UOrb.cc

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

#include <cmath>
#include <iostream>

#include "UOrb.hh"
#include "UUtils.hh"

using namespace std;

//______________________________________________________________________________
UOrb::UOrb(const std::string& name, double r)
  : VUSolid(name), fR(r), fCubicVolume(0), fSurfaceArea(0)
{
  const double epsilon = 2.e-11;  // relative tolerance of fR

  // Check radius
  //
  if (r < 10 * VUSolid::fgTolerance) // cartesian tolerance
  {
    UUtils::Exception("UOrb::UOrb()", "GeomSolids0002",
       UFatalErrorInArguments, 1, "Invalid radius > 10*kCarTolerance.");
  }
  // VUSolid::fRTolerance is radial tolerance (note: half of G4 tolerance)
  fRTolerance =  max(VUSolid::frTolerance, epsilon * r);
}

//______________________________________________________________________________
// ok
VUSolid::EnumInside UOrb::Inside(const UVector3& p) const
{
  double rad2 = p.x() * p.x() + p.y() * p.y() + p.z() * p.z();
  //  if (false) double rad = sqrt(rad2);

  double tolRMax = fR - fRTolerance * 0.5;

  // Check radial surface
  double tolRMax2 = tolRMax * tolRMax;
  if (rad2 <= tolRMax2)
    return eInside;
  else
  {
    tolRMax = fR + fRTolerance * 0.5;
    tolRMax2 = tolRMax * tolRMax;
    if (rad2 <= tolRMax2)
      return eSurface;
    else
      return eOutside;
  }
}


/*
* 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 UOrb::DistanceToIn(const UVector3& p,
                          const UVector3& v,
                          //                          UVector3 &aNormal,
                          double /*aPstep*/) const
{
  double snxt = UUtils::kInfinity;      // snxt = default return value

  double rad, pDotV3d; // , tolORMax2, tolIRMax2;
  double c, d2, s = UUtils::kInfinity;

  const double dRmax = 100.*fR;

  // General Precalcs

  rad    = sqrt(p.x() * p.x() + p.y() * p.y() + p.z() * p.z());
  pDotV3d = p.x() * v.x() + p.y() * v.y() + p.z() * v.z();

  // Radial Precalcs

  // tolORMax2 = (fR+fRTolerance*0.5)*(fR+fRTolerance*0.5);
  // tolIRMax2 = (fR-fRTolerance*0.5)*(fR-fRTolerance*0.5);

  // Outer spherical shell intersection
  // - Only if outside tolerant fR
  // - Check for if inside and outer UOrb heading through solid (-> 0)
  // - No intersect -> no intersection with UOrb
  //
  // Shell eqn: x^2+y^2+z^2 = RSPH^2
  //
  // => (px+svx)^2+(py+svy)^2+(pz+svz)^2=R^2
  //
  // => (px^2+py^2+pz^2) +2s(pxvx+pyvy+pzvz)+s^2(vx^2+vy^2+vz^2)=R^2
  // =>      rad2        +2s(pDotV3d)       +s^2                =R^2
  //
  // => s=-pDotV3d+-sqrt(pDotV3d^2-(rad2-R^2))

  c = (rad - fR) * (rad + fR); // c = (rad2-R^2))

  if (rad > fR - fRTolerance * 0.5) // not inside in terms of Inside(p)
  {
    if (c > fRTolerance * fR)
    {
      // If outside tolerant boundary of outer UOrb in terms of c
      // [ should be sqrt(rad2) - fR > fRTolerance*0.5 ]

      d2 = pDotV3d * pDotV3d - c;

