UTet.cc

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//
// ********************************************************************
// * This Software is part of the AIDA Unified Solids Library package *
// * See: https://aidasoft.web.cern.ch/USolids                        *
// ********************************************************************
//
// $Id:$
//
// --------------------------------------------------------------------
//
// UTet
//
// 19.07.13 Tatiana Nikitina
//          Created from original implementation in Geant4
// --------------------------------------------------------------------

#include <cmath>
#include <iostream>
#include <sstream>
#include "UTet.hh"
#include "UUtils.hh"

using namespace std;


//
// Constructor - create a tetrahedron
// This class is implemented separately from general polyhedra,
// because the simplex geometry can be computed very quickly,
// which may become important in situations imported from mesh generators,
// in which a very large number of UTets are created.
// A Tet has all of its geometrical information precomputed

UTet::UTet(const std::string& name,
           UVector3 anchor,
           UVector3 p2,
           UVector3 p3,
           UVector3 p4, bool* degeneracyFlag)
  : VUSolid(name), warningFlag(0)
{
  // fV<x><y> is vector from vertex <y> to vertex <x>
  //
  UVector3 fV21 = p2 - anchor;
  UVector3 fV31 = p3 - anchor;
  UVector3 fV41 = p4 - anchor;

  // make sure this is a correctly oriented set of points for the tetrahedron
  //
  double signed_vol = fV21.Cross(fV31).Dot(fV41);
  if (signed_vol < 0.0)
  {
    UVector3 temp(p4);
    p4 = p3;
    p3 = temp;
    temp = fV41;
    fV41 = fV31;
    fV31 = temp;
  }
  fCubicVolume = std::fabs(signed_vol) / 6.;

  //UVector3 fV24=p2-p4;
  UVector3 fV43 = p4 - p3;
  UVector3 fV32 = p3 - p2;

  fXMin = std::min(std::min(std::min(anchor.x, p2.x), p3.x), p4.x);
  fXMax = std::max(std::max(std::max(anchor.x, p2.x), p3.x), p4.x);
  fYMin = std::min(std::min(std::min(anchor.y, p2.y), p3.y), p4.y);
  fYMax = std::max(std::max(std::max(anchor.y, p2.y), p3.y), p4.y);
  fZMin = std::min(std::min(std::min(anchor.z, p2.z), p3.z), p4.z);
  fZMax = std::max(std::max(std::max(anchor.z, p2.z), p3.z), p4.z);

  fDx = (fXMax - fXMin) * 0.5;
  fDy = (fYMax - fYMin) * 0.5;
  fDz = (fZMax - fZMin) * 0.5;

  fMiddle = UVector3(fXMax + fXMin, fYMax + fYMin, fZMax + fZMin) * 0.5;
  fMaxSize = std::max(std::max(std::max((anchor - fMiddle).Mag(),
                                        (p2 - fMiddle).Mag()),
                               (p3 - fMiddle).Mag()),
                      (p4 - fMiddle).Mag());

  bool degenerate = std::fabs(signed_vol) < 1e-9 * fMaxSize * fMaxSize * fMaxSize;

  if (degeneracyFlag) *degeneracyFlag = degenerate;
  else if (degenerate)
  {
    UUtils::Exception("UTet::UTet()", "GeomSolids0002", FatalErrorInArguments, 1,
                      "Degenerate tetrahedron not allowed.");
  }

  fTol = 1e-9 * (std::fabs(fXMin) + std::fabs(fXMax) + std::fabs(fYMin)
                 + std::fabs(fYMax) + std::fabs(fZMin) + std::fabs(fZMax));
  //fTol=kCarTolerance;

  fAnchor = anchor;
  fP2 = p2;
  fP3 = p3;
  fP4 = p4;

  UVector3 fCenter123 = (anchor + p2 + p3) * (1.0 / 3.0); // face center
  UVector3 fCenter134 = (anchor + p4 + p3) * (1.0 / 3.0);
  UVector3 fCenter142 = (anchor + p4 + p2) * (1.0 / 3.0);
  UVector3 fCenter234 = (p2 + p3 + p4) * (1.0 / 3.0);

  // compute area of each triangular face by cross product
  // and sum for total surface area

