PerigeeCircle Class Reference

Extension of the generalized circle also caching the perigee coordinates. More...

#include <PerigeeCircle.h>

Public Member Functions
	PerigeeCircle ()
	Default constructor for ROOT compatibility.
	PerigeeCircle (double curvature, const Vector2D &phi0Vec, double impact)
	Constructor from the perigee parammeters.
	PerigeeCircle (double curvature, double phi0, double impact)
	Constructor from the perigee parammeters.
	PerigeeCircle (const PerigeeParameters &perigeeParameters)
	Constructor from the perigee parammeters.
	PerigeeCircle (const Line2D &n012)
	Constructor from a two dimensional line.
	PerigeeCircle (const GeneralizedCircle &n0123)
	Constructor promoting the generalized circle.
	PerigeeCircle (const Circle2D &circle)
	Constructor from a two dimensional circle in center / radius representation.
void	invalidate ()
	Sets all circle parameters to zero.
bool	isInvalid () const
	Indicates if all circle parameters are zero.
bool	isValid () const
	Indicates if the combination of the circle parameters makes up a valid circle.
void	reverse ()
	Flips the orientation of the circle in place.
PerigeeCircle	reversed () const
	Returns a copy of the circle with opposite orientation.
void	conformalTransform ()
	Transforms the generalized circle to conformal space inplace.
PerigeeCircle	conformalTransformed () const
	Returns a copy of the circle in conformal space.
void	passiveMoveBy (const Vector2D &by)
	Moves the coordinates system by the given vector. Updates perigee parameters in place.
PerigeeJacobian	passiveMoveByJacobian (const Vector2D &by) const
	Computes the Jacobi matrix for a move of the coordinate system by the given vector.
void	passiveMoveByJacobian (const Vector2D &by, PerigeeJacobian &jacobian) const
	Puts the Jacobi matrix for a move of the coordinate system by the given vector in the given matrix as an output argument.
Vector2D	atArcLength (double arcLength) const
	Calculates the point, which lies at the give perpendicular travel distance (counted from the perigee)
double	arcLengthTo (const Vector2D &point) const
	Calculates the arc length between the perigee and the given point.
double	arcLengthBetween (const Vector2D &from, const Vector2D &to) const
	Calculates the arc length between two points of closest approach on the circle.
double	arcLengthToCylindricalR (double cylindricalR) const
	Calculates the two dimensional arc length till the cylindrical radius is reached If the radius can not be reached return NAN.
std::pair< Vector2D, Vector2D >	atCylindricalR (double cylindricalR) const
	Calculates the two points with the given cylindrical radius on the generalised circle.
Vector2D	atCylindricalRForwardOf (const Vector2D &startPoint, double cylindricalR) const
	Approach on the circle with the given cylindrical radius that lies in the forward direction of a start point.
EForwardBackward	isForwardOrBackwardOf (const Vector2D &from, const Vector2D &to) const
	Indicates whether to given point lies in the forward direction from the perigee.
EForwardBackward	isForwardOrBackward (const Vector2D &to) const
	Indicates whether to given point lies in the forward direction from the perigee.
Vector2D	chooseNextForwardOf (const Vector2D &start, const Vector2D &end1, const Vector2D &end2) const
	Returns the one of two end point which is first reached from the given start if one stricly follows the forward direction of the circle.
Vector2D	closest (const Vector2D &point) const
	Calculates the point of closest approach on the circle to the given point.
double	distance (const Vector2D &point) const
	Getter for the proper signed distance of the point to the circle.
double	distance (double fastDistance) const
	Helper function to translate the linearised distance to the proper distance.
double	fastDistance (const Vector2D &point) const
	Getter for the linearised distance measure to a point.
double	fastImpact () const
	Getter for the linearised distance to the origin.
double	fastDistance (double distance) const
	Helper function to translate the proper distance to the linearized distance measure of the circle retaining the sign of the distance.
ERightLeft	isRightOrLeft (const Vector2D &point) const
	Indicates if the point is on the right or left side of the circle.
bool	isLine () const
	Indicates if the perigee parameters represent a line.
bool	isCircle () const
	Indicates if the perigee parameters represent a closed circle.
ERotation	orientation () const
	Getter for the orientation of the circle.
Vector2D	gradient (const Vector2D &point) const
	Gradient of the distance field, hence indicates the direction of increasing distance.
Vector2D	normal (const Vector2D &point) const
	Unit normal vector from the circle to the given point.
Vector2D	tangential (const Vector2D &point) const
	Tangential vector to the circle near the given position.
const Vector2D &	tangential () const
	Getter for the tangtial vector at the perigee.
Vector2D	perigee () const
	Getter for the perigee point.
Vector2D	center () const
	Getter for the center of the circle. If it was a line both components will be infinity.
Vector2D	apogee () const
	Getter for the apogee of the circle. If it was a line both components will be infinity.
double	minimalCylindricalR () const
	Gives the minimal cylindrical radius the circle reaches (unsigned)
double	maximalCylindricalR () const
	Gives the maximal cylindrical radius the circle reaches.
double	arcLengthPeriod () const
	Getter for the arc length for a full round of the circle.
double	perimeter () const
	Gives the signed perimeter of the circle.
double	radius () const
	Gives the signed radius of the circle. If it was a line this will be infinity.
double	absRadius () const
	Gives the signed radius of the circle. If it was a line this will be infinity.
void	setCenterAndRadius (const Vector2D &center, double absRadius, ERotation orientation=ERotation::c_CounterClockwise)
	Setter for the circle center and radius.
double	n0 () const
	Getter for the generalised circle parameter n0.
Vector2D	n12 () const
	Getter for the generalised circle parameters n1 and n2.
double	n1 () const
	Getter for the generalised circle parameters n1.
double	n2 () const
	Getter for the generalised circle parameters n2.
double	n3 () const
	Getter for the generalised circle parameter n3.
void	setN (double n0, double n1, double n2, double n3=0.0)
	Setter for four generalised circle parameters.
void	setN (double n0, const Vector2D &n12, double n3=0.0)
	Setter for four generalised circle parameters.
void	setN (const Line2D &n012)
	Setter for generalised circle parameters from a normal line.
void	setN (const GeneralizedCircle &n0123)
	Setter for four generalised circle parameters.
double	omega () const
	Getter for omega parameter of the common Belle2::Helix which is the wrong sign curvature.
double	d0 () const
	Getter for d0 parameter of the common Belle2::Helix representation.
double	curvature () const
	Getter for the signed curvature.
double	phi0 () const
	Getter for the azimuth angle of the direction of flight at the perigee.
const Vector2D &	phi0Vec () const
	Getter for the unit vector of the direction of flight at the perigee.
double	impact () const
	Getter for the signed distance of the origin to the circle.
PerigeeParameters	perigeeParameters () const
	Getter for the three perigee parameters in the order defined by EPerigeeParameter.h.
void	setCurvature (double curvature)
	Setter for signed curvature.
void	setPhi0 (double phi0)
	Sets the azimuth angle of the direction of flight at the perigee.
void	setPhi0 (const Vector2D &phi0Vec)
	Sets the unit direction of flight at the perigee.
void	setImpact (double impact)
	Sets the impact parameter of the circle.
void	setPerigeeParameters (double curvature, const Vector2D &phi0Vec, double impact)
	Setter for the perigee parameters.
void	setPerigeeParameters (double curvature, double phi0, double impact)
	Setter for the perigee parameters.

