tanyz);

  // Return minimum x/y/z distance
  //
  if (safe > saf1) safe = saf1;
  if (safe > saf2) safe = saf2;

  if (safe < 0) safe = 0;
  return safe;
}



inline double UTrd::SafetyFromInsideAccurate(const UVector3& p) const
{
  // computes the closest distance from given point to this shape, according
  // to option. The matching point on the shape is stored in spoint.

  double saf[3];
  //--- Compute safety first
  // check Z facettes
  saf[0] = fDz - std::abs(p.z);
  double fx = 0.5 * (fDx1 - fDx2) / fDz;
  double calf = 1. / std::sqrt(1.0 + fx * fx);
  // check X facettes
  double distx = 0.5 * (fDx1 + fDx2) - fx * p.z;
  if (distx < 0) saf[1] = UUtils::kInfinity;
  else         saf[1] = (distx - std::abs(p.x)) * calf;

  double fy = 0.5 * (fDy1 - fDy2) / fDz;
  calf = 1. / std::sqrt(1.0 + fy * fy);
  // check Y facettes
  distx = 0.5 * (fDy1 + fDy2) - fy * p.z;
  if (distx < 0) saf[2] = UUtils::kInfinity;
  else         saf[2] = (distx - std::abs(p.y)) * calf;

  return amin(3, saf);
}

/*
* Estimates the isotropic safety from a point outside the current solid to any
* of its surfaces. The algorithm may be accurate or should provide a fast
* underestimate.
* Note: In geant4, this method is equivalent to DistanceToIn, without given direction
* ______________________________________________________________________________
*
* Calculate distance (<= actual) to closest surface of shape from outside
* - Calculate distance to radial plane
* - Return 0 if point inside
* OK
*/
double UTrd::SafetyFromOutside(const UVector3& p, bool aAccurate) const
{
  if (aAccurate) return SafetyFromOutsideAccurate(p);

  double safe = 0.0;
  double tanxz, distx, safx;
  double tanyz, disty, safy;
  double zbase;

  safe = std::abs(p.z) - fDz;
  if (safe < 0) safe = 0;  // Also used to ensure x/y distances
  // POSITIVE
  zbase = fDz + p.z;

  // Find distance along x direction to closest x plane
  //
  tanxz = (fDx2 - fDx1) * 0.5 / fDz;
  //    widx=fDx1+tanxz*(fDz+p.z()); // x width at p.z
  //    distx=std::abs(p.x())-widx;      // distance to plane
  distx = std::abs(p.x) - (fDx1 + tanxz * zbase); // distance to point on border of trd, related to axis on which point p lies
  if (distx > safe)
  {
    safx = distx / std::sqrt(1.0 + tanxz * tanxz); // perpendicular distance calculation; vector Dist=Dist*std::cos(ang), it can be probably negative, then comparing in next statement, we will get rid of such distance, because it directs away from the solid
    if (safx > safe) safe = safx;
  }

  // Find distance along y direction to slanted wall
  tanyz = (fDy2 - fDy1) * 0.5 / fDz;
  //    widy=fDy1+tanyz*(fDz+p.z()); // y width at p.z
  //    disty=std::abs(p.y())-widy;      // distance to plane
  disty = std::abs(p.y) - (fDy1 + tanyz * zbase);
  if (disty > safe)
  {
    safy = disty / std::sqrt(1.0 + tanyz * tanyz); // distance along vector
    if (safy > safe) safe = safy;
  }
  return safe;
}

inline double UTrd::SafetyFromOutsideAccurate(const UVector3& p) const
{
  // computes the closest distance from given point to this shape, according
  // to option. The matching point on the shape is stored in spoint.

  double saf[3];
  //--- Compute safety first
  // check Z facettes
  saf[0] = fDz - std::abs(p.z);
  double fx = 0.5 * (fDx1 - fDx2) / fDz;
  double calf = 1. / std::sqrt(1.0 + fx * fx);
  // check X facettes
  double distx = 0.5 * (fDx1 + fDx2) - fx * p.z;
  if (distx < 0) saf[1] = UUtils::kInfinity;
  else         saf[1] = (distx - std::abs(p.x)) * calf;

  double fy = 0.5 * (fDy1 - fDy2) / fDz;
  calf = 1. / std::sqrt(1.0 + fy * fy);
  // check Y facettes
  distx = 0.5 * (fDy1 + fDy2) - fy * p.z;
  if (distx < 0) saf[2] = UUtils::kInfinity;
  else         saf[2] = (distx - std::abs(p.y)) * calf;

