#include <G4HelixHeum.hh>

Inheritance diagram for G4HelixHeum:

Public Member Functions
G4double	DistChord () const

void	DumbStepper (const G4double y[], G4ThreeVector Bfld, G4double h, G4double yout[])

	G4HelixHeum (G4Mag_EqRhs *EqRhs)

G4EquationOfMotion *	GetEquationOfMotion ()

const G4EquationOfMotion *	GetEquationOfMotion () const

unsigned long	GetfNoRHSCalls ()

G4int	GetNumberOfStateVariables () const

G4int	GetNumberOfVariables () const

G4int	IntegrationOrder ()

G4int	IntegratorOrder () const

G4bool	IsFSAL () const

void	NormalisePolarizationVector (G4double vec[12])

void	NormaliseTangentVector (G4double vec[6])

void	ResetfNORHSCalls ()

void	RightHandSide (const G4double y[], G4double dydx[]) const

void	RightHandSide (const G4double y[], G4double dydx[], G4double field[]) const

void	SetEquationOfMotion (G4EquationOfMotion *newEquation)

virtual void	Stepper (const G4double y[], const G4double dydx[], G4double h, G4double yout[], G4double yerr[])

	~G4HelixHeum ()

Protected Member Functions
void	AdvanceHelix (const G4double yIn[], G4ThreeVector Bfld, G4double h, G4double yHelix[], G4double yHelix2[]=0)

G4double	GetAngCurve () const

G4double	GetCurve () const

G4double	GetInverseCurve (const G4double Momentum, const G4double Bmag)

G4double	GetRadHelix () const

void	LinearStep (const G4double yIn[], G4double h, G4double yHelix[]) const

void	MagFieldEvaluate (const G4double y[], G4ThreeVector &Bfield)

void	SetAngCurve (const G4double Ang)

void	SetCurve (const G4double Curve)

void	SetFSAL (G4bool flag=true)

void	SetIntegrationOrder (G4int order)

void	SetRadHelix (const G4double Rad)

Private Attributes
G4double	fAngCurve = 0.0

G4EquationOfMotion *	fEquation_Rhs = nullptr

G4int	fIntegrationOrder = -1

G4bool	fIsFSAL = false

const G4int	fNoIntegrationVariables = 0

unsigned long	fNoRHSCalls = 0UL

const G4int	fNoStateVariables = 0

G4Mag_EqRhs *	fPtrMagEqOfMot = nullptr

G4double	frCurve = 0.0

G4double	frHelix = 0.0

G4ThreeVector	yFinal

G4ThreeVector	yInitial

G4ThreeVector	yMidPoint

Static Private Attributes
static const G4double	fUnitConstant = 0.299792458(GeV/(teslam))

Detailed Description

Definition at line 43 of file G4HelixHeum.hh.

Constructor & Destructor Documentation

◆ G4HelixHeum()

G4HelixHeum::G4HelixHeum ( G4Mag_EqRhs * EqRhs )

Definition at line 41 of file G4HelixHeum.cc.

  : G4MagHelicalStepper(EqRhs)
{
}

◆ ~G4HelixHeum()

G4HelixHeum::~G4HelixHeum ( )

Definition at line 46 of file G4HelixHeum.cc.

47{

48}

Member Function Documentation

◆ AdvanceHelix()

void G4MagHelicalStepper::AdvanceHelix	(	const G4double	yIn[],
		G4ThreeVector	Bfld,
		G4double	h,
		G4double	yHelix[],
		G4double	yHelix2[] = `0`
	)

protectedinherited

Definition at line 57 of file G4MagHelicalStepper.cc.

{
  // const G4int    nvar = 6;
 
  // OLD  const G4double approc_limit = 0.05;
  // OLD  approc_limit = 0.05 gives max.error=x^5/5!=(0.05)^5/5!=2.6*e-9
  // NEW  approc_limit = 0.005 gives max.error=x^5/5!=2.6*e-14
 
  const G4double approc_limit = 0.005;
  G4ThreeVector  Bnorm, B_x_P, vperp, vpar;
 
  G4double B_d_P;
  G4double B_v_P;
  G4double Theta;
  G4double R_1;
  G4double R_Helix;
  G4double CosT2, SinT2, CosT, SinT;
  G4ThreeVector positionMove, endTangent;
 