Static Public Member Functions
static PerigeeCircle	fromN (double n0, double n1, double n2, double n3=0)
	Constructor with the four parameters of the generalized circle.
static PerigeeCircle	fromN (double n0, const Vector2D &n12, double n3=0)
	Constructor with the four parameters of the generalized circle.
static PerigeeCircle	fromCenterAndRadius (const Vector2D &center, double absRadius, ERotation orientation=ERotation::c_CounterClockwise)
	Constructor from center, radius and a optional orientation.

Private Member Functions
	PerigeeCircle (double curvature, double phi0, const Vector2D &phi0Vec, double impact)
	Constructor taking all stored parameters for internal use.
double	arcLengthAtDeltaLength (double delta, double dr) const
	Helper method to calculate the arc length to a point at distance delta to the perigee and dr to circle.
double	arcLengthAtSecantLength (double secantLength) const
	Helper method to calculate the arc length between to points on the circle from a given direct secant length.

Private Attributes
double	m_curvature
	Memory for the signed curvature.
double	m_phi0
	Memory for the azimuth angle of the direction of flight at the perigee.
Vector2D	m_phi0Vec
	Cached unit direction of flight at the perigee.
double	m_impact
	Memory for the signed impact parameter.

Detailed Description

Extension of the generalized circle also caching the perigee coordinates.

Definition at line 36 of file PerigeeCircle.h.

Constructor & Destructor Documentation

PerigeeCircle() [1/8]

PerigeeCircle

(

)

Default constructor for ROOT compatibility.

Definition at line 42 of file PerigeeCircle.cc.

{
  invalidate();
}

PerigeeCircle() [2/8]

PerigeeCircle	(	double	curvature,
		const Vector2D &	phi0Vec,
		double	impact
	)

Constructor from the perigee parammeters.

The direction of travel at the perigee is given as vector.

Definition at line 47 of file PerigeeCircle.cc.

  : m_curvature(curvature)
  , m_phi0(phi0Vec.phi())
  , m_phi0Vec(phi0Vec)
  , m_impact(impact)
{
}

PerigeeCircle() [3/8]

PerigeeCircle	(	double	curvature,
		double	phi0,
		double	impact
	)

Constructor from the perigee parammeters.

The direction of travel at the perigee is given as azimuth angle

Definition at line 55 of file PerigeeCircle.cc.