  for (int i = 0; i < 3; i++) saf[i] = -saf[i];
  return amax(3, saf);
}

//______________________________________________________________________________
/**
*
* Return whether point inside/outside/on surface
* Split into radius checks
*
* Classify point location with respect to solid:
*  o eInside       - inside the solid
*  o eSurface      - close to surface within tolerance
*  o eOutside      - outside the solid
*/
// ok
// Geant4 routine was selected because:
// 1. it is able to detect if the point is on surface
// 2. it counts with tolerance
// 3. algorithm checks are similar:
// Geant4: x=0.5*(fDx2*zbase1+fDx1*zbase2)/fDz - fgTolerance/2;
// Root: double dx = 0.5*(fDx2*(point.z+fDz)+fDx1*(fDz-point.z))/fDz;
//
VUSolid::EnumInside UTrd::Inside(const UVector3& p) const
{
  VUSolid::EnumInside in = eOutside;
  double x, y, zbase1, zbase2;

  if (std::abs(p.z) <= fDz - fgTolerance / 2)
  {
    zbase1 = p.z + fDz; // Dist from -ve z plane
    zbase2 = fDz - p.z; // Dist from +ve z plane

    // Check whether inside x tolerance
    //
    x = 0.5 * (fDx2 * zbase1 + fDx1 * zbase2) / fDz - fgTolerance / 2; // calculate x coordinate of one corner point corresponding to p.z inside trd (on x axis), ... by using proportional calculation related to triangle
    if (std::abs(p.x) <= x)
    {
      y = 0.5 * ((fDy2 * zbase1 + fDy1 * zbase2)) / fDz - fgTolerance / 2;
      if (std::abs(p.y) <= y)
      {
        in = eInside;
      }
      else if (std::abs(p.y) <= y + fgTolerance)
      {
        in = eSurface;
      }
    }
    else if (std::abs(p.x) <= x + fgTolerance)
    {
      // y = y half width of shape at z of point + tolerant boundary
      //
      y = 0.5 * ((fDy2 * zbase1 + fDy1 * zbase2)) / fDz + fgTolerance / 2;
      if (std::abs(p.y) <= y)
      {
        in = eSurface;
      }
    }
  }
  else if (std::abs(p.z) <= fDz + fgTolerance / 2)
  {
    // Only need to check outer tolerant boundaries
    //
    zbase1 = p.z + fDz; // Dist from -ve z plane
    zbase2 = fDz - p.z; // Dist from +ve z plane

    // x = x half width of shape at z of point plus tolerance
    //
    x = 0.5 * (fDx2 * zbase1 + fDx1 * zbase2) / fDz + fgTolerance / 2;
    if (std::abs(p.x) <= x)
    {
      // y = y half width of shape at z of point
      //
      y = 0.5 * ((fDy2 * zbase1 + fDy1 * zbase2)) / fDz + fgTolerance / 2;
      if (std::abs(p.y) <= y) in = eSurface;
    }
  }
  return in;
}


/*
* Computes distance from a point presumably outside the solid to the solid
* surface. Ignores first surface if the point is actually inside. Early return
* infinity in case the safety to any surface is found greater than the proposed
* step aPstep.
* The normal vector to the crossed surface is filled only in case the Orb is
* crossed, otherwise aNormal.IsNull() is true.
*/
double UTrd::DistanceToIn(const UVector3& p,
                          const UVector3& v,
                          //                          UVector3 &aNormal,
                          double) const
{
  double snxt = UUtils::kInfinity;    // snxt = default return value
  double smin, smax;
  double s1, s2, tanxz, tanyz, ds1, ds2;
  double ss1, ss2, sn1 = 0., sn2 = 0., dist;

  if (v.z)    // Calculate valid z intersect range
  {
    if (v.z > 0)     // Calculate smax: must be +ve or no intersection.
    {
      dist = fDz - p.z ;  // to plane at +dz

      if (dist >= 0.5 * VUSolid::fgTolerance)
      {
        smax = dist / v.z; // distance to intersection with +dz, maximum
        smin = -(fDz + p.z) / v.z; // distance to intersection with +dz, minimum
      }
      else  return snxt ;
    }
    else // v.z <0
    {
      dist = fDz + p.z; // plane at -dz

      if (dist >= 0.5 * VUSolid::fgTolerance)
      {
        smax = -dist / v.z;
        smin = (fDz - p.z) / v.z;
      }
      else return snxt ;
    }
    if (smin < 0) smin = 0 ;
  }
  else // v.z=0
  {
    if (std::abs(p.z) >= fDz) return snxt ;      // Outside & no intersect
    else
    {
      smin = 0 ;    // Always inside z range
      smax = UUtils::kInfinity;
    }
  }