  UVector3 normal123 = fV31.Cross(fV21);
  UVector3 normal134 = fV41.Cross(fV31);
  UVector3 normal142 = fV21.Cross(fV41);
  UVector3 normal234 = fV32.Cross(fV43);

  fSurfaceArea = (
                   normal123.Mag() +
                   normal134.Mag() +
                   normal142.Mag() +
                   normal234.Mag()
                 ) / 2.0;

  fNormal123 = normal123.Unit();
  fNormal134 = normal134.Unit();
  fNormal142 = normal142.Unit();
  fNormal234 = normal234.Unit();

  fCdotN123 = fCenter123.Dot(fNormal123);
  fCdotN134 = fCenter134.Dot(fNormal134);
  fCdotN142 = fCenter142.Dot(fNormal142);
  fCdotN234 = fCenter234.Dot(fNormal234);
}

//
// Fake default constructor - sets only member data and allocates memory
//                            for usage restricted to object persistency.
//
UTet::UTet( __void__&)
  : VUSolid(""), fCubicVolume(0.), fSurfaceArea(0.),
    fAnchor(0,0,0), fP2(0,0,0), fP3(0,0,0), fP4(0,0,0), fMiddle(0,0,0),
    fNormal123(0,0,0), fNormal142(0,0,0), fNormal134(0,0,0),
    fNormal234(0,0,0), warningFlag(0),
    fCdotN123(0.), fCdotN142(0.), fCdotN134(0.), fCdotN234(0.),
    fXMin(0.), fXMax(0.), fYMin(0.), fYMax(0.), fZMin(0.), fZMax(0.),
    fDx(0.), fDy(0.), fDz(0.), fTol(0.), fMaxSize(0.)
{
}

//
// Destructor

UTet::~UTet()
{
}

//
// Copy constructor

UTet::UTet(const UTet& rhs)
  : VUSolid(rhs),
    fCubicVolume(rhs.fCubicVolume), fSurfaceArea(rhs.fSurfaceArea),
    fAnchor(rhs.fAnchor),
    fP2(rhs.fP2), fP3(rhs.fP3), fP4(rhs.fP4), fMiddle(rhs.fMiddle),
    fNormal123(rhs.fNormal123), fNormal142(rhs.fNormal142),
    fNormal134(rhs.fNormal134), fNormal234(rhs.fNormal234),
    warningFlag(rhs.warningFlag), fCdotN123(rhs.fCdotN123),
    fCdotN142(rhs.fCdotN142), fCdotN134(rhs.fCdotN134),
    fCdotN234(rhs.fCdotN234), fXMin(rhs.fXMin), fXMax(rhs.fXMax),
    fYMin(rhs.fYMin), fYMax(rhs.fYMax), fZMin(rhs.fZMin), fZMax(rhs.fZMax),
    fDx(rhs.fDx), fDy(rhs.fDy), fDz(rhs.fDz), fTol(rhs.fTol),
    fMaxSize(rhs.fMaxSize)
{
}


//
// Assignment operator

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

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

  // Copy data
  //
  fCubicVolume = rhs.fCubicVolume;
  fSurfaceArea = rhs.fSurfaceArea;
  fAnchor = rhs.fAnchor;
  fP2 = rhs.fP2;
  fP3 = rhs.fP3;
  fP4 = rhs.fP4;
  fMiddle = rhs.fMiddle;
  fNormal123 = rhs.fNormal123;
  fNormal142 = rhs.fNormal142;
  fNormal134 = rhs.fNormal134;
  fNormal234 = rhs.fNormal234;
  warningFlag = rhs.warningFlag;
  fCdotN123 = rhs.fCdotN123;
  fCdotN142 = rhs.fCdotN142;
  fCdotN134 = rhs.fCdotN134;
  fCdotN234 = rhs.fCdotN234;
  fXMin = rhs.fXMin;
  fXMax = rhs.fXMax;
  fYMin = rhs.fYMin;
  fYMax = rhs.fYMax;
  fZMin = rhs.fZMin;
  fZMax = rhs.fZMax;
  fDx = rhs.fDx;
  fDy = rhs.fDy;
  fDz = rhs.fDz;
  fTol = rhs.fTol;
  fMaxSize = rhs.fMaxSize;

  return *this;
}

//
// Return whether point inside/outside/on surface, using tolerance

VUSolid::EnumInside UTet::Inside(const UVector3& p) const
{
  double r123, r134, r142, r234;

