G4PolyconeSide.cc

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//
// Implementation of G4PolyconeSide, the face representing
// one conical side of a polycone
//
// Author: David C. Williams ([email protected])
// --------------------------------------------------------------------
 
#include "G4PolyconeSide.hh"
#include "meshdefs.hh"
#include "G4PhysicalConstants.hh"
#include "G4IntersectingCone.hh"
#include "G4ClippablePolygon.hh"
#include "G4AffineTransform.hh"
#include "G4SolidExtentList.hh"
#include "G4GeometryTolerance.hh"
 
#include "Randomize.hh"
 
// This new field helps to use the class G4PlSideManager.
//
G4PlSideManager G4PolyconeSide::subInstanceManager;
 
// This macro changes the references to fields that are now encapsulated
// in the class G4PlSideData.
//
#define G4MT_pcphix ((subInstanceManager.offset[instanceID]).fPhix)
#define G4MT_pcphiy ((subInstanceManager.offset[instanceID]).fPhiy)
#define G4MT_pcphiz ((subInstanceManager.offset[instanceID]).fPhiz)
#define G4MT_pcphik ((subInstanceManager.offset[instanceID]).fPhik)
 
// Returns the private data instance manager.
//
const G4PlSideManager& G4PolyconeSide::GetSubInstanceManager()
{
  return subInstanceManager;
}
 
// Constructor
//
// Values for r1,z1 and r2,z2 should be specified in clockwise
// order in (r,z).
//
G4PolyconeSide::G4PolyconeSide( const G4PolyconeSideRZ* prevRZ,
                                const G4PolyconeSideRZ* tail,
                                const G4PolyconeSideRZ* head,
                                const G4PolyconeSideRZ* nextRZ,
                                      G4double thePhiStart, 
                                      G4double theDeltaPhi, 
                                      G4bool thePhiIsOpen, 
                                      G4bool isAllBehind )
{
  instanceID = subInstanceManager.CreateSubInstance();
 
  kCarTolerance = G4GeometryTolerance::GetInstance()->GetSurfaceTolerance();
  G4MT_pcphix = 0.0; G4MT_pcphiy = 0.0; G4MT_pcphiz = 0.0; G4MT_pcphik = 0.0;
 
  //
  // Record values
  //
  r[0] = tail->r; z[0] = tail->z;
  r[1] = head->r; z[1] = head->z;
  
  phiIsOpen = thePhiIsOpen;
  if (phiIsOpen)
  {
    deltaPhi = theDeltaPhi;
    startPhi = thePhiStart;
 
    //
    // Set phi values to our conventions
    //
    while (deltaPhi < 0.0)    // Loop checking, 13.08.2015, G.Cosmo
     deltaPhi += twopi;
    while (startPhi < 0.0)    // Loop checking, 13.08.2015, G.Cosmo
     startPhi += twopi;
    
    //
    // Calculate corner coordinates
    //
    ncorners = 4;
    corners = new G4ThreeVector[ncorners];
    
    corners[0] = G4ThreeVector( tail->r*std::cos(startPhi),
                                tail->r*std::sin(startPhi), tail->z );
    corners[1] = G4ThreeVector( head->r*std::cos(startPhi),
                                head->r*std::sin(startPhi), head->z );
    corners[2] = G4ThreeVector( tail->r*std::cos(startPhi+deltaPhi),
                                tail->r*std::sin(startPhi+deltaPhi), tail->z );
    corners[3] = G4ThreeVector( head->r*std::cos(startPhi+deltaPhi),
                                head->r*std::sin(startPhi+deltaPhi), head->z );
  }
  else
  {
    deltaPhi = twopi;
    startPhi = 0.0;
  }
  
  allBehind = isAllBehind;
    
  //
  // Make our intersecting cone
  //
  cone = new G4IntersectingCone( r, z );
  
  //
  // Calculate vectors in r,z space
  //
  rS = r[1]-r[0]; zS = z[1]-z[0];
  length = std::sqrt( rS*rS + zS*zS);
  rS /= length; zS /= length;
  
  rNorm = +zS;
  zNorm = -rS;
  