  // Calculate x intersection range
  //
  // Calc half width at p.z, and components towards planes

  tanxz = (fDx2 - fDx1) * 0.5 / fDz ;
  s1    = 0.5 * (fDx1 + fDx2) + tanxz * p.z ; // x half width at p.z
  ds1   = v.x - tanxz * v.z ;     // Components of v towards faces at +-x
  ds2   = v.x + tanxz * v.z ;
  ss1   = s1 - p.x;         // -delta x to +ve plane
  // -ve when outside
  ss2   = -s1 - p.x;        // -delta x to -ve plane
  // +ve when outside
  if (ss1 < 0 && ss2 <= 0)
  {
    if (ds1 < 0)   // In +ve coord Area
    {
      sn1 = ss1 / ds1 ;

      if (ds2 < 0) sn2 = ss2 / ds2 ;
      else           sn2 = UUtils::kInfinity ;
    }
    else return snxt ;
  }
  else if (ss1 >= 0 && ss2 > 0)
  {
    if (ds2 > 0)    // In -ve coord Area
    {
      sn1 = ss2 / ds2 ;

      if (ds1 > 0)  sn2 = ss1 / ds1 ;
      else          sn2 = UUtils::kInfinity;

    }
    else   return snxt ;
  }
  else if (ss1 >= 0 && ss2 <= 0)
  {
    // Inside Area - calculate leaving distance
    // *Don't* use exact distance to side for tolerance
    //                                             = ss1*std::cos(ang xz)
    //                                             = ss1/std::sqrt(1.0+tanxz*tanxz)
    sn1 = 0 ;

    if (ds1 > 0)
    {
      if (ss1 > 0.5 * VUSolid::fgTolerance) sn2 = ss1 / ds1 ; // Leave +ve side extent
      else                         return snxt ;   // Leave immediately by +ve
    }
    else  sn2 = UUtils::kInfinity ;

    if (ds2 < 0)
    {
      if (ss2 < -0.5 * VUSolid::fgTolerance)
      {
        dist = ss2 / ds2 ;          // Leave -ve side extent
        if (dist < sn2) sn2 = dist ;
      }
      else return snxt ;
    }
  }
  else if (ss1 < 0 && ss2 > 0)
  {
    // Within +/- plane cross-over areas (not on boundaries ss1||ss2==0)

    if (ds1 >= 0 || ds2 <= 0)
    {
      return snxt ;
    }
    else  // Will intersect & stay inside
    {
      sn1  = ss1 / ds1 ;
      dist = ss2 / ds2 ;
      if (dist > sn1) sn1 = dist ;
      sn2 = UUtils::kInfinity ;
    }
  }

  // Reduce allowed range of distances as appropriate

  if (sn1 > smin) smin = sn1 ;
  if (sn2 < smax) smax = sn2 ;

  // Check for incompatible ranges (eg z intersects between 50 ->100 and x
  // only 10-40 -> no intersection)

  if (smax < smin) return snxt ;

  // Calculate valid y intersection range
  // (repeat of x intersection code)

  tanyz = (fDy2 - fDy1) * 0.5 / fDz ;
  s2    = 0.5 * (fDy1 + fDy2) + tanyz * p.z; // y half width at p.z
  ds1   = v.y - tanyz * v.z;     // Components of v towards faces at +-y
  ds2   = v.y + tanyz * v.z;
  ss1   = s2 - p.y;         // -delta y to +ve plane
  ss2   = -s2 - p.y;        // -delta y to -ve plane

  if (ss1 < 0 && ss2 <= 0)
  {
    if (ds1 < 0)  // In +ve coord Area
    {
      sn1 = ss1 / ds1 ;
      if (ds2 < 0)  sn2 = ss2 / ds2 ;
      else            sn2 = UUtils::kInfinity ;
    }
    else   return snxt ;
  }
  else if (ss1 >= 0 && ss2 > 0)
  {
    if (ds2 > 0)    // In -ve coord Area
    {
      sn1 = ss2 / ds2 ;
      if (ds1 > 0)  sn2 = ss1 / ds1 ;
      else            sn2 = UUtils::kInfinity ;
    }
    else   return snxt ;
  }
  else if (ss1 >= 0 && ss2 <= 0)
  {
    // Inside Area - calculate leaving distance
    // *Don't* use exact distance to side for tolerance
    //                                          = ss1*std::cos(ang yz)
    //                                          = ss1/std::sqrt(1.0+tanyz*tanyz)
    sn1 = 0 ;