  G4double Bmag = Bfld.mag();
  const G4double* pIn = yIn+3;
  G4ThreeVector initVelocity = G4ThreeVector( pIn[0], pIn[1], pIn[2]);
  G4double      velocityVal = initVelocity.mag();
  G4ThreeVector initTangent = (1.0/velocityVal) * initVelocity;
  
  R_1 = GetInverseCurve(velocityVal,Bmag);
 
  // for too small magnetic fields there is no curvature
  // (include momentum here) FIXME
 
  if( (std::fabs(R_1) < 1e-10)||(Bmag<1e-12) )
  {
    LinearStep( yIn, h, yHelix );
 
    // Store and/or calculate parameters for chord distance
 
    SetAngCurve(1.);     
    SetCurve(h);
    SetRadHelix(0.);
  }
  else
  {
    Bnorm = (1.0/Bmag)*Bfld;
 
    // calculate the direction of the force
    
    B_x_P = Bnorm.cross(initTangent);
 
    // parallel and perp vectors
 
    B_d_P = Bnorm.dot(initTangent); // this is the fraction of P parallel to B
 
    vpar = B_d_P * Bnorm;       // the component parallel      to B
    vperp= initTangent - vpar;  // the component perpendicular to B
    
    B_v_P  = std::sqrt( 1 - B_d_P * B_d_P); // Fraction of P perp to B
 
    // calculate  the stepping angle
  
    Theta   = R_1 * h; // * B_v_P;
 
    // Trigonometrix
      
    if( std::fabs(Theta) > approc_limit )
    {
       SinT     = std::sin(Theta);
       CosT     = std::cos(Theta);
    }
    else
    {
      G4double Theta2 = Theta*Theta;
      G4double Theta3 = Theta2 * Theta;
      G4double Theta4 = Theta2 * Theta2;
      SinT     = Theta - 1.0/6.0 * Theta3;
      CosT     = 1 - 0.5 * Theta2 + 1.0/24.0 * Theta4;
    }
 
    // the actual "rotation"
 
    G4double R = 1.0 / R_1;
 
    positionMove  = R * ( SinT * vperp + (1-CosT) * B_x_P) + h * vpar;
    endTangent    = CosT * vperp + SinT * B_x_P + vpar;
 
    // Store the resulting position and tangent
 
    yHelix[0]   = yIn[0] + positionMove.x(); 
    yHelix[1]   = yIn[1] + positionMove.y(); 
    yHelix[2]   = yIn[2] + positionMove.z();
    yHelix[3] = velocityVal * endTangent.x();
    yHelix[4] = velocityVal * endTangent.y();
    yHelix[5] = velocityVal * endTangent.z();
 
    // Store 2*h step Helix if exist
 
    if(yHelix2)
    {
      SinT2     = 2.0 * SinT * CosT;
      CosT2     = 1.0 - 2.0 * SinT * SinT;
      endTangent    = (CosT2 * vperp + SinT2 * B_x_P + vpar);
      positionMove  = R * ( SinT2 * vperp + (1-CosT2) * B_x_P) + h*2 * vpar;
      
      yHelix2[0]   = yIn[0] + positionMove.x(); 
      yHelix2[1]   = yIn[1] + positionMove.y(); 
      yHelix2[2]   = yIn[2] + positionMove.z(); 
      yHelix2[3] = velocityVal * endTangent.x();
      yHelix2[4] = velocityVal * endTangent.y();
      yHelix2[5] = velocityVal * endTangent.z();
    }
 
    // Store and/or calculate parameters for chord distance
 
    G4double ptan=velocityVal*B_v_P;
 
    G4double particleCharge = fPtrMagEqOfMot->FCof() / (eplus*c_light); 
    R_Helix =std::abs( ptan/(fUnitConstant  * particleCharge*Bmag));
       
    SetAngCurve(std::abs(Theta));
    SetCurve(std::abs(R));
    SetRadHelix(R_Helix);
  }
}

References source.hepunit::c_light, CLHEP::Hep3Vector::cross(), CLHEP::Hep3Vector::dot(), eplus, G4Mag_EqRhs::FCof(), G4MagHelicalStepper::fPtrMagEqOfMot, G4MagHelicalStepper::fUnitConstant, G4MagHelicalStepper::GetInverseCurve(), G4MagHelicalStepper::LinearStep(), CLHEP::Hep3Vector::mag(), G4MagHelicalStepper::SetAngCurve(), G4MagHelicalStepper::SetCurve(), G4MagHelicalStepper::SetRadHelix(), CLHEP::Hep3Vector::x(), CLHEP::Hep3Vector::y(), and CLHEP::Hep3Vector::z().