  G4double lAdj;
  
  prevRS = r[0]-prevRZ->r;
  prevZS = z[0]-prevRZ->z;
  lAdj = std::sqrt( prevRS*prevRS + prevZS*prevZS );
  prevRS /= lAdj;
  prevZS /= lAdj;
 
  rNormEdge[0] = rNorm + prevZS;
  zNormEdge[0] = zNorm - prevRS;
  lAdj = std::sqrt( rNormEdge[0]*rNormEdge[0] + zNormEdge[0]*zNormEdge[0] );
  rNormEdge[0] /= lAdj;
  zNormEdge[0] /= lAdj;
 
  nextRS = nextRZ->r-r[1];
  nextZS = nextRZ->z-z[1];
  lAdj = std::sqrt( nextRS*nextRS + nextZS*nextZS );
  nextRS /= lAdj;
  nextZS /= lAdj;
 
  rNormEdge[1] = rNorm + nextZS;
  zNormEdge[1] = zNorm - nextRS;
  lAdj = std::sqrt( rNormEdge[1]*rNormEdge[1] + zNormEdge[1]*zNormEdge[1] );
  rNormEdge[1] /= lAdj;
  zNormEdge[1] /= lAdj;
}
 
// Fake default constructor - sets only member data and allocates memory
//                            for usage restricted to object persistency.
//
G4PolyconeSide::G4PolyconeSide( __void__& )
  : startPhi(0.), deltaPhi(0.),
    rNorm(0.), zNorm(0.), rS(0.), zS(0.), length(0.),
    prevRS(0.), prevZS(0.), nextRS(0.), nextZS(0.),
    kCarTolerance(0.), instanceID(0)
{
  r[0] = r[1] = 0.;
  z[0] = z[1] = 0.;
  rNormEdge[0]= rNormEdge[1] = 0.;
  zNormEdge[0]= zNormEdge[1] = 0.;
}
 
// Destructor
//  
G4PolyconeSide::~G4PolyconeSide()
{
  delete cone;
  if (phiIsOpen)  { delete [] corners; }
}
 
// Copy constructor
//
G4PolyconeSide::G4PolyconeSide( const G4PolyconeSide& source )
{
  instanceID = subInstanceManager.CreateSubInstance();
 
  CopyStuff( source );
}
 
// Assignment operator
//
G4PolyconeSide& G4PolyconeSide::operator=( const G4PolyconeSide& source )
{
  if (this == &source)  { return *this; }
 
  delete cone;
  if (phiIsOpen)  { delete [] corners; }
  
  CopyStuff( source );
  
  return *this;
}
 
// CopyStuff
//
void G4PolyconeSide::CopyStuff( const G4PolyconeSide& source )
{
  r[0]    = source.r[0];
  r[1]    = source.r[1];
  z[0]    = source.z[0];
  z[1]    = source.z[1];
  
  startPhi  = source.startPhi;
  deltaPhi  = source.deltaPhi;
  phiIsOpen  = source.phiIsOpen;
  allBehind  = source.allBehind;
 
  kCarTolerance = source.kCarTolerance;
  fSurfaceArea = source.fSurfaceArea;
  
  cone    = new G4IntersectingCone( *source.cone );
  
  rNorm    = source.rNorm;
  zNorm    = source.zNorm;
  rS    = source.rS;
  zS    = source.zS;
  length    = source.length;
  prevRS    = source.prevRS;
  prevZS    = source.prevZS;
  nextRS    = source.nextRS;
  nextZS    = source.nextZS;
  
  rNormEdge[0]   = source.rNormEdge[0];
  rNormEdge[1]  = source.rNormEdge[1];
  zNormEdge[0]  = source.zNormEdge[0];
  zNormEdge[1]  = source.zNormEdge[1];
  
  if (phiIsOpen)
  {
    ncorners = 4;
    corners = new G4ThreeVector[ncorners];
    
    corners[0] = source.corners[0];
    corners[1] = source.corners[1];
    corners[2] = source.corners[2];
    corners[3] = source.corners[3];
  }
}
 
// Intersect
//
G4bool G4PolyconeSide::Intersect( const G4ThreeVector& p,
                                  const G4ThreeVector& v,  
                                        G4bool outgoing,
                                        G4double surfTolerance,
                                        G4double& distance,
                                        G4double& distFromSurface,
                                        G4ThreeVector& normal,
                                        G4bool& isAllBehind )
{
  G4double s1=0., s2=0.;
  G4double normSign = outgoing ? +1 : -1;
  
  isAllBehind = allBehind;
 
  //
  // Check for two possible intersections
  //
  G4int nside = cone->LineHitsCone( p, v, &s1, &s2 );
  if (nside == 0) return false;
    