    if (ds1 > 0)
    {
      if (ss1 > 0.5 * VUSolid::fgTolerance) sn2 = ss1 / ds1 ; // Leave +ve side extent
      else                         return snxt ;   // Leave immediately by +ve
    }
    else  sn2 = UUtils::kInfinity ;

    if (ds2 < 0)
    {
      if (ss2 < -0.5 * VUSolid::fgTolerance)
      {
        dist = ss2 / ds2 ; // Leave -ve side extent
        if (dist < sn2) sn2 = dist;
      }
      else return snxt ;
    }
  }
  else if (ss1 < 0 && ss2 > 0)
  {
    // Within +/- plane cross-over areas (not on boundaries ss1||ss2==0)

    if (ds1 >= 0 || ds2 <= 0)
    {
      return snxt ;
    }
    else  // Will intersect & stay inside
    {
      sn1 = ss1 / ds1 ;
      dist = ss2 / ds2 ;
      if (dist > sn1) sn1 = dist ;
      sn2 = UUtils::kInfinity ;
    }
  }

  // Reduce allowed range of distances as appropriate

  if (sn1 > smin) smin = sn1 ;
  if (sn2 < smax) smax = sn2 ;

  // Check for incompatible ranges (eg x intersects between 50 ->100 and y
  // only 10-40 -> no intersection). Set snxt if ok

  if (smax > smin) snxt = smin ;
  if (snxt < 0.5 * VUSolid::fgTolerance) snxt = 0.0 ;

  return snxt ;
}



//_____________________________________________________________________________

/*
* Computes distance from a point presumably intside the solid to the solid
* surface. Ignores first surface along each axis systematically (for points
* inside or outside. Early returns zero in case the second surface is behind
* the starting point.
* o The proposed step is ignored.
* o The normal vector to the crossed surface is always filled.
* ______________________________________________________________________________
*/


inline double UTrd::DistanceToOut(const UVector3&  p, const UVector3& v,
                                  UVector3& n, bool& aConvex, double /*aPstep*/) const
{
  ESide side = kUndefined, snside = kUndefined;
  aConvex = true;
  double snxt, pdist;
  double central, ss1, ss2, ds1, ds2, sn = 0., sn2 = 0.;
  double tanxz = 0., cosxz = 0., tanyz = 0., cosyz = 0.;

  // Calculate z plane intersection
  if (v.z > 0)
  {
    pdist = fDz - p.z;
    if (pdist > VUSolid::fgTolerance / 2)
    {
      snxt = pdist / v.z;
      side = kPZ;
    }
    else
    {
      n = UVector3(0, 0, 1);
      return snxt = 0;
    }
  }
  else if (v.z < 0)
  {
    pdist = fDz + p.z;
    if (pdist > VUSolid::fgTolerance / 2)
    {
      snxt = -pdist / v.z;
      side = kMZ;
    }
    else
    {
      //      if (calcNorm)
      {
        n = UVector3(0, 0, -1);
      }
      return snxt = 0;
    }
  }
  else
  {
    snxt = UUtils::kInfinity;
  }

  //
  // Calculate x intersection
  //
  tanxz = (fDx2 - fDx1) * 0.5 / fDz;
  central = 0.5 * (fDx1 + fDx2);

  // +ve plane (1)
  //
  ss1 = central + tanxz * p.z - p.x; // distance || x axis to plane
  // (+ve if point inside)
  ds1 = v.x - tanxz * v.z; // component towards plane at +x
  // (-ve if +ve -> -ve direction)
  // -ve plane (2)
  //
  ss2 = -tanxz * p.z - p.x - central; //distance || x axis to plane
  // (-ve if point inside)
  ds2 = tanxz * v.z + v.x; // component towards plane at -x