Referenced by G4ExactHelixStepper::DumbStepper(), G4HelixExplicitEuler::DumbStepper(), DumbStepper(), G4HelixImplicitEuler::DumbStepper(), G4HelixMixedStepper::DumbStepper(), G4HelixSimpleRunge::DumbStepper(), G4HelixExplicitEuler::Stepper(), G4ExactHelixStepper::Stepper(), and G4HelixMixedStepper::Stepper().

◆ DistChord()

G4double G4MagHelicalStepper::DistChord ( ) const

virtualinherited

Implements G4MagIntegratorStepper.

Definition at line 235 of file G4MagHelicalStepper.cc.

{
  // Check whether h/R >  pi  !!
  // Method DistLine is good only for <  pi
 
  G4double Ang=GetAngCurve();
  if(Ang<=pi)
  {
    return GetRadHelix()*(1-std::cos(0.5*Ang));
  }
  else
  {
    if(Ang<twopi)
    {
      return GetRadHelix()*(1+std::cos(0.5*(twopi-Ang)));
    }
    else  // return Diameter of projected circle
    {
      return 2*GetRadHelix();
    }
  }
}

References G4MagHelicalStepper::GetAngCurve(), G4MagHelicalStepper::GetRadHelix(), pi, and twopi.

◆ DumbStepper()

void G4HelixHeum::DumbStepper	(	const G4double	y[],
		G4ThreeVector	Bfld,
		G4double	h,
		G4double	yout[]
	)

virtual

Implements G4MagHelicalStepper.

Definition at line 51 of file G4HelixHeum.cc.

{
  const G4int nvar = 6 ;
 
  G4ThreeVector Bfield_Temp, Bfield_Temp2;
  G4double yTemp[6], yAdd1[6], yAdd2[6] , yTemp2[6];
 
  AdvanceHelix( yIn, Bfld, h, yAdd1 );
  
  AdvanceHelix( yIn, Bfld, h/3.0, yTemp );
  MagFieldEvaluate(yTemp,Bfield_Temp);
 
  AdvanceHelix( yIn, Bfield_Temp, (2.0 / 3.0) * h, yTemp2 );
  
  MagFieldEvaluate(yTemp2,Bfield_Temp2);
 
  AdvanceHelix( yIn, Bfield_Temp2, h, yAdd2 );
 
  for( G4int i = 0; i < nvar; ++i )
  {
    yOut[i] = ( 0.25 * yAdd1[i] + 0.75 * yAdd2[i]);
  }
 
  // NormaliseTangentVector( yOut );           
}  

References G4MagHelicalStepper::AdvanceHelix(), and G4MagHelicalStepper::MagFieldEvaluate().

◆ GetAngCurve()

G4double G4MagHelicalStepper::GetAngCurve ( ) const

inlineprotectedinherited

Referenced by G4ExactHelixStepper::DistChord(), G4HelixExplicitEuler::DistChord(), G4HelixMixedStepper::DistChord(), G4MagHelicalStepper::DistChord(), and G4HelixExplicitEuler::Stepper().

◆ GetCurve()

G4double G4MagHelicalStepper::GetCurve ( ) const

inlineprotectedinherited

◆ GetEquationOfMotion() [1/2]

G4EquationOfMotion * G4MagIntegratorStepper::GetEquationOfMotion ( )

inlineinherited

Referenced by G4MagInt_Driver::GetEquationOfMotion(), G4OldMagIntDriver::GetEquationOfMotion(), G4NystromRK4::GetField(), G4DormandPrince745::GetSpecificEquation(), G4NystromRK4::SetDistanceForConstantField(), G4RKG3_Stepper::StepNoErr(), and G4RKG3_Stepper::Stepper().