  : m_curvature(curvature)
  , m_phi0(phi0)
  , m_phi0Vec(Vector2D::Phi(phi0))
  , m_impact(impact)
{
}

PerigeeCircle() [4/8]

PerigeeCircle ( const PerigeeParameters &  perigeeParameters )

explicit

Constructor from the perigee parammeters.

Definition at line 63 of file PerigeeCircle.cc.

  : PerigeeCircle(perigeeParameters(EPerigeeParameter::c_Curv),
                  perigeeParameters(EPerigeeParameter::c_Phi0),
                  perigeeParameters(EPerigeeParameter::c_I))
{
}

PerigeeCircle() [5/8]

PerigeeCircle ( double  curvature, double  phi0, const Vector2D &  phi0Vec, double  impact  )

private

Constructor taking all stored parameters for internal use.

Nothing to do here

Definition at line 70 of file PerigeeCircle.cc.

  : m_curvature(curvature)
  , m_phi0(phi0)
  , m_phi0Vec(phi0Vec)
  , m_impact(impact)
{
}

PerigeeCircle() [6/8]

PerigeeCircle ( const Line2D &  n012 )

explicit

Constructor from a two dimensional line.

Definition at line 79 of file PerigeeCircle.cc.

{
  setN(n012);
}

PerigeeCircle() [7/8]

PerigeeCircle ( const GeneralizedCircle &  n0123 )

explicit

Constructor promoting the generalized circle.

Definition at line 84 of file PerigeeCircle.cc.

{
  setN(n0123);
}

PerigeeCircle() [8/8]

PerigeeCircle ( const Circle2D &  circle )

explicit

Constructor from a two dimensional circle in center / radius representation.

Definition at line 89 of file PerigeeCircle.cc.

{
  setCenterAndRadius(circle.center(), circle.absRadius(), circle.orientation());
}

Member Function Documentation

absRadius()

double absRadius ( ) const

inline

Gives the signed radius of the circle. If it was a line this will be infinity.

Definition at line 340 of file PerigeeCircle.h.

      {
        return fabs(radius());
      }

apogee()

Vector2D apogee ( ) const

inline

Getter for the apogee of the circle. If it was a line both components will be infinity.

Definition at line 304 of file PerigeeCircle.h.

      {
        return phi0Vec().orthogonal() * (impact() + 2 * radius());
      }

arcLengthAtDeltaLength()

double arcLengthAtDeltaLength ( double  delta, double  dr  ) const

private

Helper method to calculate the arc length to a point at distance delta to the perigee and dr to circle.

Definition at line 266 of file PerigeeCircle.cc.

{
  const double secantLength = sqrt((delta + dr) * (delta - dr) / (1 + dr * curvature()));
  const double arcLength = arcLengthAtSecantLength(secantLength);
  return arcLength;
}

arcLengthAtSecantLength()

double arcLengthAtSecantLength ( double  secantLength ) const

private

Helper method to calculate the arc length between to points on the circle from a given direct secant length.

Definition at line 273 of file PerigeeCircle.cc.

{
  double x = secantLength * curvature() / 2.0;
  double arcLengthFactor = asinc(x);
  return secantLength * arcLengthFactor;
}

arcLengthBetween()

double arcLengthBetween	(	const Vector2D &	from,
		const Vector2D &	to
	)		const

Calculates the arc length between two points of closest approach on the circle.

The arc length is signed positiv for travel in orientation direction. In the circle case the arc length is between -pi*radius and pi*radius, hence the discontinuity is on the far side of the circle relative to the given from point. The points are essentially first taken to their closest approach before we take the length on the curve. For the line case the length is the distance component parallel to the line.

Definition at line 244 of file PerigeeCircle.cc.

{
  EForwardBackward lengthSign = isForwardOrBackwardOf(from, to);
  if (not NForwardBackward::isValid(lengthSign)) return NAN;
  // Handling the rare case that from and to correspond to opposing points on the circle
  if (lengthSign == EForwardBackward::c_Unknown) lengthSign = EForwardBackward::c_Forward;
  Vector2D closestAtFrom = closest(from);
  Vector2D closestAtTo = closest(to);
  double secantLength = closestAtFrom.distance(closestAtTo);
  return static_cast<double>(lengthSign) * arcLengthAtSecantLength(secantLength);
}

arcLengthPeriod()

double arcLengthPeriod ( ) const

inline

Getter for the arc length for a full round of the circle.

Definition at line 322 of file PerigeeCircle.h.

      {
        return std::fabs(perimeter());
      }

arcLengthTo()

double arcLengthTo

(

const Vector2D &

point

)

const

Calculates the arc length between the perigee and the given point.

Definition at line 236 of file PerigeeCircle.cc.