  if (ss1 > 0 && ss2 < 0)
  {
    // Normal case - entirely inside region
    if (ds1 <= 0 && ds2 < 0)
    {
      if (ss2 < -VUSolid::fgTolerance / 2)
      {
        sn = ss2 / ds2; // Leave by -ve side
        snside = kMX;
      }
      else
      {
        sn = 0; // Leave immediately by -ve side
        snside = kMX;
      }
    }
    else if (ds1 > 0 && ds2 >= 0)
    {
      if (ss1 > VUSolid::fgTolerance / 2)
      {
        sn = ss1 / ds1; // Leave by +ve side
        snside = kPX;
      }
      else
      {
        sn = 0; // Leave immediately by +ve side
        snside = kPX;
      }
    }
    else if (ds1 > 0 && ds2 < 0)
    {
      if (ss1 > VUSolid::fgTolerance / 2)
      {
        // sn=ss1/ds1;  // Leave by +ve side
        if (ss2 < -VUSolid::fgTolerance / 2)
        {
          sn = ss1 / ds1; // Leave by +ve side
          sn2 = ss2 / ds2;
          if (sn2 < sn)
          {
            sn = sn2;
            snside = kMX;
          }
          else
          {
            snside = kPX;
          }
        }
        else
        {
          sn = 0; // Leave immediately by -ve
          snside = kMX;
        }
      }
      else
      {
        sn = 0; // Leave immediately by +ve side
        snside = kPX;
      }
    }
    else
    {
      // Must be || to both
      //
      sn = UUtils::kInfinity;  // Don't leave by either side
    }
  }
  else if (ss1 <= 0 && ss2 < 0)
  {
    // Outside, in +ve Area

    if (ds1 > 0)
    {
      sn = 0;     // Away from shape
      // Left by +ve side
      snside = kPX;
    }
    else
    {
      if (ds2 < 0)
      {
        // Ignore +ve plane and use -ve plane intersect
        //
        sn = ss2 / ds2; // Leave by -ve side
        snside = kMX;
      }
      else
      {
        // Must be || to both -> exit determined by other axes
        //
        sn = UUtils::kInfinity; // Don't leave by either side
      }
    }
  }
  else if (ss1 > 0 && ss2 >= 0)
  {
    // Outside, in -ve Area

    if (ds2 < 0)
    {
      sn = 0;     // away from shape
      // Left by -ve side
      snside = kMX;
    }
    else
    {
      if (ds1 > 0)
      {
        // Ignore +ve plane and use -ve plane intersect
        //
        sn = ss1 / ds1; // Leave by +ve side
        snside = kPX;
      }
      else
      {
        // Must be || to both -> exit determined by other axes
        //
        sn = UUtils::kInfinity; // Don't leave by either side
      }
    }
  }

  // Update minimum exit distance

  if (sn < snxt)
  {
    snxt = sn;
    side = snside;
  }
  if (snxt > 0)
  {
    // Calculate y intersection
    tanyz = (fDy2 - fDy1) * 0.5 / fDz;
    central = 0.5 * (fDy1 + fDy2);

    // +ve plane (1)
    //
    ss1 = central + tanyz * p.z - p.y; // distance || y axis to plane
    // (+ve if point inside)
    ds1 = v.y - tanyz * v.z; // component towards +ve plane
    // (-ve if +ve -> -ve direction)
    // -ve plane (2)
    //
    ss2 = -tanyz * p.z - p.y - central; // distance || y axis to plane
    // (-ve if point inside)
    ds2 = tanyz * v.z + v.y; // component towards -ve plane

    if (ss1 > 0 && ss2 < 0)
    {
      // Normal case - entirely inside region

      if (ds1 <= 0 && ds2 < 0)
      {
        if (ss2 < -VUSolid::fgTolerance / 2)
        {
          sn = ss2 / ds2; // Leave by -ve side
          snside = kMY;
        }
        else
        {
          sn = 0; // Leave immediately by -ve side
          snside = kMY;
        }
      }
      else if (ds1 > 0 && ds2 >= 0)
      {
        if (ss1 > VUSolid::fgTolerance / 2)
        {
          sn = ss1 / ds1; // Leave by +ve side
          snside = kPY;
        }
        else
        {
          sn = 0; // Leave immediately by +ve side
          snside = kPY;
        }
      }
      else if (ds1 > 0 && ds2 < 0)
      {
        if (ss1 > VUSolid::fgTolerance / 2)
        {
          // sn=ss1/ds1;  // Leave by +ve side
          if (ss2 < -VUSolid::fgTolerance / 2)
          {
            sn = ss1 / ds1; // Leave by +ve side
            sn2 = ss2 / ds2;
            if (sn2 < sn)
            {
              sn = sn2;
              snside = kMY;
            }
            else
            {
              snside = kPY;
            }
          }
          else
          {
            sn = 0; // Leave immediately by -ve
            snside = kMY;
          }
        }
        else
        {
          sn = 0; // Leave immediately by +ve side
          snside = kPY;
        }
      }
      else
      {
        // Must be || to both
        //
        sn = UUtils::kInfinity;  // Don't leave by either side
      }
    }
    else if (ss1 <= 0 && ss2 < 0)
    {
      // Outside, in +ve Area