  // this is written to allow if-statement truncation so the outside test
  // (where most of the world is) can fail very quickly and efficiently

  if ((r123 = p.Dot(fNormal123) - fCdotN123) > fTol ||
      (r134 = p.Dot(fNormal134) - fCdotN134) > fTol ||
      (r142 = p.Dot(fNormal142) - fCdotN142) > fTol ||
      (r234 = p.Dot(fNormal234) - fCdotN234) > fTol)
  {
    return eOutside; // at least one is out!
  }
  else if ((r123 < -fTol) && (r134 < -fTol) && (r142 < -fTol) && (r234 < -fTol))
  {
    return eInside; // all are definitively inside
  }
  else
  {
    return eSurface; // too close to tell
  }
}

//
// Calculate side nearest to p, and return normal
// If two sides are equidistant, normal of first side (x/y/z)
// encountered returned.
// This assumes that we are looking from the inside!

bool UTet::Normal(const UVector3& p, UVector3& n) const
{
  double r123 = std::fabs(p.Dot(fNormal123) - fCdotN123);
  double r134 = std::fabs(p.Dot(fNormal134) - fCdotN134);
  double r142 = std::fabs(p.Dot(fNormal142) - fCdotN142);
  double r234 = std::fabs(p.Dot(fNormal234) - fCdotN234);

  static const double delta = 0.5 * fTol;
  UVector3 sumnorm(0., 0., 0.);
  int noSurfaces = 0;

  if (r123 <= delta)
  {
    noSurfaces ++;
    sumnorm = fNormal123;
  }

  if (r134 <= delta)
  {
    noSurfaces ++;
    sumnorm += fNormal134;
  }

  if (r142 <= delta)
  {
    noSurfaces ++;
    sumnorm += fNormal142;
  }
  if (r234 <= delta)
  {
    noSurfaces ++;
    sumnorm += fNormal234;
  }

  if (noSurfaces > 0)
  {
    if (noSurfaces == 1)
    {
      n = sumnorm;
      return true;
    }
    else
    {
      n = sumnorm.Unit();
      return true;
    }
  }
  else // Approximative Surface Normal
  {

    if ((r123 <= r134) && (r123 <= r142) && (r123 <= r234))
    {
      n = fNormal123;
    }
    else if ((r134 <= r142) && (r134 <= r234))
    {
      n = fNormal134;
    }
    else if (r142 <= r234)
    {
      n = fNormal142;
    }
    n = fNormal234;
    return false;
  }


}

//
// Calculate distance to box from an outside point
// - return kInfinity if no intersection.
// All this is very unrolled, for speed.

double UTet::DistanceToIn(const UVector3& p,
                          const UVector3& v, double /*aPstep*/) const
{
  UVector3 vu(v.Unit()), hp;
  double vdotn, t, tmin = UUtils::kInfinity;

  double extraDistance = 10.0 * fTol; // a little ways into the solid

  vdotn = -vu.Dot(fNormal123);
  if (vdotn > 1e-12)
  {
    // this is a candidate face, since it is pointing at us
    t = (p.Dot(fNormal123) - fCdotN123) / vdotn; // #  distance to intersection
    if ((t >= -fTol) && (t < tmin))
    {
      // if not true, we're going away from this face or it's not close
      hp = p + vu * (t + extraDistance); // a little beyond point of intersection
      if ((hp.Dot(fNormal134) - fCdotN134 < 0.0) &&
          (hp.Dot(fNormal142) - fCdotN142 < 0.0) &&
          (hp.Dot(fNormal234) - fCdotN234 < 0.0))
      {
        tmin = t;
      }
    }
  }

  vdotn = -vu.Dot(fNormal134);
  if (vdotn > 1e-12)
  {
    // # this is a candidate face, since it is pointing at us
    t = (p.Dot(fNormal134) - fCdotN134) / vdotn; // #  distance to intersection
    if ((t >= -fTol) && (t < tmin))
    {
      // if not true, we're going away from this face
      hp = p + vu * (t + extraDistance); // a little beyond point of intersection
      if ((hp.Dot(fNormal123) - fCdotN123 < 0.0) &&
          (hp.Dot(fNormal142) - fCdotN142 < 0.0) &&
          (hp.Dot(fNormal234) - fCdotN234 < 0.0))
      {
        tmin = t;
      }
    }
  }

  vdotn = -vu.Dot(fNormal142);
  if (vdotn > 1e-12)
  {
    // # this is a candidate face, since it is pointing at us
    t = (p.Dot(fNormal142) - fCdotN142) / vdotn; // #  distance to intersection
    if ((t >= -fTol) && (t < tmin))
    {
      // if not true, we're going away from this face
      hp = p + vu * (t + extraDistance); // a little beyond point of intersection
      if ((hp.Dot(fNormal123) - fCdotN123 < 0.0) &&
          (hp.Dot(fNormal134) - fCdotN134 < 0.0) &&
          (hp.Dot(fNormal234) - fCdotN234 < 0.0))
      {
        tmin = t;
      }
    }
  }