      if (d2 >= 0)
      {
        s = -pDotV3d - sqrt(d2); // ok! = [ ( -2 p dot v) +- sqrt [(-2p dot v)2 - 4*(rad - fR)*(rad + fR)] ] /  2
        // pDotV3d must be positive always, if not use alternative http://en.wikipedia.org/wiki/Quadratic_equation#Alternative_quadratic_formula
        if (s >= 0)
        {
          if (s > dRmax)   // Avoid rounding errors due to precision issues seen on
          {
            // 64 bits systems. Split long distances and recompute
            double fTerm = s - fmod(s, dRmax);
            s = fTerm + DistanceToIn(p + fTerm * v, v);
          }
          return snxt = s;
        }
      }
      else    // No intersection with UOrb
      {
        return snxt = UUtils::kInfinity;
      }
    }
    else // not outside in terms of c
    {
      if (c > -fRTolerance * fR)  // on surface
      {
        d2 = pDotV3d * pDotV3d - c;
        if ((d2 < fRTolerance * fR) || (pDotV3d >= 0)) // pDotV3d = cos si >= 0
        {
          return snxt = UUtils::kInfinity;
        }
        else
        {
          return snxt = 0.;
        }
      }
    }
  }
#ifdef UDEBUG
  else // inside ???
  {
    UUtils::Exception("UOrb::DistanceToIn(p,v)", "GeomSolids1002", UWarning, 1, "Point p is inside !?");
  }
#endif

  return snxt;
}

double UOrb::DistanceToOutForOutsidePoints(const UVector3&  p, const UVector3& v, UVector3& n) const
{
  double distanceIn = DistanceToIn(p, v);
  UVector3 shift = distanceIn * v;
  UVector3 surfacePoint = p + shift;
  UVector3 normal;
  ((UOrb&)*this).Normal(surfacePoint, normal);
  double dot = normal.Dot(v);
  if (dot > 0) return 0;
  else
  {
    bool convex;
    double distanceOut = DistanceToOut(surfacePoint, v, n, convex);
    return distanceIn + distanceOut;
  }
}

/*
* 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.
* ______________________________________________________________________________
*/
double UOrb::DistanceToOut(const UVector3&  p, const UVector3& v,
                           UVector3& n, bool& convex, double /*aPstep*/) const
{
  double snxt = 0;     // snxt: distance to next surface, is default return value
  bool notOutside = false;
  convex = true; // orb is always convex, if we leave surface of Orb, we will neber bump on the orb again ...

  double rad2, pDotV3d;
  double xi, yi, zi;    // Intersection point
  double c, d2;

  rad2    = p.x() * p.x() + p.y() * p.y() + p.z() * p.z();
  pDotV3d = p.x() * v.x() + p.y() * v.y() + p.z() * v.z();

  // Radial Intersection from UOrb::DistanceToIn
  //
  // Outer spherical shell intersection
  // - Only if outside tolerant fR
  // - Check for if inside and outer UOrb heading through solid (-> 0)
  // - No intersect -> no intersection with UOrb
  //
  // Shell eqn: x^2+y^2+z^2=RSPH^2
  //
  // => (px+svx)^2+(py+svy)^2+(pz+svz)^2=R^2
  //
  // => (px^2+py^2+pz^2) +2s(pxvx+pyvy+pzvz)+s^2(vx^2+vy^2+vz^2)=R^2
  // =>      rad2        +2s(pDotV3d)       +s^2                =R^2
  //
  // => s=-pDotV3d+-sqrt(pDotV3d^2-(rad2-R^2))

  const double rPlus = fR + fRTolerance;
  double rad = sqrt(rad2);

  if (rad <= rPlus)
  {
    c = (rad - fR) * (rad + fR); // rad2 - fR2

    if (c < fRTolerance * fR)
    {
      // Within tolerant Outer radius
      //
      // The test is
      //     rad  - fR < 0.5*fRTolerance
      // =>  rad  < fR + 0.5*kRadTol
      // =>  rad2 < (fR + 0.5*kRadTol)^2
      // =>  rad2 < fR^2 + 2.*0.5*fR*kRadTol + 0.25*kRadTol*kRadTol
      // =>  rad2 - fR^2    <~    fR*kRadTol

      d2 = pDotV3d * pDotV3d - c;