{
  Vector2D closestToPoint = closest(point);
  double secantLength = perigee().distance(closestToPoint);
  double deltaParallel = phi0Vec().dot(point);
  return copysign(arcLengthAtSecantLength(secantLength), deltaParallel);
}

arcLengthToCylindricalR()

double arcLengthToCylindricalR

(

double

cylindricalR

)

const

Calculates the two dimensional arc length till the cylindrical radius is reached If the radius can not be reached return NAN.

Note that there are two solutions which have equivalent arc lengths with different sign Always return the positive solution.

Definition at line 256 of file PerigeeCircle.cc.

{
  // Slight trick here
  // Since the sought point is on the helix we treat it as the perigee
  // and the origin as the point to extrapolate to.
  // We know the distance of the origin to the circle, which is just d0
  // The direct distance from the origin to the imaginary perigee is just the given cylindricalR.
  return arcLengthAtDeltaLength(cylindricalR, impact());
}

atArcLength()

Vector2D atArcLength

(

double

arcLength

)

const

Calculates the point, which lies at the give perpendicular travel distance (counted from the perigee)

Definition at line 116 of file PerigeeCircle.cc.

{
  double chi = arcLength * curvature();
  double chiHalf = chi / 2.0;
 
  double atX = arcLength * sinc(chi);
  double atY = arcLength * sinc(chiHalf) * sin(chiHalf) + impact();
  return Vector2D::compose(phi0Vec(), atX, atY);
}

atCylindricalR()

std::pair< Vector2D, Vector2D > atCylindricalR

(

double

cylindricalR

)

const

Calculates the two points with the given cylindrical radius on the generalised circle.

Definition at line 280 of file PerigeeCircle.cc.

{
  const double u = (1 + curvature() * impact());
  const double orthogonal = ((square(impact()) + square(cylindricalR)) * curvature() / 2.0 + impact()) / u;
  const double parallel = sqrt(square(cylindricalR) - square(orthogonal));
  Vector2D atCylindricalR1 = Vector2D::compose(phi0Vec(), -parallel, orthogonal);
  Vector2D atCylindricalR2 = Vector2D::compose(phi0Vec(), parallel, orthogonal);
  std::pair<Vector2D, Vector2D> result(atCylindricalR1, atCylindricalR2);
  return result;
}

atCylindricalRForwardOf()

Vector2D atCylindricalRForwardOf	(	const Vector2D &	startPoint,
		double	cylindricalR
	)		const

Approach on the circle with the given cylindrical radius that lies in the forward direction of a start point.

Calculates the point on the circle with cylindrical radius cylindricalR, which is closest following the circle in the direction of positive forward orientation This is particularly useful to extraplotate into a certain layer. In case no intersection with this cylindrical radius exists the function returns Vector2D(NAN,NAN)

Parameters

startPoint	Start point from which to follow in the circle in the forward direction
cylindricalR	Cylindrical radius of interest

Returns

Close point in forward direction with same cylindrical radius on the circle.

Definition at line 291 of file PerigeeCircle.cc.

{
  std::pair<Vector2D, Vector2D> candidatePoints = atCylindricalR(cylindricalR);
  return chooseNextForwardOf(startPoint, candidatePoints.first, candidatePoints.second);
}

center()

Vector2D center ( ) const

inline

Getter for the center of the circle. If it was a line both components will be infinity.

Definition at line 298 of file PerigeeCircle.h.

      {
        return phi0Vec().orthogonal() * (impact() + radius());
      }

chooseNextForwardOf()

Vector2D chooseNextForwardOf	(	const Vector2D &	start,
		const Vector2D &	end1,
		const Vector2D &	end2
	)		const

Returns the one of two end point which is first reached from the given start if one stricly follows the forward direction of the circle.

If the generalized circle is truely a line none of the points might lie in the forward direction and Vector2D(NAN,NAN) is returned.

Parameters

start	Point to start the traversal
end1	One possible end point
end2	Other possible end point

Returns

end1 or end2 depending, which lies closer to start in the forward direction or Vector2D(NAN,NAN) if neither end1 nor end2 are reachable in the forward direction (line case only)

Definition at line 298 of file PerigeeCircle.cc.

{
  double arcLength1 = arcLengthBetween(start, end1);
  double arcLength2 = arcLengthBetween(start, end2);
  if (arcLength1 < 0) arcLength1 += arcLengthPeriod();
  if (arcLength2 < 0) arcLength2 += arcLengthPeriod();
  if (fmin(arcLength1, arcLength2) == arcLength1) {
    return end1;
  } else if (fmin(arcLength1, arcLength2) == arcLength2) {
    return end2;
  } else {
    return Vector2D(NAN, NAN);
  }
}

closest()

Vector2D closest

(

const Vector2D &

point

)

const

Calculates the point of closest approach on the circle to the given point.

Definition at line 315 of file PerigeeCircle.cc.

{
  return point - normal(point) * distance(point);
}

conformalTransform()

void conformalTransform

(

)

Transforms the generalized circle to conformal space inplace.