  //
  // Check the first side first, since it is (supposed to be) closest
  //
  G4ThreeVector hit = p + s1*v;
  
  if (PointOnCone( hit, normSign, p, v, normal ))
  {
    //
    // Good intersection! What about the normal? 
    //
    if (normSign*v.dot(normal) > 0)
    {
      //
      // We have a valid intersection, but it could very easily
      // be behind the point. To decide if we tolerate this,
      // we have to see if the point p is on the surface near
      // the intersecting point.
      //
      // What does it mean exactly for the point p to be "near"
      // the intersection? It means that if we draw a line from
      // p to the hit, the line remains entirely within the
      // tolerance bounds of the cone. To test this, we can
      // ask if the normal is correct near p.
      //
      G4double pr = p.perp();
      if (pr < DBL_MIN) pr = DBL_MIN;
      G4ThreeVector pNormal( rNorm*p.x()/pr, rNorm*p.y()/pr, zNorm );
      if (normSign*v.dot(pNormal) > 0)
      {
        //
        // p and intersection in same hemisphere
        //
        G4double distOutside2;
        distFromSurface = -normSign*DistanceAway( p, false, distOutside2 );
        if (distOutside2 < surfTolerance*surfTolerance)
        {
          if (distFromSurface > -surfTolerance)
          {
            //
            // We are just inside or away from the
            // surface. Accept *any* value of distance.
            //
            distance = s1;
            return true;
          }
        }
      }
      else 
        distFromSurface = s1;
      
      //
      // Accept positive distances
      //
      if (s1 > 0)
      {
        distance = s1;
        return true;
      }
    }
  }  
  
  if (nside==1) return false;
  
  //
  // Well, try the second hit
  //  
  hit = p + s2*v;
  
  if (PointOnCone( hit, normSign, p, v, normal ))
  {
    //
    // Good intersection! What about the normal? 
    //
    if (normSign*v.dot(normal) > 0)
    {
      G4double pr = p.perp();
      if (pr < DBL_MIN) pr = DBL_MIN;
      G4ThreeVector pNormal( rNorm*p.x()/pr, rNorm*p.y()/pr, zNorm );
      if (normSign*v.dot(pNormal) > 0)
      {
        G4double distOutside2;
        distFromSurface = -normSign*DistanceAway( p, false, distOutside2 );
        if (distOutside2 < surfTolerance*surfTolerance)
        {
          if (distFromSurface > -surfTolerance)
          {
            distance = s2;
            return true;
          }
        }
      }
      else 
        distFromSurface = s2;
      
      if (s2 > 0)
      {
        distance = s2;
        return true;
      }
    }
  }  
 
  //
  // Better luck next time
  //
  return false;
}
 
// Distance
//
G4double G4PolyconeSide::Distance( const G4ThreeVector& p, G4bool outgoing )
{
  G4double normSign = outgoing ? -1 : +1;
  G4double distFrom, distOut2;
  
  //
  // We have two tries for each hemisphere. Try the closest first.
  //
  distFrom = normSign*DistanceAway( p, false, distOut2 );
  if (distFrom > -0.5*kCarTolerance )
  {
    //
    // Good answer
    //
    if (distOut2 > 0) 
      return std::sqrt( distFrom*distFrom + distOut2 );
    else 
      return std::fabs(distFrom);
  }
  
  //
  // Try second side. 
  //
  distFrom = normSign*DistanceAway( p,  true, distOut2 );
  if (distFrom > -0.5*kCarTolerance)
  {
 
    if (distOut2 > 0) 
      return std::sqrt( distFrom*distFrom + distOut2 );
    else
      return std::fabs(distFrom);
  }
  
  return kInfinity;
}
 
// Inside
//
EInside G4PolyconeSide::Inside( const G4ThreeVector& p,
                                      G4double tolerance, 
                                      G4double* bestDistance )
{
  G4double distFrom, distOut2, dist2;
  G4double edgeRZnorm;
     
  distFrom =  DistanceAway( p, distOut2, &edgeRZnorm );
  dist2 = distFrom*distFrom + distOut2;
 
  *bestDistance = std::sqrt( dist2);
  
  // Okay then, inside or out?
  //
  if ( (std::fabs(edgeRZnorm) < tolerance)
    && (distOut2< tolerance*tolerance) )
    return kSurface;
  else if (edgeRZnorm < 0)
    return kInside;
  else
    return kOutside;
}
 
// Normal
//
G4ThreeVector G4PolyconeSide::Normal( const G4ThreeVector& p,
                                            G4double* bestDistance )
{
  if (p == G4ThreeVector(0.,0.,0.))  { return p; }
 
  G4double dFrom, dOut2;
  
  dFrom = DistanceAway( p, false, dOut2 );
  