◆ GetEquationOfMotion() [2/2]

const G4EquationOfMotion * G4MagIntegratorStepper::GetEquationOfMotion ( ) const

inlineinherited

◆ GetfNoRHSCalls()

unsigned long G4MagIntegratorStepper::GetfNoRHSCalls ( )

inlineinherited

◆ GetInverseCurve()

G4double G4MagHelicalStepper::GetInverseCurve	(	const G4double	Momentum,
		const G4double	Bmag
	)

inlineprotectedinherited

Referenced by G4MagHelicalStepper::AdvanceHelix(), and G4HelixMixedStepper::Stepper().

◆ GetNumberOfStateVariables()

G4int G4MagIntegratorStepper::GetNumberOfStateVariables ( ) const

inlineinherited

Referenced by G4BogackiShampine45::G4BogackiShampine45(), G4CashKarpRKF45::G4CashKarpRKF45(), G4SimpleRunge::G4SimpleRunge(), G4TSimpleRunge< T_Equation, N >::G4TSimpleRunge(), G4TsitourasRK45::G4TsitourasRK45(), G4BogackiShampine23::makeStep(), G4RK547FEq1::makeStep(), G4RK547FEq2::makeStep(), G4RK547FEq3::makeStep(), G4ConstRK4::Stepper(), G4MagErrorStepper::Stepper(), and G4TMagErrorStepper< T_Stepper, T_Equation, N >::Stepper().

◆ GetNumberOfVariables()

G4int G4MagIntegratorStepper::GetNumberOfVariables ( ) const

inlineinherited

Referenced by G4ExplicitEuler::DumbStepper(), G4ImplicitEuler::DumbStepper(), G4ClassicalRK4::DumbStepper(), G4ChordFinder::G4ChordFinder(), G4BogackiShampine45::GetLastDydx(), G4DoLoMcPriRK34::Interpolate(), G4TsitourasRK45::Interpolate(), G4DormandPrince745::Interpolate4thOrder(), G4DormandPrince745::Interpolate5thOrder(), G4DormandPrinceRK56::Interpolate_high(), G4DormandPrinceRK56::Interpolate_low(), G4BogackiShampine45::InterpolateHigh(), G4BogackiShampine23::makeStep(), G4RK547FEq1::makeStep(), G4RK547FEq2::makeStep(), G4RK547FEq3::makeStep(), G4DormandPrinceRK56::SetupInterpolate_high(), G4DormandPrinceRK56::SetupInterpolate_low(), G4DormandPrince745::SetupInterpolation5thOrder(), G4BogackiShampine45::SetupInterpolationHigh(), G4BogackiShampine45::Stepper(), G4CashKarpRKF45::Stepper(), G4DoLoMcPriRK34::Stepper(), G4DormandPrinceRK56::Stepper(), G4DormandPrinceRK78::Stepper(), G4MagErrorStepper::Stepper(), G4TsitourasRK45::Stepper(), and G4DormandPrince745::Stepper().

◆ GetRadHelix()

G4double G4MagHelicalStepper::GetRadHelix ( ) const

inlineprotectedinherited

Referenced by G4ExactHelixStepper::DistChord(), G4HelixExplicitEuler::DistChord(), G4HelixMixedStepper::DistChord(), and G4MagHelicalStepper::DistChord().

◆ IntegrationOrder()

G4int G4MagIntegratorStepper::IntegrationOrder ( )

inlineinherited

◆ IntegratorOrder()

G4int G4HelixHeum::IntegratorOrder ( ) const

inlinevirtual

Implements G4MagIntegratorStepper.

Definition at line 58 of file G4HelixHeum.hh.

58{ return 2; }

◆ IsFSAL()

G4bool G4MagIntegratorStepper::IsFSAL ( ) const

inlineinherited

◆ LinearStep()

void G4MagHelicalStepper::LinearStep	(	const G4double	yIn[],
		G4double	h,
		G4double	yHelix[]
	)		const

inlineprotectedinherited

Referenced by G4MagHelicalStepper::AdvanceHelix().

◆ MagFieldEvaluate()

void G4MagHelicalStepper::MagFieldEvaluate	(	const G4double	y[],
		G4ThreeVector &	Bfield
	)

inlineprotectedinherited

Referenced by DumbStepper(), G4HelixImplicitEuler::DumbStepper(), G4HelixSimpleRunge::DumbStepper(), G4HelixExplicitEuler::Stepper(), G4ExactHelixStepper::Stepper(), G4HelixMixedStepper::Stepper(), and G4MagHelicalStepper::Stepper().