Applies the conformal map in the self-inverse from X = x / (x^2 + y^2) and Y = y / (x^2 +y^2) inplace It works most easily by the exchange of the circle parameters n0 <-> n3

Definition at line 139 of file PerigeeCircle.cc.

{
  double denominator = 2 + curvature() * impact();
  std::swap(m_impact, m_curvature);
  m_curvature *= denominator;
  m_impact /= denominator;
  // Also properly fixing the orientation to the opposite.
  reverse();
}

conformalTransformed()

PerigeeCircle conformalTransformed

(

)

const

Returns a copy of the circle in conformal space.

Applies the conformal map in the self-inverse from X = x / (x^2 + y^2) and Y = y / (x^2 +y^2) and returns the result as a new circle It works most easily by the exchange of the circle parameters n0 <-> n3

Definition at line 149 of file PerigeeCircle.cc.

{
  double denominator = 2 + curvature() * impact();
  // Properly fixing the orientation to the opposite by the minus signs
  double newCurvature = -impact() * denominator;
  double newPhi0 = AngleUtil::reversed(phi0());
  Vector2D newPhi0Vec = -phi0Vec();
  double newImpact = -curvature() / denominator;
  return PerigeeCircle(newCurvature, newPhi0, newPhi0Vec, newImpact);
}

curvature()

double curvature ( ) const

inline

Getter for the signed curvature.

Definition at line 416 of file PerigeeCircle.h.

      {
        return m_curvature;
      }

d0()

double d0 ( ) const

inline

Getter for d0 parameter of the common Belle2::Helix representation.

Definition at line 410 of file PerigeeCircle.h.

      {
        return -impact();
      }

distance() [1/2]

double distance ( const Vector2D &  point ) const

inline

Getter for the proper signed distance of the point to the circle.

Definition at line 210 of file PerigeeCircle.h.

      {
        return distance(fastDistance(point));
      }

distance() [2/2]

double distance

(

double

fastDistance

)

const

Helper function to translate the linearised distance to the proper distance.

Definition at line 320 of file PerigeeCircle.cc.

{
  double A = 2 * fastDistance;
  double U = std::sqrt(1 + A * curvature());
  return A / (1.0 + U);
}

fastDistance() [1/2]

double fastDistance

(

const Vector2D &

point

)

const

Getter for the linearised distance measure to a point.

Gives a fast signed approximation of the distance to the circle. The absolute value of the fast distance is accurate up to first order of distance/circle radius, hence best used with big circles and small distances. The sign of the fast distance indicates if the point is to the right or to the left of the circle.

Definition at line 327 of file PerigeeCircle.cc.

{
  Vector2D delta = point - perigee();
  double deltaOrthogonal = phi0Vec().cross(delta);
  return -deltaOrthogonal + curvature() * delta.normSquared() / 2;
}

fastDistance() [2/2]

double fastDistance ( double  distance ) const

inline

Helper function to translate the proper distance to the linearized distance measure of the circle retaining the sign of the distance.

Definition at line 238 of file PerigeeCircle.h.

      {
        return distance * (1.0 + distance * curvature() / 2);
      }

fastImpact()

double fastImpact ( ) const

inline

Getter for the linearised distance to the origin.

Definition at line 229 of file PerigeeCircle.h.

      {
        return fastDistance(impact());
      }

fromCenterAndRadius()

PerigeeCircle fromCenterAndRadius ( const Vector2D &  center, double  absRadius, ERotation  orientation = ERotation::c_CounterClockwise  )

static

Constructor from center, radius and a optional orientation.

The center and radius alone do not carry any orientation. However the perigee parameterisation does. Therefore the constructor also excepts an orientated representation from them. If no orientation is given, it defaults to mathematical positiv counterclockwise.

Definition at line 109 of file PerigeeCircle.cc.

{
  PerigeeCircle circle;
  circle.setCenterAndRadius(center, absRadius, orientation);
  return circle;
}

fromN() [1/2]

PerigeeCircle fromN ( double  n0, const Vector2D &  n12, double  n3 = 0  )

static

Constructor with the four parameters of the generalized circle.

Definition at line 101 of file PerigeeCircle.cc.

{
  PerigeeCircle circle;
  circle.setN(n0, n12, n3);
  return circle;
}

fromN() [2/2]

PerigeeCircle fromN ( double  n0, double  n1, double  n2, double  n3 = 0  )

static

Constructor with the four parameters of the generalized circle.

Definition at line 94 of file PerigeeCircle.cc.

{
  PerigeeCircle circle;
  circle.setN(n0, n1, n2, n3);
  return circle;
}

gradient()

Vector2D gradient ( const Vector2D &  point ) const

inline

Gradient of the distance field, hence indicates the direction of increasing distance.

Definition at line 268 of file PerigeeCircle.h.

      {
        return (point - perigee()) * curvature() - phi0Vec().orthogonal();
      }

impact()

double impact ( ) const

inline

Getter for the signed distance of the origin to the circle.

Definition at line 434 of file PerigeeCircle.h.