  *bestDistance = std::sqrt( dFrom*dFrom + dOut2 );
  
  G4double rds = p.perp();
  if (rds!=0.) { return {rNorm*p.x()/rds,rNorm*p.y()/rds,zNorm}; }
  return G4ThreeVector( 0.,0., zNorm ).unit();
}
 
// Extent
//
G4double G4PolyconeSide::Extent( const G4ThreeVector axis )
{
  if (axis.perp2() < DBL_MIN)
  {
    //
    // Special case
    //
    return axis.z() < 0 ? -cone->ZLo() : cone->ZHi();
  }
 
  //
  // Is the axis pointing inside our phi gap?
  //
  if (phiIsOpen)
  {
    G4double phi = GetPhi(axis);
    while( phi < startPhi )    // Loop checking, 13.08.2015, G.Cosmo
      phi += twopi;
    
    if (phi > deltaPhi+startPhi)
    {
      //
      // Yeah, looks so. Make four three vectors defining the phi
      // opening
      //
      G4double cosP = std::cos(startPhi), sinP = std::sin(startPhi);
      G4ThreeVector a( r[0]*cosP, r[0]*sinP, z[0] );
      G4ThreeVector b( r[1]*cosP, r[1]*sinP, z[1] );
      cosP = std::cos(startPhi+deltaPhi); sinP = std::sin(startPhi+deltaPhi);
      G4ThreeVector c( r[0]*cosP, r[0]*sinP, z[0] );
      G4ThreeVector d( r[1]*cosP, r[1]*sinP, z[1] );
      
      G4double ad = axis.dot(a),
               bd = axis.dot(b),
               cd = axis.dot(c),
               dd = axis.dot(d);
      
      if (bd > ad) ad = bd;
      if (cd > ad) ad = cd;
      if (dd > ad) ad = dd;
      
      return ad;
    }
  }
 
  //
  // Check either end
  //
  G4double aPerp = axis.perp();
  
  G4double a = aPerp*r[0] + axis.z()*z[0];
  G4double b = aPerp*r[1] + axis.z()*z[1];
  
  if (b > a) a = b;
  
  return a;
}
 
// CalculateExtent
//
// See notes in G4VCSGface
//
void G4PolyconeSide::CalculateExtent( const EAxis axis, 
                                      const G4VoxelLimits& voxelLimit,
                                      const G4AffineTransform& transform,
                                            G4SolidExtentList& extentList )
{
  G4ClippablePolygon polygon;
  
  //
  // Here we will approximate (ala G4Cons) and divide our conical section
  // into segments, like G4Polyhedra. When doing so, the radius
  // is extented far enough such that the segments always lie
  // just outside the surface of the conical section we are
  // approximating.
  //
  
  //
  // Choose phi size of our segment(s) based on constants as
  // defined in meshdefs.hh
  //
  G4int numPhi = (G4int)(deltaPhi/kMeshAngleDefault) + 1;
  if (numPhi < kMinMeshSections) 
    numPhi = kMinMeshSections;
  else if (numPhi > kMaxMeshSections)
    numPhi = kMaxMeshSections;
    
  G4double sigPhi = deltaPhi/numPhi;
  
  //
  // Determine radius factor to keep segments outside
  //
  G4double rFudge = 1.0/std::cos(0.5*sigPhi);
  
  //
  // Decide which radius to use on each end of the side,
  // and whether a transition mesh is required
  //
  // {r0,z0}  - Beginning of this side
  // {r1,z1}  - Ending of this side
  // {r2,z0}  - Beginning of transition piece connecting previous
  //            side (and ends at beginning of this side)
  //
  // So, order is 2 --> 0 --> 1.
  //                    -------
  //
  // r2 < 0 indicates that no transition piece is required
  //
  G4double r0, r1, r2, z0, z1;
  
  r2 = -1;  // By default: no transition piece
  
  if (rNorm < -DBL_MIN)
  {
    //
    // This side faces *inward*, and so our mesh has
    // the same radius
    //
    r1 = r[1];
    z1 = z[1];
    z0 = z[0];
    r0 = r[0];
    
    r2 = -1;
    
    if (prevZS > DBL_MIN)
    {
      //
      // The previous side is facing outwards
      //
      if ( prevRS*zS - prevZS*rS > 0 )
      {
        //
        // Transition was convex: build transition piece
        //
        if (r[0] > DBL_MIN) r2 = r[0]*rFudge;
      }
      else
      {
        //
        // Transition was concave: short this side
        //
        FindLineIntersect( z0, r0, zS, rS,
                           z0, r0*rFudge, prevZS, prevRS*rFudge, z0, r0 );
      }
    }
    