◆ NormalisePolarizationVector()

void G4MagIntegratorStepper::NormalisePolarizationVector ( G4double vec[12] )

inlineinherited

Referenced by G4SimpleHeum::DumbStepper(), and G4ClassicalRK4::DumbStepper().

◆ NormaliseTangentVector()

void G4MagIntegratorStepper::NormaliseTangentVector ( G4double vec[6] )

inlineinherited

◆ ResetfNORHSCalls()

void G4MagIntegratorStepper::ResetfNORHSCalls ( )

inlineinherited

◆ RightHandSide() [1/2]

void G4MagIntegratorStepper::RightHandSide	(	const G4double	y[],
		G4double	dydx[]
	)		const

inlineinherited

◆ RightHandSide() [2/2]

void G4MagIntegratorStepper::RightHandSide	(	const G4double	y[],
		G4double	dydx[],
		G4double	field[]
	)		const

inlineinherited

◆ SetAngCurve()

void G4MagHelicalStepper::SetAngCurve ( const G4double Ang )

inlineprotectedinherited

Referenced by G4MagHelicalStepper::AdvanceHelix(), G4HelixExplicitEuler::Stepper(), and G4HelixMixedStepper::Stepper().

◆ SetCurve()

void G4MagHelicalStepper::SetCurve ( const G4double Curve )

inlineprotectedinherited

Referenced by G4MagHelicalStepper::AdvanceHelix(), and G4HelixMixedStepper::Stepper().

◆ SetEquationOfMotion()

void G4MagIntegratorStepper::SetEquationOfMotion ( G4EquationOfMotion * newEquation )

inlineinherited

Referenced by G4MagInt_Driver::SetEquationOfMotion(), and G4OldMagIntDriver::SetEquationOfMotion().

◆ SetFSAL()

void G4MagIntegratorStepper::SetFSAL ( G4bool flag = true )

inlineprotectedinherited

Referenced by G4BogackiShampine23::G4BogackiShampine23().

◆ SetIntegrationOrder()

void G4MagIntegratorStepper::SetIntegrationOrder ( G4int order )

inlineprotectedinherited

Referenced by G4BogackiShampine23::G4BogackiShampine23().

◆ SetRadHelix()

void G4MagHelicalStepper::SetRadHelix ( const G4double Rad )

inlineprotectedinherited

Referenced by G4MagHelicalStepper::AdvanceHelix().

◆ Stepper()

void G4MagHelicalStepper::Stepper	(	const G4double	y[],
		const G4double	dydx[],
		G4double	h,
		G4double	yout[],
		G4double	yerr[]
	)

virtualinherited

Implements G4MagIntegratorStepper.

Reimplemented in G4ExactHelixStepper, and G4HelixMixedStepper.

Definition at line 188 of file G4MagHelicalStepper.cc.

{  
   const G4int nvar = 6;
 
   // correction for Richardson Extrapolation.
   // G4double  correction = 1. / ( (1 << IntegratorOrder()) -1 );
   
   G4double      yTemp[8], yIn[8] ;
   G4ThreeVector Bfld_initial, Bfld_midpoint;
   
   //  Saving yInput because yInput and yOut can be aliases for same array
   //
   for(G4int i=0; i<nvar; ++i)
   {
     yIn[i]=yInput[i];
   }
 
   G4double h = hstep * 0.5; 
 
   MagFieldEvaluate(yIn, Bfld_initial) ;      
 
   // Do two half steps
   //
   DumbStepper(yIn, Bfld_initial, h, yTemp);
   MagFieldEvaluate(yTemp, Bfld_midpoint) ;     
   DumbStepper(yTemp, Bfld_midpoint, h, yOut); 
 
   // Do a full Step
   //
   h = hstep ;
   DumbStepper(yIn, Bfld_initial, h, yTemp);
 
   // Error estimation
   //
   for(G4int i=0; i<nvar; ++i)
   {
     yErr[i] = yOut[i] - yTemp[i] ;
   }
   
   return;
}

References G4MagHelicalStepper::DumbStepper(), and G4MagHelicalStepper::MagFieldEvaluate().

Field Documentation

◆ fAngCurve

G4double G4MagHelicalStepper::fAngCurve = 0.0

privateinherited

Definition at line 120 of file G4MagHelicalStepper.hh.