      {
        return m_impact;
      }

invalidate()

void invalidate

(

)

Sets all circle parameters to zero.

Definition at line 160 of file PerigeeCircle.cc.

{
  m_curvature = 0.0;
  m_phi0 = NAN;
  m_phi0Vec = Vector2D(0.0, 0.0);
  m_impact = 0;
}

isCircle()

bool isCircle ( ) const

inline

Indicates if the perigee parameters represent a closed circle.

Definition at line 256 of file PerigeeCircle.h.

      {
        return curvature() != 0.0;
      }

isForwardOrBackward()

EForwardBackward isForwardOrBackward ( const Vector2D &  to ) const

inline

Indicates whether to given point lies in the forward direction from the perigee.

Definition at line 186 of file PerigeeCircle.h.

      {
        return tangential().isForwardOrBackwardOf(to);
      }

isForwardOrBackwardOf()

EForwardBackward isForwardOrBackwardOf ( const Vector2D &  from, const Vector2D &  to  ) const

inline

Indicates whether to given point lies in the forward direction from the perigee.

Definition at line 180 of file PerigeeCircle.h.

      {
        return tangential(from).isForwardOrBackwardOf(to - from);
      }

isInvalid()

bool isInvalid

(

)

const

Indicates if all circle parameters are zero.

Definition at line 168 of file PerigeeCircle.cc.

{
  return (not std::isfinite(phi0()) or not std::isfinite(curvature()) or
          not std::isfinite(impact()) or phi0Vec().isNull());
}

isLine()

bool isLine ( ) const

inline

Indicates if the perigee parameters represent a line.

Definition at line 250 of file PerigeeCircle.h.

      {
        return curvature() == 0.0;
      }

isRightOrLeft()

ERightLeft isRightOrLeft ( const Vector2D &  point ) const

inline

Indicates if the point is on the right or left side of the circle.

Definition at line 244 of file PerigeeCircle.h.

      {
        return static_cast<ERightLeft>(sign(fastDistance(point)));
      }

isValid()

bool isValid ( ) const

inline

Indicates if the combination of the circle parameters makes up a valid circle.

Definition at line 94 of file PerigeeCircle.h.

      {
        return not isInvalid();
      }

maximalCylindricalR()

double maximalCylindricalR ( ) const

inline

Gives the maximal cylindrical radius the circle reaches.

Definition at line 316 of file PerigeeCircle.h.

      {
        return fabs(impact() + 2 * radius());
      }

minimalCylindricalR()

double minimalCylindricalR ( ) const

inline

Gives the minimal cylindrical radius the circle reaches (unsigned)

Definition at line 310 of file PerigeeCircle.h.

      {
        return fabs(impact());
      }

n0()

double n0 ( ) const

inline

Getter for the generalised circle parameter n0.

Definition at line 351 of file PerigeeCircle.h.

      {
        return impact() * (impact() * curvature() / 2.0 + 1.0);
      }

n1()

double n1 ( ) const

inline

Getter for the generalised circle parameters n1.

Definition at line 363 of file PerigeeCircle.h.

      {
        return n12().x();
      }

n12()

Vector2D n12 ( ) const

inline

Getter for the generalised circle parameters n1 and n2.

Definition at line 357 of file PerigeeCircle.h.

      {
        return -phi0Vec().orthogonal() * (1 + curvature() * impact());
      }

n2()

double n2 ( ) const

inline

Getter for the generalised circle parameters n2.

Definition at line 370 of file PerigeeCircle.h.

      {
        return n12().y();
      }

n3()

double n3 ( ) const

inline

Getter for the generalised circle parameter n3.

Definition at line 377 of file PerigeeCircle.h.

      {
        return curvature() / 2.0;
      }

normal()

Vector2D normal ( const Vector2D &  point ) const

inline

Unit normal vector from the circle to the given point.

Definition at line 274 of file PerigeeCircle.h.

      {
        return gradient(point).unit();
      }

omega()

double omega ( ) const

inline

Getter for omega parameter of the common Belle2::Helix which is the wrong sign curvature.

Definition at line 404 of file PerigeeCircle.h.

      {
        return -curvature();
      }

orientation()

ERotation orientation ( ) const

inline

Getter for the orientation of the circle.

Definition at line 262 of file PerigeeCircle.h.

      {
        return static_cast<ERotation>(sign(curvature()));
      }

passiveMoveBy()

void passiveMoveBy

(

const Vector2D &

by

)

Moves the coordinates system by the given vector. Updates perigee parameters in place.

Definition at line 174 of file PerigeeCircle.cc.

{
  double arcLength = arcLengthTo(by);
  m_impact = distance(by);
  m_phi0 = m_phi0 + curvature() * arcLength;
  AngleUtil::normalise(m_phi0);
  m_phi0Vec = Vector2D::Phi(m_phi0);
}

passiveMoveByJacobian() [1/2]

PerigeeJacobian passiveMoveByJacobian

(

const Vector2D &

by

)

const

Computes the Jacobi matrix for a move of the coordinate system by the given vector.