  vdotn = -vu.Dot(fNormal234);
  if (vdotn > 1e-12)
  {
    // # this is a candidate face, since it is pointing at us
    t = (p.Dot(fNormal234) - fCdotN234) / vdotn; // #  distance to intersection
    if ((t >= -fTol) && (t < tmin))
    {
      // if not true, we're going away from this face
      hp = p + vu * (t + extraDistance); // a little beyond point of intersection
      if ((hp.Dot(fNormal123) - fCdotN123 < 0.0) &&
          (hp.Dot(fNormal134) - fCdotN134 < 0.0) &&
          (hp.Dot(fNormal142) - fCdotN142 < 0.0))
      {
        tmin = t;
      }
    }
  }

  return std::max(0.0, tmin);
}

//
// Approximate distance to tet.
// returns distance to sphere centered on bounding box
// - If inside return 0
double UTet::SafetyFromOutside(const UVector3& p, bool /*aAccurate*/) const

{
  double dd = (p - fMiddle).Mag() - fMaxSize - fTol;
  return std::max(0.0, dd);
}

//
// Calcluate distance to surface of box from inside
// by calculating distances to box's x/y/z planes.
// Smallest distance is exact distance to exiting.
double UTet::DistanceToOut(const UVector3&  p, const UVector3& v,
                           UVector3& n, bool& convex, double /*aPstep*/) const
{
  UVector3 vu(v.Unit());
  double t1 = UUtils::kInfinity, t2 = UUtils::kInfinity, t3 = UUtils::kInfinity, t4 = UUtils::kInfinity, vdotn, tt;

  vdotn = vu.Dot(fNormal123);
  if (vdotn > 1e-12) // #we're heading towards this face, so it is a candidate
  {
    t1 = (fCdotN123 - p.Dot(fNormal123)) / vdotn; // #  distance to intersection
  }

  vdotn = vu.Dot(fNormal134);
  if (vdotn > 1e-12) // #we're heading towards this face, so it is a candidate
  {
    t2 = (fCdotN134 - p.Dot(fNormal134)) / vdotn; // #  distance to intersection
  }

  vdotn = vu.Dot(fNormal142);
  if (vdotn > 1e-12) // #we're heading towards this face, so it is a candidate
  {
    t3 = (fCdotN142 - p.Dot(fNormal142)) / vdotn; // #  distance to intersection
  }

  vdotn = vu.Dot(fNormal234);
  if (vdotn > 1e-12) // #we're heading towards this face, so it is a candidate
  {
    t4 = (fCdotN234 - p.Dot(fNormal234)) / vdotn; // #  distance to intersection
  }

  tt = std::min(std::min(std::min(t1, t2), t3), t4);

  if (warningFlag && (tt == UUtils::kInfinity || tt < -fTol))
  {
    // DumpInfo();
    std::ostringstream message;
    message << "No good intersection found or already outside!?" << std::endl
            << "p = " << p  << std::endl
            << "v = " << v  << std::endl
            << "t1, t2, t3, t4  "
            << t1 << ", " << t2 << ", " << t3 << ", " << t4;

    UUtils::Exception("UTet::DistanceToOut(p,v,...)", "GeomSolids1002",
                      Warning, 1, message.str().c_str());
    if (convex)
    {
      convex = false; // flag normal as meaningless
    }
  }
  else
  {
    static UVector3 normal;
    if (tt == t1)
    {
      normal = fNormal123;
    }
    else if (tt == t2)
    {
      normal = fNormal134;
    }
    else if (tt == t3)
    {
      normal = fNormal142;
    }
    else if (tt == t4)
    {
      normal = fNormal234;
    }
    n = normal;
    if (convex)
    {
      convex = true;
    }
  }

  return std::max(tt, 0.0); // avoid tt<0.0 by a tiny bit
  // if we are right on a face
}

//
// Calculate exact shortest distance to any boundary from inside
// - If outside return 0
double UTet::SafetyFromInside(const UVector3& p, bool /*aAccurate*/) const
{
  double t1, t2, t3, t4;
  t1 = fCdotN123 - p.Dot(fNormal123); //  distance to plane, positive if inside
  t2 = fCdotN134 - p.Dot(fNormal134); //  distance to plane
  t3 = fCdotN142 - p.Dot(fNormal142); //  distance to plane
  t4 = fCdotN234 - p.Dot(fNormal234); //  distance to plane

