A line with a support point and tangential vector. More...

#include <ParameterLine2D.h>

Collaboration diagram for ParameterLine2D:

Public Member Functions
	ParameterLine2D ()
	Default constructor for ROOT compatibility.

	ParameterLine2D (const Vector2D &support, const Vector2D &tangential)
	Standard constructor taking the support point and the tangential vector.

	ParameterLine2D (const Line2D &line)
	Upcast the normal representation to a parameter line. More...

	operator Line2D ()
	Downcast the line to the normal representation. More...

const Vector2D &	tangential () const
	Gives the tangential vector of the line.

Vector2D	normal () const
	Gives the normal vector of the line.

const Vector2D &	support () const
	Gives the support vector of the line.

Vector2D	at (const double parameter) const
	Evaluates the line formula at the parameter given.

EForwardBackward	alignedWithFirst () const
	Indicates if the tangential vector point in a commmon direction with the first coordinate axes.

EForwardBackward	alignedWithSecond () const
	Indicates if the tangential vector point in a commmon direction with the second coordinate axes.

void	normalize ()
	Normalizes the tangential vector inplace. More...

void	invalidate ()
	Clear all information from the line.

bool	isInvalid () const
	Check it the line is in an invalid state.

void	reverse ()
	Reverses the tangential vector inplace.

ParameterLine2D	reversed () const
	Makes a copy line which has the opposite tangential vector but same support point.

double	distance (const Vector2D &point) const
	Gives the signed distance of a point to the line. More...

double	distance (const double first, const double second) const
	Calculates the signed distance of the point given by its to coordinates to the line. More...

double	distanceToOrigin () const
	Gives the signed distance of the origin.

double	absoluteDistance (const Vector2D &point) const
	Gives the unsigned distance of a point to the line.

ERightLeft	isRightOrLeft (const Vector2D &point) const
	Return if the point given is right or left of the line.

bool	isLeft (const Vector2D &rhs) const
	Return if the point given is left of the line.

bool	isRight (const Vector2D &rhs) const
	Return if the point given is right of the line.

Vector2D	closest (const Vector2D &point) const
	Gives the position at the closest approach on the line to point.

double	closestAt (const Vector2D &point) const
	Gives the line parameter at the closest approach to point.

Vector2D	closestToOrigin () const
	Gives the position of closest approach to the origin.

double	closestToOriginAt () const
	Gives the line parameter at the closest approach to the origin.

double	lengthOnCurve (const Vector2D &from, const Vector2D &to) const
	Denotes the length on the line between the two points.

double	intersectionAt (const Line2D &line) const
	Gives the line parameter where the two lines meet. Infinity for parallels.

double	intersectionAt (const ParameterLine2D &line) const
	Gives the line parameter of this line where the two lines meet. Infinity for parallels.

std::pair< double, double >	intersectionsAt (const GeneralizedCircle &genCircle) const
	Gives the line parameters of this line, where it intersects with the generalized circle. More...

Vector2D	intersection (const Line2D &line) const
	Gives the point where the two lines meet. Infinities for parallels.

Vector2D	intersection (const ParameterLine2D &line) const
	Gives the point where the two lines meet. Infinities for parallels.

Transformations of the line
void	passiveMoveAtBy (const double delta)
	Moves the support point by the given amount of the parameter in the forward direction. More...

void	moveBy (const Vector2D &by)
	Moves the line in the given direction in place. Corresponds to an active transformation.

void	moveAlongFirst (const double first)
	Moves the line along the first coordinate axes in place. More...

void	moveAlongSecond (const double second)
	Moves the line along the second coordinate axes in place. More...

void	passiveMoveBy (const Vector2D &by)
	Moves the coordinate system in the given direction in place. More...

void	passiveMoveAlongFirst (const double first)
	Moves the coordinate system along the first coordinate axes in place. More...

void	passiveMoveAlongSecond (const double second)
	Moves the coordinate system along the second coordinate axes in place. More...

Line as a function of the first coordinate
The next couple of methods are to interpret the line as a function mapping from first to second coordinate
double	slope () const
	The line slope.

double	inverseSlope () const
	The inveres line slope.

double	intercept () const
	Second coordinate for first being zero.

double	zero () const
	First coordinate for second being zero.

double	map (const double first) const
	Method mapping the first coordinate to the second according to the line.

double	operator() (const double first) const
	Operator mapping the first coordinate to the second according to the line.

double	inverseMap (const double second) const
	Method for the inverse mapping the second coordinate to the first according to the line.

void	invert ()
	Turns the line into its inverse function in place. Orientation will be flipped as well.

ParameterLine2D	inverted () const
	Gives the line assoziated with the inverse function as a copy.

Static Public Member Functions
static ParameterLine2D	fromSlopeIntercept (const double slope, const double intercept)
	Constructs a line with slope and intercept. More...

static ParameterLine2D	fromSlopeIntercept (const double slope, const double intercept, const EForwardBackward orientation)
	Constructs a line with slope and intercept. More...

static ParameterLine2D	throughPoints (const Vector2D &start, const Vector2D &end)
	Static constructor for a line between to points. More...

static ParameterLine2D	touchingCircles (const Vector2D &fromCenter, double fromSignedRadius, const Vector2D &toCenter, double toSignedRadius)
	Constructs a line touching two circles in one point each. More...

Private Attributes
Vector2D	m_support
	Support vector of the line.

Vector2D	m_tangential
	Tangential vector of the line.

Detailed Description

A line with a support point and tangential vector.

Implements the representation $x = s + \lambda \cdot t$ where
is the support point and is the tangential vector
$\lambda$ is called the parameter of the line. In the same sense as the Line2D
this line defines a direction of positiv advance ( the tangential vector ) as well as
a right and a left half plane.