Definition at line 183 of file PerigeeCircle.cc.

{
  PerigeeJacobian jacobian = PerigeeUtil::identity();
  passiveMoveByJacobian(by, jacobian);
  return jacobian;
}

passiveMoveByJacobian() [2/2]

void passiveMoveByJacobian	(	const Vector2D &	by,
		PerigeeJacobian &	jacobian
	)		const

Puts the Jacobi matrix for a move of the coordinate system by the given vector in the given matrix as an output argument.

Definition at line 190 of file PerigeeCircle.cc.

{
  Vector2D deltaVec = by - perigee();
  double delta = deltaVec.norm();
  double deltaParallel = phi0Vec().dot(deltaVec);
  // double deltaOrthogonal = phi0Vec().cross(deltaVec);
  // double zeta = deltaVec.normSquared();
 
  Vector2D UVec = gradient(by);
  double U = UVec.norm();
  double USquared = UVec.normSquared();
  double UOrthogonal = phi0Vec().cross(UVec);
  // double UParallel = phi0Vec().dot(UVec);
 
  // Vector2D CB = gradient(by).orthogonal();
  // double U = sqrt(1 + curvature() * A);
  // double xi = 1.0 / CB.normSquared();
  // double nu = 1 - curvature() * deltaOrthogonal;
  // double mu = 1.0 / (U * (U + 1)) + curvature() * lambda;
  // double mu = 1.0 / U / 2.0;
  // double nu = -UOrthogonal;
  // double xi = 1 / USquared;
 
  // double halfA = fastDistance(by);
  // double A = 2 * halfA;
  // double lambda = halfA / ((1 + U) * (1 + U) * U);
  double dr = distance(by);
 
  // Vector2D uVec = gradient(Vector2D(0.0, 0.0));
  // double u = uVec.norm();
  double u = 1 + curvature() * impact(); //= n12().cylindricalR()
 
  using namespace NPerigeeParameterIndices;
  jacobian(c_Curv, c_Curv) = 1;
  jacobian(c_Curv, c_Phi0) = 0;
  jacobian(c_Curv, c_I) = 0;
 
  jacobian(c_Phi0, c_Curv) = deltaParallel / USquared;
  jacobian(c_Phi0, c_Phi0) = -u * UOrthogonal / USquared;
  jacobian(c_Phi0, c_I) = -curvature() * curvature() * deltaParallel / USquared;
 
  jacobian(c_I, c_Curv) = (delta - dr) * (delta + dr) / U / 2;
  jacobian(c_I, c_Phi0) = u * deltaParallel / U;
  jacobian(c_I, c_I) = -UOrthogonal / U;
}

perigee()

Vector2D perigee ( ) const

inline

Getter for the perigee point.

Definition at line 292 of file PerigeeCircle.h.

      {
        return phi0Vec().orthogonal() * impact();
      }

perigeeParameters()

PerigeeParameters perigeeParameters ( ) const

inline

Getter for the three perigee parameters in the order defined by EPerigeeParameter.h.

Definition at line 440 of file PerigeeCircle.h.

      {
        using namespace NPerigeeParameterIndices;
        PerigeeParameters result;
        result(c_Curv) = curvature();
        result(c_Phi0) = phi0();
        result(c_I) = impact();
        return result;
      }

perimeter()

double perimeter ( ) const

inline

Gives the signed perimeter of the circle.

Definition at line 328 of file PerigeeCircle.h.

      {
        return 2 * M_PI * radius();
      }

phi0()

double phi0 ( ) const

inline

Getter for the azimuth angle of the direction of flight at the perigee.

Definition at line 422 of file PerigeeCircle.h.

      {
        return m_phi0;
      }

phi0Vec()

const Vector2D & phi0Vec ( ) const

inline

Getter for the unit vector of the direction of flight at the perigee.

Definition at line 428 of file PerigeeCircle.h.

      {
        return m_phi0Vec;
      }

radius()

double radius ( ) const

inline

Gives the signed radius of the circle. If it was a line this will be infinity.

Definition at line 334 of file PerigeeCircle.h.

      {
        return 1 / curvature();
      }

reverse()

void reverse

(

)

Flips the orientation of the circle in place.

Definition at line 126 of file PerigeeCircle.cc.

{
  m_curvature = -m_curvature;
  m_phi0 = AngleUtil::reversed(m_phi0);
  m_phi0Vec.reverse();
  m_impact = -m_impact;
}

reversed()

PerigeeCircle reversed

(

)

const

Returns a copy of the circle with opposite orientation.

Definition at line 134 of file PerigeeCircle.cc.

{
  return PerigeeCircle(-m_curvature, AngleUtil::reversed(m_phi0), -m_phi0Vec, -m_impact);
}

setCenterAndRadius()

void setCenterAndRadius	(	const Vector2D &	center,
		double	absRadius,
		ERotation	orientation = ERotation::c_CounterClockwise
	)

Setter for the circle center and radius.