  // if any one of these is negative, we are outside,
  // so return zero in that case

  double tmin = std::min(std::min(std::min(t1, t2), t3), t4);
  return (tmin < fTol) ? 0 : tmin;
}


//
// Stream object contents to an output stream

std::ostream& UTet::StreamInfo(std::ostream& os) const
{
  int oldprc = os.precision(16);
  os << "-----------------------------------------------------------\n"
     << "    *** Dump for solid - " << GetName() << " ***\n"
     << "    ===================================================\n"
     << " Solid type: UTet\n"
     << " Parameters: \n"
     << "    anchor: " << fAnchor << "  \n"
     << "    p2: " << fP2 << "  \n"
     << "    p3: " << fP3 << "  \n"
     << "    p4: " << fP4 << "  \n"
     << "    normal123: " << fNormal123 << " \n"
     << "    normal134: " << fNormal134 << " \n"
     << "    normal142: " << fNormal142 << " \n"
     << "    normal234: " << fNormal234 << " \n"
     << "-----------------------------------------------------------\n";
  os.precision(oldprc);

  return os;
}


//
// GetPointOnFace
//
// Auxiliary method for get point on surface

UVector3 UTet::GetPointOnFace(UVector3 p1, UVector3 p2,
                              UVector3 p3, double& area) const
{
  double lambda1, lambda2;
  UVector3 v, w;

  v = p3 - p1;
  w = p1 - p2;

  lambda1 = UUtils::Random(0., 1.);
  lambda2 = UUtils::Random(0., lambda1);

  area = 0.5 * (v.Cross(w)).Mag();
  return (p2 + lambda1 * w + lambda2 * v);
}

//
// GetPointOnSurface

UVector3 UTet::GetPointOnSurface() const
{
  double chose, aOne, aTwo, aThree, aFour;
  UVector3 p1, p2, p3, p4;

  p1 = GetPointOnFace(fAnchor, fP2, fP3, aOne);
  p2 = GetPointOnFace(fAnchor, fP4, fP3, aTwo);
  p3 = GetPointOnFace(fAnchor, fP4, fP2, aThree);
  p4 = GetPointOnFace(fP4, fP3, fP2, aFour);

  chose = UUtils::Random(0., aOne + aTwo + aThree + aFour);
  if ((chose >= 0.) && (chose < aOne))
  {
    return p1;
  }
  else if ((chose >= aOne) && (chose < aOne + aTwo))
  {
    return p2;
  }
  else if ((chose >= aOne + aTwo) && (chose < aOne + aTwo + aThree))
  {
    return p3;
  }
  return p4;
}

//
// GetVertices

std::vector<UVector3> UTet::GetVertices() const
{
  std::vector<UVector3> vertices(4);
  vertices[0] = fAnchor;
  vertices[1] = fP2;
  vertices[2] = fP3;
  vertices[3] = fP4;

  return vertices;
}
//______________________________________________________________________________
void UTet::Extent(UVector3& aMin, UVector3& aMax) const
{
  // Returns the full 3D cartesian extent of the solid.
  aMin.x = fXMin;
  aMax.x = fXMax;
  aMin.y = fYMin;
  aMax.y = fYMax;
  aMin.z = fZMin;
  aMax.z = fZMax;
}
//______________________________________________________________________________
void UTet::GetParametersList(int, double* aArray) const
{
  aArray[0] = fAnchor.x;
  aArray[1] = fAnchor.y;
  aArray[2] = fAnchor.z;
  aArray[3] = fP2.x;
  aArray[4] = fP2.y;
  aArray[5] = fP2.z;
  aArray[6] = fP3.x;
  aArray[7] = fP3.y;
  aArray[8] = fP3.z;
  aArray[9] = fP4.x;
  aArray[10] = fP4.y;
  aArray[11] = fP4.z;
}
//______________________________________________________________________________
VUSolid* UTet::Clone() const
{
  return new UTet(*this);
}
//______________________________________________________________________________
UGeometryType UTet::GetEntityType() const
{
  return "Tet";
}
//______________________________________________________________________________
double UTet::Capacity()
{
   return fCubicVolume;
}
//______________________________________________________________________________
double UTet::SurfaceArea()
{
   return fSurfaceArea;
}