    if ( nextZS > DBL_MIN && (rS*nextZS - zS*nextRS < 0) )
    {
      //
      // The next side is facing outwards, forming a 
      // concave transition: short this side
      //
      FindLineIntersect( z1, r1, zS, rS,
                         z1, r1*rFudge, nextZS, nextRS*rFudge, z1, r1 );
    }
  }
  else if (rNorm > DBL_MIN)
  {
    //
    // This side faces *outward* and is given a boost to
    // it radius
    //
    r0 = r[0]*rFudge;
    z0 = z[0];
    r1 = r[1]*rFudge;
    z1 = z[1];
    
    if (prevZS < -DBL_MIN)
    {
      //
      // The previous side is facing inwards
      //
      if ( prevRS*zS - prevZS*rS > 0 )
      {
        //
        // Transition was convex: build transition piece
        //
        if (r[0] > DBL_MIN) r2 = r[0];
      }
      else
      {
        //
        // Transition was concave: short this side
        //
        FindLineIntersect( z0, r0, zS, rS*rFudge,
                           z0, r[0], prevZS, prevRS, z0, r0 );
      }
    }
    
    if ( nextZS < -DBL_MIN && (rS*nextZS - zS*nextRS < 0) )
    {
      //
      // The next side is facing inwards, forming a 
      // concave transition: short this side
      //
      FindLineIntersect( z1, r1, zS, rS*rFudge,
                         z1, r[1], nextZS, nextRS, z1, r1 );
    }
  }
  else
  {
    //
    // This side is perpendicular to the z axis (is a disk)
    //
    // Whether or not r0 needs a rFudge factor depends
    // on the normal of the previous edge. Similar with r1
    // and the next edge. No transition piece is required.
    //
    r0 = r[0];
    r1 = r[1];
    z0 = z[0];
    z1 = z[1];
    
    if (prevZS > DBL_MIN) r0 *= rFudge;
    if (nextZS > DBL_MIN) r1 *= rFudge;
  }
  
  //
  // Loop
  //
  G4double phi = startPhi, 
           cosPhi = std::cos(phi), 
           sinPhi = std::sin(phi);
  
  G4ThreeVector v0( r0*cosPhi, r0*sinPhi, z0 ),
                    v1( r1*cosPhi, r1*sinPhi, z1 ),
  v2, w0, w1, w2;
  transform.ApplyPointTransform( v0 );
  transform.ApplyPointTransform( v1 );
  
  if (r2 >= 0)
  {
    v2 = G4ThreeVector( r2*cosPhi, r2*sinPhi, z0 );
    transform.ApplyPointTransform( v2 );
  }
 
  do    // Loop checking, 13.08.2015, G.Cosmo
  {
    phi += sigPhi;
    if (numPhi == 1) phi = startPhi+deltaPhi;  // Try to avoid roundoff
    cosPhi = std::cos(phi), 
    sinPhi = std::sin(phi);
    
    w0 = G4ThreeVector( r0*cosPhi, r0*sinPhi, z0 );
    w1 = G4ThreeVector( r1*cosPhi, r1*sinPhi, z1 );
    transform.ApplyPointTransform( w0 );
    transform.ApplyPointTransform( w1 );
    
    G4ThreeVector deltaV = r0 > r1 ? w0-v0 : w1-v1;
    
    //
    // Build polygon, taking special care to keep the vertices
    // in order
    //
    polygon.ClearAllVertices();
 
    polygon.AddVertexInOrder( v0 );
    polygon.AddVertexInOrder( v1 );
    polygon.AddVertexInOrder( w1 );
    polygon.AddVertexInOrder( w0 );
 
    //
    // Get extent
    //
    if (polygon.PartialClip( voxelLimit, axis ))
    {
      //
      // Get dot product of normal with target axis
      //
      polygon.SetNormal( deltaV.cross(v1-v0).unit() );
      
      extentList.AddSurface( polygon );
    }
    
    if (r2 >= 0)
    {
      //
      // Repeat, for transition piece
      //
      w2 = G4ThreeVector( r2*cosPhi, r2*sinPhi, z0 );
      transform.ApplyPointTransform( w2 );
 
      polygon.ClearAllVertices();
 
      polygon.AddVertexInOrder( v2 );
      polygon.AddVertexInOrder( v0 );
      polygon.AddVertexInOrder( w0 );
      polygon.AddVertexInOrder( w2 );
 
      if (polygon.PartialClip( voxelLimit, axis ))
      {
        polygon.SetNormal( deltaV.cross(v0-v2).unit() );
        
        extentList.AddSurface( polygon );
      }
      
      v2 = w2;
    }
    
    //
    // Next vertex
    //    
    v0 = w0;
    v1 = w1;
  } while( --numPhi > 0 );
  