      if ((c > -2 * fRTolerance * fR) &&      // => point is on tolerant surface (i.e. within +- tolerance)
          ((pDotV3d >= 0)   || (d2 < 0)))         // if (pDotV3d >= 0 ) => leaving outside from Rmax; i.e. from surface
        // not re-entering
        // if (d2 < 0) => it means the point is already outside
      {
        // if(calcNorm) // NOTE: we do not have this variable, calcNorm is true always
        {
          //          *validNorm = true; // NOTE: we do not have this variable, probably always true
          n = UVector3(p.x() / fR, p.y() / fR, p.z() / fR);
        }
        return snxt = 0;
      }
      else
      {
        // we are inside, with + version of quadratic eq. solution we calculate solution for distance
        snxt = -pDotV3d + sqrt(d2);    // second root since inside Rmax
        // the solution is safe because pDotV3d is negative
        // c alternative formula, see http://en.wikipedia.org/wiki/Quadratic_equation#Alternative_quadratic_formula
        // is not neccessary in this case
        notOutside = true;
      }
    }
  }
  else // p is outside ???
  {
    // Rule 2: DistanceToOut
    // Surface points = 0
    // Outside points: If pointing outwards (dot product with normal positive) return 0, otherwise ignore first surface, another surface should always be on the direction line, use instead distance to this one.

    //    double res = DistanceToOutForOutsidePoints(p, v, n);

    cout.precision(16);
    cout << endl;
    //    DumpInfo();
    cout << "Position:"  << endl << endl;
    cout << "p.x() = "   << p.x() << endl;
    cout << "p.y() = "   << p.y() << endl;
    cout << "p.z() = "   << p.z() << endl << endl;
    cout << "Rp = " << sqrt(p.x() * p.x() + p.y() * p.y() + p.z() * p.z()) << endl << endl;
    cout << "Direction:" << endl << endl;
    cout << "v.x() = "   << v.x() << endl;
    cout << "v.y() = "   << v.y() << endl;
    cout << "v.z() = "   << v.z() << endl << endl;
    cout << "Proposed distance :" << endl << endl;
    cout << "snxt = "    << snxt << endl << endl;



    cout.precision(6);
    UUtils::Exception("UOrb::DistanceToOut(p,v,..)", "GeomSolids1002",
                      UWarning, 1, "Logic error: snxt = kInfinity ???");

  }

  // if (calcNorm)    // Output switch operator
  {
    if (notOutside)
    {
      xi = p.x() + snxt * v.x(); // we move to the point on surface, then return normal at that point which for orb, see method bool UOrb::Normal( const UVector3& p, UVector3 &n)
      yi = p.y() + snxt * v.y();
      zi = p.z() + snxt * v.z();
      n = UVector3(xi / fR, yi / fR, zi / fR); // we return normalized vector
    }
    else
    {

      cout.precision(16);
      cout << endl;
      //        DumpInfo();
      cout << "Position:"  << endl << endl;
      cout << "p.x() = "   << p.x() << " mm" << endl;
      cout << "p.y() = "   << p.y() << " mm" << endl;
      cout << "p.z() = "   << p.z() << " mm" << endl << endl;
      cout << "Direction:" << endl << endl;
      cout << "v.x() = "   << v.x() << endl;
      cout << "v.y() = "   << v.y() << endl;
      cout << "v.z() = "   << v.z() << endl << endl;
      cout << "Proposed distance :" << endl << endl;
      cout << "snxt = "    << snxt << " mm" << endl << endl;
      cout.precision(6);


      UUtils::Exception("UOrb::DistanceToOut(p,v,..)", "GeomSolids1002",
           UWarning, 1, "Undefined side for valid surface normal to solid.");
    }
  }
  return snxt;
}

/*
* Estimates the isotropic safety from a point inside the current solid to any
* of its surfaces. The algorithm may be accurate or should provide a fast
* underestimate.
* ______________________________________________________________________________
* Note: In geant4, these methods are DistanceToOut, without given direction
* Note: ??? Should not Return 0 anymore if point outside, just the value
* OK
*/
double UOrb::SafetyFromInside(const UVector3& p, bool /*aAccurate*/) const
{