Definition at line 334 of file PerigeeCircle.cc.

{
  m_curvature = static_cast<double>(orientation) / std::fabs(absRadius);
  m_phi0Vec = center.orthogonal(NRotation::reversed(orientation));
  m_phi0Vec.normalize();
  m_phi0 = m_phi0Vec.phi();
  m_impact = (center.norm() - std::fabs(absRadius)) * static_cast<double>(orientation);
}

setCurvature()

void setCurvature ( double  curvature )

inline

Setter for signed curvature.

Definition at line 451 of file PerigeeCircle.h.

      {
        m_curvature = curvature;
      }

setImpact()

void setImpact ( double  impact )

inline

Sets the impact parameter of the circle.

Definition at line 471 of file PerigeeCircle.h.

      {
        m_impact = impact;
      }

setN() [1/4]

void setN ( const GeneralizedCircle &  n0123 )

inline

Setter for four generalised circle parameters.

Definition at line 398 of file PerigeeCircle.h.

      {
        setN(n0123.n0(), n0123.n12(), n0123.n3());
      }

setN() [2/4]

void setN ( const Line2D &  n012 )

inline

Setter for generalised circle parameters from a normal line.

Definition at line 392 of file PerigeeCircle.h.

      {
        setN(n012.n0(), n012.n12());
      }

setN() [3/4]

void setN	(	double	n0,
		const Vector2D &	n12,
		double	n3 = 0.0
	)

Setter for four generalised circle parameters.

Definition at line 345 of file PerigeeCircle.cc.

{
  double normalization = sqrt(n12.normSquared() - 4 * n0 * n3);
  m_curvature = 2 * n3 / normalization;
  m_phi0Vec = n12.orthogonal();
  m_phi0Vec.normalize();
  m_phi0 = m_phi0Vec.phi();
  m_impact = distance(n0 / normalization); // Uses the new curvature
}

setN() [4/4]

void setN ( double  n0, double  n1, double  n2, double  n3 = 0.0  )

inline

Setter for four generalised circle parameters.

Definition at line 383 of file PerigeeCircle.h.

      {
        setN(n0, Vector2D(n1, n2), n3);
      }

setPerigeeParameters() [1/2]

void setPerigeeParameters ( double  curvature, const Vector2D &  phi0Vec, double  impact  )

inline

Setter for the perigee parameters.

Definition at line 477 of file PerigeeCircle.h.

      {
        m_impact = impact;
        m_phi0 = phi0Vec.phi();
        m_phi0Vec = phi0Vec.unit();
        m_curvature = curvature;
      }

setPerigeeParameters() [2/2]

void setPerigeeParameters ( double  curvature, double  phi0, double  impact  )

inline

Setter for the perigee parameters.

Definition at line 486 of file PerigeeCircle.h.

      {
        m_impact = impact;
        m_phi0 = phi0;
        m_phi0Vec = Vector2D::Phi(phi0);
        m_curvature = curvature;
      }

setPhi0() [1/2]

void setPhi0 ( const Vector2D &  phi0Vec )

inline

Sets the unit direction of flight at the perigee.

Definition at line 464 of file PerigeeCircle.h.

      {
        m_phi0 = phi0Vec.phi();
        m_phi0Vec = phi0Vec.unit();
      }

setPhi0() [2/2]

void setPhi0 ( double  phi0 )

inline

Sets the azimuth angle of the direction of flight at the perigee.

Definition at line 457 of file PerigeeCircle.h.

      {
        m_phi0 = phi0;
        m_phi0Vec = Vector2D::Phi(phi0);
      }

tangential() [1/2]

const Vector2D & tangential ( ) const

inline

Getter for the tangtial vector at the perigee.

Definition at line 286 of file PerigeeCircle.h.

      {
        return phi0Vec();
      }

tangential() [2/2]

Vector2D tangential ( const Vector2D &  point ) const

inline

Tangential vector to the circle near the given position.

Definition at line 280 of file PerigeeCircle.h.

      {
        return normal(point).orthogonal();
      }

Member Data Documentation

m_curvature

double m_curvature

private

Memory for the signed curvature.

Definition at line 503 of file PerigeeCircle.h.

m_impact

double m_impact

private

Memory for the signed impact parameter.

Definition at line 512 of file PerigeeCircle.h.

m_phi0

double m_phi0

private

Memory for the azimuth angle of the direction of flight at the perigee.

Definition at line 506 of file PerigeeCircle.h.

m_phi0Vec

Vector2D m_phi0Vec

private

Cached unit direction of flight at the perigee.

Definition at line 509 of file PerigeeCircle.h.

---

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

• tracking/trackFindingCDC/geometry/include/PerigeeCircle.h
• tracking/trackFindingCDC/geometry/src/PerigeeCircle.cc