  //
  // We are almost done. But, it is important that we leave no
  // gaps in the surface of our solid. By using rFudge, however,
  // we've done exactly that, if we have a phi segment. 
  // Add two additional faces if necessary
  //
  if (phiIsOpen && rNorm > DBL_MIN)
  {    
    cosPhi = std::cos(startPhi);
    sinPhi = std::sin(startPhi);
 
    G4ThreeVector a0( r[0]*cosPhi, r[0]*sinPhi, z[0] ),
                  a1( r[1]*cosPhi, r[1]*sinPhi, z[1] ),
                  b0( r0*cosPhi, r0*sinPhi, z[0] ),
                  b1( r1*cosPhi, r1*sinPhi, z[1] );
  
    transform.ApplyPointTransform( a0 );
    transform.ApplyPointTransform( a1 );
    transform.ApplyPointTransform( b0 );
    transform.ApplyPointTransform( b1 );
 
    polygon.ClearAllVertices();
 
    polygon.AddVertexInOrder( a0 );
    polygon.AddVertexInOrder( a1 );
    polygon.AddVertexInOrder( b0 );
    polygon.AddVertexInOrder( b1 );
    
    if (polygon.PartialClip( voxelLimit , axis))
    {
      G4ThreeVector normal( sinPhi, -cosPhi, 0 );
      polygon.SetNormal( transform.TransformAxis( normal ) );
        
      extentList.AddSurface( polygon );
    }
    
    cosPhi = std::cos(startPhi+deltaPhi);
    sinPhi = std::sin(startPhi+deltaPhi);
    
    a0 = G4ThreeVector( r[0]*cosPhi, r[0]*sinPhi, z[0] ),
    a1 = G4ThreeVector( r[1]*cosPhi, r[1]*sinPhi, z[1] ),
    b0 = G4ThreeVector( r0*cosPhi, r0*sinPhi, z[0] ),
    b1 = G4ThreeVector( r1*cosPhi, r1*sinPhi, z[1] );
    transform.ApplyPointTransform( a0 );
    transform.ApplyPointTransform( a1 );
    transform.ApplyPointTransform( b0 );
    transform.ApplyPointTransform( b1 );
 
    polygon.ClearAllVertices();
 
    polygon.AddVertexInOrder( a0 );
    polygon.AddVertexInOrder( a1 );
    polygon.AddVertexInOrder( b0 );
    polygon.AddVertexInOrder( b1 );
    
    if (polygon.PartialClip( voxelLimit, axis ))
    {
      G4ThreeVector normal( -sinPhi, cosPhi, 0 );
      polygon.SetNormal( transform.TransformAxis( normal ) );
        
      extentList.AddSurface( polygon );
    }
  }
    
  return;
}
 
// GetPhi
//
// Calculate Phi for a given 3-vector (point), if not already cached for the
// same point, in the attempt to avoid consecutive computation of the same
// quantity
//
G4double G4PolyconeSide::GetPhi( const G4ThreeVector& p )
{
  G4double val=0.;
  G4ThreeVector vphi(G4MT_pcphix, G4MT_pcphiy, G4MT_pcphiz);
 
  if (vphi != p)
  {
    val = p.phi();
    G4MT_pcphix = p.x(); G4MT_pcphiy = p.y(); G4MT_pcphiz = p.z();
    G4MT_pcphik = val;
  }
  else
  {
    val = G4MT_pcphik;
  }
  return val;
}
 
// DistanceAway
//
// Calculate distance of a point from our conical surface, including the effect
// of any phi segmentation
//
// Arguments:
//  p             - (in) Point to check
//  opposite      - (in) If true, check opposite hemisphere (see below)
//  distOutside   - (out) Additional distance outside the edges of the surface
//  edgeRZnorm    - (out) if negative, point is inside
//
//  return value = distance from the conical plane, if extrapolated beyond edges,
//                 signed by whether the point is in inside or outside the shape
//
// Notes:
//  * There are two answers, depending on which hemisphere is considered.
//
G4double G4PolyconeSide::DistanceAway( const G4ThreeVector& p,
                                             G4bool opposite,
                                             G4double& distOutside2,
                                             G4double* edgeRZnorm  )
{
  //
  // Convert our point to r and z
  //
  G4double rx = p.perp(), zx = p.z();
  