      if (ds1 > 0)
      {
        sn = 0;     // Away from shape
        // Left by +ve side
        snside = kPY;
      }
      else
      {
        if (ds2 < 0)
        {
          // Ignore +ve plane and use -ve plane intersect
          //
          sn = ss2 / ds2; // Leave by -ve side
          snside = kMY;
        }
        else
        {
          // Must be || to both -> exit determined by other axes
          //
          sn = UUtils::kInfinity; // Don't leave by either side
        }
      }
    }
    else if (ss1 > 0 && ss2 >= 0)
    {
      // Outside, in -ve Area
      if (ds2 < 0)
      {
        sn = 0;     // away from shape
        // Left by -ve side
        snside = kMY;
      }
      else
      {
        if (ds1 > 0)
        {
          // Ignore +ve plane and use -ve plane intersect
          //
          sn = ss1 / ds1; // Leave by +ve side
          snside = kPY;
        }
        else
        {
          // Must be || to both -> exit determined by other axes
          //
          sn = UUtils::kInfinity; // Don't leave by either side
        }
      }
    }

    // Update minimum exit distance

    if (sn < snxt)
    {
      snxt = sn;
      side = snside;
    }
  }

  {
    switch (side)
    {
      case kPX:
        cosxz = 1.0 / std::sqrt(1.0 + tanxz * tanxz);
        n.Set(cosxz, 0, -tanxz * cosxz);
        break;
      case kMX:
        cosxz = -1.0 / std::sqrt(1.0 + tanxz * tanxz);
        n.Set(cosxz, 0, tanxz * cosxz);
        break;
      case kPY:
        cosyz = 1.0 / std::sqrt(1.0 + tanyz * tanyz);
        n.Set(0, cosyz, -tanyz * cosyz);
        break;
      case kMY:
        cosyz = -1.0 / std::sqrt(1.0 + tanyz * tanyz);
        n.Set(0, cosyz, tanyz * cosyz);
        break;
      case kPZ:
        n.Set(0, 0, 1);
        break;
      case kMZ:
        n.Set(0, 0, -1);
        break;
      default:
        UUtils::Exception("G4Trd::DistanceToOut(p,v,..)", "Notification", Warning, 1, "Undefined side for valid surface normal to solid.");
        break;
    }
  }

  return snxt;
}


bool UTrd::Normal(const UVector3& p, UVector3& norm) const
{
  UVector3 sumnorm(0., 0., 0.);
  int noSurfaces = 0;
  double z = 2.0 * fDz;
  double delta = 0.5 * fgTolerance;

  double tanx  = (fDx2 - fDx1) / z;
  double secx  = std::sqrt(1.0 + tanx * tanx);
  double newpx = std::abs(p.x) - p.z * tanx;
  double widx  = fDx2 - fDz * tanx;

  double tany  = (fDy2 - fDy1) / z;
  double secy  = std::sqrt(1.0 + tany * tany);
  double newpy = std::abs(p.y) - p.z * tany;
  double widy  = fDy2 - fDz * tany;

  double distx = std::abs(newpx - widx) / secx;   // perp. distance to x side
  double disty = std::abs(newpy - widy) / secy;   //                to y side
  double distz = std::abs(std::abs(p.z) - fDz); //                to z side

  if (distx <= delta) // we are near the x corner?
  {
    double fcos = 1.0 / secx;
    noSurfaces ++;
    if (p.x >= 0.) sumnorm.x += fcos;
    else sumnorm.x -= fcos;
    sumnorm.z -= tanx * fcos;
  }
  if (disty <= delta) // y corner ...
  {
    double fcos = 1.0 / secy;
    noSurfaces++;
    if (p.y >= 0.) sumnorm.y += fcos;
    else sumnorm.y -= fcos;
    sumnorm.z -= tany * fcos;
  }
  if (distz <= delta)
  {
    noSurfaces++;
    sumnorm.z += (p.z >= 0.) ? 1.0 : -1.0;
  }
  if (noSurfaces == 0)
  {
#ifdef UDEBUG
    UUtils::Exception("G4Trd::SurfaceNormal(p)", "Notification", Warning, 1, "Point p is not on surface !?");
#endif
    // point is not on surface, calculate normal closest to surface. this is not likely to be used too often..., normally the user gives point on surface...
    //     norm = ApproxSurfaceNormal(p);