  //
  // Calculate distance (<=actual) to closest surface of shape from inside

  double safe = 0.0, rad = sqrt(p.x() * p.x() + p.y() * p.y() + p.z() * p.z());

#ifdef UDEBUG
  if (Inside(p) == kOutside)
  {
    //     int oldprc = cout.precision(16);
    cout << endl;
    //     DumpInfo();
    cout << "Position:"  << endl << endl;
    cout << "p.x = "   << p.x() << endl;
    cout << "p.y = "   << p.y() << endl;
    cout << "p.z = "   << p.z() << endl << endl;
    //     cout.precision(oldprc);
    UUtils::Exception("UOrb::DistanceToOut(p)", "GeomSolids1002", UWarning, 1,
                      "Point p is outside !?");
  }
#endif

  safe = fR - rad;
  if (safe < 0.) safe = 0.;
  return safe;
}


/*
* 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 UOrb::SafetyFromOutside(const UVector3& p, bool /*aAccurate*/) const
{
  double safe = 0.0;
  double rad  = sqrt(p.x() * p.x() + p.y() * p.y() + p.z() * p.z());
  safe = rad - fR;
  if (safe < 0)
  {
    safe = 0.;
  }
  return safe;
}


bool UOrb::Normal(const UVector3& p, UVector3& n) const
{
  double rad2 = p.x() * p.x() + p.y() * p.y() + p.z() * p.z();
  double rad = sqrt(rad2);

  n = UVector3(p.x() / rad, p.y() / rad, p.z() / rad);

  double tolRMaxP = fR + fRTolerance;
  double tolRMaxM = fR - fRTolerance;

  // Check radial surface
  bool result = ((rad2 <= tolRMaxP * tolRMaxP) && (rad2 >= tolRMaxM * tolRMaxM)); // means we are on surface
  return result;
}


void UOrb::Extent(UVector3& aMin, UVector3& aMax) const
{
  aMin.Set(-fR);
  aMax.Set(fR);
}


//
// Stream object contents to an output stream

std::ostream& UOrb::StreamInfo(std::ostream& os) const
{
  int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "               *** Dump for solid - " << GetName() << " ***\n"
     << "               ===================================================\n"
     << " Solid type: UOrb\n"
     << " Parameters: \n"

     << "               outer radius: " << fR << " mm \n"
     << "-----------------------------------------------------------\n";
  os.precision(oldprc);

  return os;
}

//
// GetPointOnSurface

UVector3 UOrb::GetPointOnSurface() const
{
  //  generate a random number from zero to 2UUtils::kPi...
  //
  double phi      = UUtils::Random(0., 2.*UUtils::kPi);
  double cosphi  = std::cos(phi);
  double sinphi  = std::sin(phi);

  // generate a random point uniform in area
  double costheta = UUtils::Random(-1., 1.);
  double sintheta = std::sqrt(1. - UUtils::sqr(costheta));

  return UVector3(fR * sintheta * cosphi, fR * sintheta * sinphi, fR * costheta);
}

VUSolid* UOrb:: Clone() const
{
  return new UOrb(*this);
}

// Copy constructor

UOrb::UOrb(const UOrb& rhs)
  : VUSolid(rhs), fR(rhs.fR), fRTolerance(rhs.fRTolerance), fCubicVolume(rhs.fCubicVolume), fSurfaceArea(rhs.fSurfaceArea)
{
}

//
// Assignment operator

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

  // Copy base class data
  //
  VUSolid::operator=(rhs);

  // Copy data
  //
  fR = rhs.fR;
  fRTolerance = rhs.fRTolerance;
  fCubicVolume = rhs.fCubicVolume;
  fSurfaceArea = rhs.fSurfaceArea;
  return *this;
}
//
// Get Parameters List for visualisation

void UOrb::GetParametersList(int, double* aArray)const
{
  aArray[0] = GetRadius();
}
//
// Get Entity Type

UGeometryType UOrb::GetEntityType() const
{
   return "Orb";
}