  //
  // Change sign of r if opposite says we should
  //
  if (opposite) rx = -rx;
  
  //
  // Calculate return value
  //
  G4double deltaR  = rx - r[0], deltaZ = zx - z[0];
  G4double answer = deltaR*rNorm + deltaZ*zNorm;
  
  //
  // Are we off the surface in r,z space?
  //
  G4double q = deltaR*rS + deltaZ*zS;
  if (q < 0)
  {
    distOutside2 = q*q;
    if (edgeRZnorm != nullptr)
      *edgeRZnorm = deltaR*rNormEdge[0] + deltaZ*zNormEdge[0];
  }
  else if (q > length)
  {
    distOutside2 = sqr( q-length );
    if (edgeRZnorm != nullptr)
    {
      deltaR = rx - r[1];
      deltaZ = zx - z[1];
      *edgeRZnorm = deltaR*rNormEdge[1] + deltaZ*zNormEdge[1];
    }
  }
  else
  {
    distOutside2 = 0.;
    if (edgeRZnorm != nullptr) *edgeRZnorm = answer;
  }
 
  if (phiIsOpen)
  {
    //
    // Finally, check phi
    //
    G4double phi = GetPhi(p);
    while( phi < startPhi )    // Loop checking, 13.08.2015, G.Cosmo
      phi += twopi;
    
    if (phi > startPhi+deltaPhi)
    {
      //
      // Oops. Are we closer to the start phi or end phi?
      //
      G4double d1 = phi-startPhi-deltaPhi;
      while( phi > startPhi )    // Loop checking, 13.08.2015, G.Cosmo
        phi -= twopi;
      G4double d2 = startPhi-phi;
      
      if (d2 < d1) d1 = d2;
      
      //
      // Add result to our distance
      //
      G4double dist = d1*rx;
      
      distOutside2 += dist*dist;
      if (edgeRZnorm != nullptr)
      {
        *edgeRZnorm = std::max(std::fabs(*edgeRZnorm),std::fabs(dist));
      }
    }
  }
 
  return answer;
}
 
// DistanceAway
//
// Special version of DistanceAway for Inside.
// Opposite parameter is not used, instead use sign of rx for choosing the side
//
G4double G4PolyconeSide::DistanceAway( const G4ThreeVector& p,
                                             G4double& distOutside2,
                                             G4double* edgeRZnorm  )
{
  //
  // Convert our point to r and z
  //
  G4double rx = p.perp(), zx = p.z();
  
  //
  // Change sign of r if we should
  //
  G4int part = 1;
  if (rx < 0) part = -1;
  
  //
  // Calculate return value
  //
  G4double deltaR = rx - r[0]*part, deltaZ = zx - z[0];
  G4double answer = deltaR*rNorm*part + deltaZ*zNorm;
  
  //
  // Are we off the surface in r,z space?
  //
  G4double q = deltaR*rS*part + deltaZ*zS;
  if (q < 0)
  {
    distOutside2 = q*q;
    if (edgeRZnorm != nullptr)
    {
      *edgeRZnorm = deltaR*rNormEdge[0]*part + deltaZ*zNormEdge[0];
    }
  }
  else if (q > length)
  {
    distOutside2 = sqr( q-length );
    if (edgeRZnorm != nullptr)
    {
      deltaR = rx - r[1]*part;
      deltaZ = zx - z[1];
      *edgeRZnorm = deltaR*rNormEdge[1]*part + deltaZ*zNormEdge[1];
    }
  }
  else
  {
    distOutside2 = 0.;
    if (edgeRZnorm != nullptr) *edgeRZnorm = answer;
  }
 
  if (phiIsOpen)
  {
    //
    // Finally, check phi
    //
    G4double phi = GetPhi(p);
    while( phi < startPhi )    // Loop checking, 13.08.2015, G.Cosmo
      phi += twopi;
    
    if (phi > startPhi+deltaPhi)
    {
      //
      // Oops. Are we closer to the start phi or end phi?
      //
      G4double d1 = phi-startPhi-deltaPhi;
      while( phi > startPhi )    // Loop checking, 13.08.2015, G.Cosmo
        phi -= twopi;
      G4double d2 = startPhi-phi;
      
      if (d2 < d1) d1 = d2;
      