    // find closest side
    //
    double fcos;

    if (distx <= disty)
    {
      if (distx <= distz)
      {
        // Closest to X
        //
        fcos = 1.0 / secx;
        // normal=(+/-std::cos(ang),0,-std::sin(ang))
        if (p.x >= 0)
          norm = UVector3(fcos, 0, -tanx * fcos);
        else
          norm = UVector3(-fcos, 0, -tanx * fcos);
      }
      else
      {
        // Closest to Z
        //
        if (p.z >= 0)
          norm = UVector3(0, 0, 1);
        else
          norm = UVector3(0, 0, -1);
      }
    }
    else
    {
      if (disty <= distz)
      {
        // Closest to Y
        //
        fcos = 1.0 / secy;
        if (p.y >= 0)
          norm = UVector3(0, fcos, -tany * fcos);
        else
          norm = UVector3(0, -fcos, -tany * fcos);
      }
      else
      {
        // Closest to Z
        //
        if (p.z >= 0)
          norm = UVector3(0, 0, 1);
        else
          norm = UVector3(0, 0, -1);
      }
    }
  }
  else
  {
    norm = sumnorm;
    // if we added to the vector more than once, we have to normalize the vector
    if (noSurfaces > 1) norm.Normalize();
  }
  return noSurfaces > 0; // (Inside(p) == eSurface);
}


/////////////////////////////////////////////////////////////////////////////
//
// Algorithm for SurfaceNormal() following the original specification
// for points not on the surface

inline UVector3 UTrd::ApproxSurfaceNormal(const UVector3& p) const
{
  UVector3 norm;
  double z, tanx, secx, newpx, widx;
  double tany, secy, newpy, widy;
  double distx, disty, distz, fcos;

  z = 2.0 * fDz;

  tanx = (fDx2 - fDx1) / z;
  secx = std::sqrt(1.0 + tanx * tanx);
  newpx = std::abs(p.x) - p.z * tanx;
  widx = fDx2 - fDz * tanx;

  tany = (fDy2 - fDy1) / z;
  secy = std::sqrt(1.0 + tany * tany);
  newpy = std::abs(p.y) - p.z * tany;
  widy = fDy2 - fDz * tany;

  distx = std::abs(newpx - widx) / secx; // perpendicular distance to x side
  disty = std::abs(newpy - widy) / secy; //                        to y side
  distz = std::abs(std::abs(p.z) - fDz); //                        to z side

  // find closest side
  //
  if (distx <= disty)
  {
    if (distx <= distz)
    {
      // Closest to X
      //
      fcos = 1.0 / secx;
      // normal=(+/-std::cos(ang),0,-std::sin(ang))
      if (p.x >= 0)
        norm = UVector3(fcos, 0, -tanx * fcos);
      else
        norm = UVector3(-fcos, 0, -tanx * fcos);
    }
    else
    {
      // Closest to Z
      //
      if (p.z >= 0)
        norm = UVector3(0, 0, 1);
      else
        norm = UVector3(0, 0, -1);
    }
  }
  else
  {
    if (disty <= distz)
    {
      // Closest to Y
      //
      fcos = 1.0 / secy;
      if (p.y >= 0)
        norm = UVector3(0, fcos, -tany * fcos);
      else
        norm = UVector3(0, -fcos, -tany * fcos);
    }
    else
    {
      // Closest to Z
      //
      if (p.z >= 0)
        norm = UVector3(0, 0, 1);
      else
        norm = UVector3(0, 0, -1);
    }
  }
  return norm;
}



/**
* Returns the full 3D cartesian extent of the solid.
* OK
*/
void UTrd::Extent(UVector3& aMin, UVector3& aMax) const
{
  aMin.Set(-std::max(fDx1, fDx2), -std::max(fDy1, fDy2), -fDz);
  aMax.Set(std::max(fDx1, fDx2), std::max(fDy1, fDy2), fDz);
}


//////////////////////////////////////////////////////////////////////////
//
// Stream object contents to an output stream

std::ostream& UTrd::StreamInfo(std::ostream& os) const
{
  int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "       *** Dump for solid - " << GetName() << " ***\n"
     << "       ===================================================\n"
     << " Solid type: UTrd\n"
     << " Parameters: \n"
     << "       half length X, surface -dZ: " << fDx1 << " mm \n"
     << "       half length X, surface +dZ: " << fDx2 << " mm \n"
     << "       half length Y, surface -dZ: " << fDy1 << " mm \n"
     << "       half length Y, surface +dZ: " << fDy2 << " mm \n"
     << "       half length Z                        : " << fDz << " mm \n"
     << "-----------------------------------------------------------\n";
  os.precision(oldprc);

  return os;
}

////////////////////////////////////////////////////////////////////////
//
// GetPointOnSurface
//
// Return a point (UVector3) randomly and uniformly
// selected on the solid surface