◆ fEquation_Rhs

G4EquationOfMotion* G4MagIntegratorStepper::fEquation_Rhs = nullptr

privateinherited

Definition at line 124 of file G4MagIntegratorStepper.hh.

◆ fIntegrationOrder

G4int G4MagIntegratorStepper::fIntegrationOrder = -1

privateinherited

Definition at line 134 of file G4MagIntegratorStepper.hh.

◆ fIsFSAL

G4bool G4MagIntegratorStepper::fIsFSAL = false

privateinherited

Definition at line 136 of file G4MagIntegratorStepper.hh.

◆ fNoIntegrationVariables

const G4int G4MagIntegratorStepper::fNoIntegrationVariables = 0

privateinherited

Definition at line 125 of file G4MagIntegratorStepper.hh.

◆ fNoRHSCalls

unsigned long G4MagIntegratorStepper::fNoRHSCalls = 0UL

mutableprivateinherited

Definition at line 128 of file G4MagIntegratorStepper.hh.

◆ fNoStateVariables

const G4int G4MagIntegratorStepper::fNoStateVariables = 0

privateinherited

Definition at line 126 of file G4MagIntegratorStepper.hh.

◆ fPtrMagEqOfMot

G4Mag_EqRhs* G4MagHelicalStepper::fPtrMagEqOfMot = nullptr

privateinherited

Definition at line 116 of file G4MagHelicalStepper.hh.

Referenced by G4MagHelicalStepper::AdvanceHelix().

◆ frCurve

G4double G4MagHelicalStepper::frCurve = 0.0

privateinherited

Definition at line 121 of file G4MagHelicalStepper.hh.

◆ frHelix

G4double G4MagHelicalStepper::frHelix = 0.0

privateinherited

Definition at line 122 of file G4MagHelicalStepper.hh.

◆ fUnitConstant

const G4double G4MagHelicalStepper::fUnitConstant = 0.299792458*(GeV/(tesla*m))

staticprivateinherited

Definition at line 113 of file G4MagHelicalStepper.hh.

Referenced by G4MagHelicalStepper::AdvanceHelix().

◆ yFinal

G4ThreeVector G4MagHelicalStepper::yFinal

privateinherited

Definition at line 123 of file G4MagHelicalStepper.hh.

◆ yInitial

G4ThreeVector G4MagHelicalStepper::yInitial

privateinherited

Definition at line 123 of file G4MagHelicalStepper.hh.

◆ yMidPoint

G4ThreeVector G4MagHelicalStepper::yMidPoint

privateinherited

Definition at line 123 of file G4MagHelicalStepper.hh.

The documentation for this class was generated from the following files:

source/geometry/magneticfield/include/G4HelixHeum.hh
source/geometry/magneticfield/src/G4HelixHeum.cc

Public Member Functions

Protected Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ G4HelixHeum()

◆ ~G4HelixHeum()

Member Function Documentation

◆ AdvanceHelix()

◆ DistChord()

◆ DumbStepper()

◆ GetAngCurve()

◆ GetCurve()

◆ GetEquationOfMotion() [1/2]

◆ GetEquationOfMotion() [2/2]

◆ GetfNoRHSCalls()

◆ GetInverseCurve()

◆ GetNumberOfStateVariables()

◆ GetNumberOfVariables()

◆ GetRadHelix()

◆ IntegrationOrder()

◆ IntegratorOrder()

◆ IsFSAL()

◆ LinearStep()

◆ MagFieldEvaluate()

◆ NormalisePolarizationVector()

◆ NormaliseTangentVector()

◆ ResetfNORHSCalls()

◆ RightHandSide() [1/2]

◆ RightHandSide() [2/2]

◆ SetAngCurve()

◆ SetCurve()

◆ SetEquationOfMotion()

◆ SetFSAL()

◆ SetIntegrationOrder()

◆ SetRadHelix()

◆ Stepper()

Field Documentation

◆ fAngCurve

◆ fEquation_Rhs

◆ fIntegrationOrder

◆ fIsFSAL

◆ fNoIntegrationVariables

◆ fNoRHSCalls

◆ fNoStateVariables

◆ fPtrMagEqOfMot

◆ frCurve

◆ frHelix

◆ fUnitConstant

◆ yFinal

◆ yInitial

◆ yMidPoint