      //
      // Add result to our distance
      //
      G4double dist = d1*rx*part;
      
      distOutside2 += dist*dist;
      if (edgeRZnorm != nullptr)
      {
        *edgeRZnorm = std::max(std::fabs(*edgeRZnorm),std::fabs(dist));
      }
    }
  }
 
  return answer;
}
 
// PointOnCone
//
// Decide if a point is on a cone and return normal if it is
//
G4bool G4PolyconeSide::PointOnCone( const G4ThreeVector& hit,
                                          G4double normSign,
                                    const G4ThreeVector& p,
                                    const G4ThreeVector& v,
                                          G4ThreeVector& normal )
{
  G4double rx = hit.perp();
  //
  // Check radial/z extent, as appropriate
  //
  if (!cone->HitOn( rx, hit.z() )) return false;
  
  if (phiIsOpen)
  {
    G4double phiTolerant = 2.0*kCarTolerance/(rx+kCarTolerance);
    //
    // Check phi segment. Here we have to be careful
    // to use the standard method consistent with
    // PolyPhiFace. See PolyPhiFace::InsideEdgesExact
    //
    G4double phi = GetPhi(hit);
    while( phi < startPhi-phiTolerant )   // Loop checking, 13.08.2015, G.Cosmo
      phi += twopi;
    
    if (phi > startPhi+deltaPhi+phiTolerant) return false;
    
    if (phi > startPhi+deltaPhi-phiTolerant)
    {
      //
      // Exact treatment
      //
      G4ThreeVector qx = p + v;
      G4ThreeVector qa = qx - corners[2],
              qb = qx - corners[3];
      G4ThreeVector qacb = qa.cross(qb);
      
      if (normSign*qacb.dot(v) < 0) return false;
    }
    else if (phi < phiTolerant)
    {
      G4ThreeVector qx = p + v;
      G4ThreeVector qa = qx - corners[1],
              qb = qx - corners[0];
      G4ThreeVector qacb = qa.cross(qb);
      
      if (normSign*qacb.dot(v) < 0) return false;
    }
  }
  
  //
  // We have a good hit! Calculate normal
  //
  if (rx < DBL_MIN) 
    normal = G4ThreeVector( 0, 0, zNorm < 0 ? -1 : 1 );
  else
    normal = G4ThreeVector( rNorm*hit.x()/rx, rNorm*hit.y()/rx, zNorm );
  return true;
}
 
// FindLineIntersect
//
// Decide the point at which two 2-dimensional lines intersect
//
// Equation of line: x = x1 + s*tx1
//                   y = y1 + s*ty1
//
// It is assumed that the lines are *not* parallel
//
void G4PolyconeSide::FindLineIntersect( G4double x1,  G4double y1,
                                        G4double tx1, G4double ty1,
                                        G4double x2,  G4double y2,
                                        G4double tx2, G4double ty2,
                                        G4double& x,  G4double& y )
{
  //
  // The solution is a simple linear equation
  //
  G4double deter = tx1*ty2 - tx2*ty1;
  
  G4double s1 = ((x2-x1)*ty2 - tx2*(y2-y1))/deter;
  G4double s2 = ((x2-x1)*ty1 - tx1*(y2-y1))/deter;
 
  //
  // We want the answer to not depend on which order the
  // lines were specified. Take average.
  //
  x = 0.5*( x1+s1*tx1 + x2+s2*tx2 );
  y = 0.5*( y1+s1*ty1 + y2+s2*ty2 );
}
 
// Calculate surface area for GetPointOnSurface()
//
G4double G4PolyconeSide::SurfaceArea() 
{ 
  if(fSurfaceArea==0.)
  {
    fSurfaceArea = (r[0]+r[1])* std::sqrt(sqr(r[0]-r[1])+sqr(z[0]-z[1]));
    fSurfaceArea *= 0.5*(deltaPhi);
  }  
  return fSurfaceArea;
}
 
// GetPointOnFace
//
G4ThreeVector G4PolyconeSide::GetPointOnFace()
{
  G4double x,y,zz;
  G4double rr,phi,dz,dr;
  dr=r[1]-r[0];dz=z[1]-z[0];
  phi=startPhi+deltaPhi*G4UniformRand();
  rr=r[0]+dr*G4UniformRand();
 
  x=rr*std::cos(phi);
  y=rr*std::sin(phi);
 
  // PolyconeSide has a Ring Form
  //
  if (dz==0.)
  {
    zz=z[0];
  }
  else
  {
    if(dr==0.)  // PolyconeSide has a Tube Form
    {
      zz = z[0]+dz*G4UniformRand();
    }
    else
    {
      zz = z[0]+(rr-r[0])*dz/dr;
    }
  }
 
  return {x,y,zz};
}