UVector3 UTrd::GetPointOnSurface() const
{
  double px, py, pz, tgX, tgY, secX, secY, select, sumS, tmp;
  double Sxy1, Sxy2, Sxy, Sxz, Syz;

  tgX = 0.5 * (fDx2 - fDx1) / fDz;
  secX = std::sqrt(1 + tgX * tgX);
  tgY = 0.5 * (fDy2 - fDy1) / fDz;
  secY = std::sqrt(1 + tgY * tgY);

  // calculate 0.25 of side surfaces, sumS is 0.25 of total surface

  Sxy1 = fDx1 * fDy1;
  Sxy2 = fDx2 * fDy2;
  Sxy = Sxy1 + Sxy2;
  Sxz = (fDx1 + fDx2) * fDz * secY;
  Syz = (fDy1 + fDy2) * fDz * secX;
  sumS = Sxy + Sxz + Syz;

  select = sumS * UUtils::Random();

  if (select < Sxy)                  // Sxy1 or Sxy2
  {
    if (select < Sxy1)
    {
      pz = -fDz;
      px = -fDx1 + 2 * fDx1 * UUtils::Random();
      py = -fDy1 + 2 * fDy1 * UUtils::Random();
    }
    else
    {
      pz =  fDz;
      px = -fDx2 + 2 * fDx2 * UUtils::Random();
      py = -fDy2 + 2 * fDy2 * UUtils::Random();
    }
  }
  else if ((select - Sxy) < Sxz)        // Sxz
  {
    pz  = -fDz  + 2 * fDz * UUtils::Random();
    tmp = fDx1 + (pz + fDz) * tgX;
    px  = -tmp  + 2 * tmp * UUtils::Random();
    tmp = fDy1 + (pz + fDz) * tgY;

    if (UUtils::Random() > 0.5)
    {
      py = tmp;
    }
    else
    {
      py = -tmp;
    }
  }
  else                                   // Syz
  {
    pz  = -fDz  + 2 * fDz * UUtils::Random();
    tmp = fDy1 + (pz + fDz) * tgY;
    py  = -tmp  + 2 * tmp * UUtils::Random();
    tmp = fDx1 + (pz + fDz) * tgX;

    if (UUtils::Random() > 0.5)
    {
      px = tmp;
    }
    else
    {
      px = -tmp;
    }
  }
  return UVector3(px, py, pz);
}

//////////////////////////////////////////////////////////////////////////
//
// Copy constructor

UTrd::UTrd(const UTrd& rhs)
  : VUSolid(rhs), fDx1(rhs.fDx1), fDx2(rhs.fDx2),
    fDy1(rhs.fDy1), fDy2(rhs.fDy2), fDz(rhs.fDz),
    fCubicVolume(rhs.fCubicVolume), fSurfaceArea(rhs.fSurfaceArea)
{
}

//////////////////////////////////////////////////////////////////////////
//
// Assignment operator

UTrd& UTrd::operator = (const UTrd& rhs)
{
  // Check assignment to self
  //
  if (this == &rhs)
  {
    return *this;
  }


  // Copy data
  //
  fDx1 = rhs.fDx1;
  fDx2 = rhs.fDx2;
  fDy1 = rhs.fDy1;
  fDy2 = rhs.fDy2;
  fDz = rhs.fDz;
  fCubicVolume = rhs.fCubicVolume;
  fSurfaceArea = rhs.fSurfaceArea;

  return *this;

}
//////////////////////////////////////////////////////////////////////////
//
// Get Parameters List for Visualisation

void UTrd::GetParametersList(int, double* aArray) const
{
  aArray[0] = GetXHalfLength1();
  aArray[1] = GetXHalfLength2();
  aArray[2] = GetYHalfLength1();
  aArray[3] = GetYHalfLength2();
  aArray[4] = GetZHalfLength();
}
//////////////////////////////////////////////////////////////////////////
//
// Clone

VUSolid* UTrd::Clone() const
{
  return new UTrd(*this);
}
//////////////////////////////////////////////////////////////////////////
//
// Get Entity Type

UGeometryType UTrd::GetEntityType() const
{
   return "Trd";
}