Definition at line 38 of file ParameterLine2D.h.

Constructor & Destructor Documentation

◆ ParameterLine2D()

ParameterLine2D ( const Line2D & line )

inlineexplicit

Upcast the normal representation to a parameter line.

Upcasting requires some additional information to be set namely the support point and the scale of the tangential. The support is set the point closest to the origin. The tangential is of unit length. Note the orientation of the line remains the same.

Definition at line 93 of file ParameterLine2D.h.

         : m_support(line.support())
         , m_tangential(line.tangential())
       {
       }

Member Function Documentation

◆ distance() [1/2]

double distance	(	const double	first,
		const double	second
	)		const

inline

Calculates the signed distance of the point given by its to coordinates to the line.

Returns the signed distance of the point to the line. The sign is positiv
for the right side of the line and negativ for the left side.

Definition at line 209 of file ParameterLine2D.h.

◆ distance() [2/2]

double distance ( const Vector2D & point ) const

inline

Gives the signed distance of a point to the line.

Returns the signed distance of the point to the line. The sign is positiv
for the right side of the line and negativ for the left side.

Definition at line 201 of file ParameterLine2D.h.

◆ fromSlopeIntercept() [1/2]

static ParameterLine2D fromSlopeIntercept	(	const double	slope,
		const double	intercept
	)

inlinestatic

Constructs a line with slope and intercept.

Orientation will be coaligned with the first axes. Tangential vector is normalized to have a unit in the first coordinate.

Definition at line 59 of file ParameterLine2D.h.

◆ fromSlopeIntercept() [2/2]

static ParameterLine2D fromSlopeIntercept	(	const double	slope,
		const double	intercept,
		const EForwardBackward	orientation
	)

inlinestatic

Constructs a line with slope and intercept.

Orientation means the alignment with the first axes. Orientation will be coaligned or antialigned as given. Tangential vector is normalized to have a unit in the first coordinate.

Definition at line 69 of file ParameterLine2D.h.

◆ intersectionsAt()

std::pair<double, double> intersectionsAt ( const GeneralizedCircle & genCircle ) const

inline

Gives the line parameters of this line, where it intersects with the generalized circle.

Calculates the two line parameters of the intersections with the circle as a pair. The second of the pair is always the small of the two solutions, which is closer to the support point.

Definition at line 296 of file ParameterLine2D.h.

◆ moveAlongFirst()

void moveAlongFirst ( const double first )

inline

Moves the line along the first coordinate axes in place.

Corresponds to an active transformation.

Definition at line 336 of file ParameterLine2D.h.

◆ moveAlongSecond()

void moveAlongSecond ( const double second )

inline

Moves the line along the second coordinate axes in place.

Corresponds to an active transformation.

Definition at line 343 of file ParameterLine2D.h.

◆ normalize()

void normalize ( )

inline

Normalizes the tangential vector inplace.

Normalizes the line representation such that the parameter is indentical with the distance from the support point of a point on the line. This can be usefull if you want to give the parameter a certain meaning where you have to get rid of the proportional factor assizated with the length of the tangential.

Definition at line 167 of file ParameterLine2D.h.

◆ operator Line2D()

operator Line2D ( )

inline

Downcast the line to the normal representation.

Downcasting the parameter line to the line representation using the normal vector. You loose the information where the support point is and the scale of the parameter. However the same points lie on the line and distance to is remain the same

Definition at line 118 of file ParameterLine2D.h.

◆ passiveMoveAlongFirst()

void passiveMoveAlongFirst ( const double first )

inline

Moves the coordinate system along the first coordinate axes in place.

Corresponds to a passive transformation.

Definition at line 357 of file ParameterLine2D.h.

◆ passiveMoveAlongSecond()

void passiveMoveAlongSecond ( const double second )

inline

Moves the coordinate system along the second coordinate axes in place.

Corresponds to a passive transformation.

Definition at line 364 of file ParameterLine2D.h.

◆ passiveMoveAtBy()

void passiveMoveAtBy ( const double delta )

inline

Moves the support point by the given amount of the parameter in the forward direction.

This moves the parameter by -delta and the following relation hold
old at(p) = new at(p - delta) hence the coordinate at is diminished
This corresponds to a passive movement of the coordinate system on the line

Definition at line 323 of file ParameterLine2D.h.

◆ passiveMoveBy()

void passiveMoveBy ( const Vector2D & by )

inline

Moves the coordinate system in the given direction in place.

Corresponds to a passive transformation.

Definition at line 350 of file ParameterLine2D.h.

◆ throughPoints()

static ParameterLine2D throughPoints	(	const Vector2D &	start,
		const Vector2D &	end
	)

inlinestatic

Static constructor for a line between to points.

The resulting line will have start as support. Tangential vector is the difference between end and start. Hence at(0) == start and at(1) == end for the constructed line.

Definition at line 82 of file ParameterLine2D.h.

◆ touchingCircles()

ParameterLine2D touchingCircles	(	const Vector2D &	fromCenter,
		double	fromSignedRadius,
		const Vector2D &	toCenter,
		double	toSignedRadius
	)

static

Constructs a line touching two circles in one point each.

Parameters

[in]	fromCenter	first circle center
[in]	fromSignedRadius	radius of the first circle multiplied with the right left passage information
[in]	toCenter	second circle center
[in]	toSignedRadius	radius of the first circle multiplied with the right left passage information.

Returns: the line being tangential to both circles. Note : the touch points reside at(0) for the first and at(1) for the second

Definition at line 17 of file ParameterLine2D.cc.

 {
   Vector2D connecting = toCenter - fromCenter;
  
   // Normalize to the coordinate system vector, but keep the original norm
   const double norm = connecting.normalize();
  
   double kappa = (fromSignedRadius - toSignedRadius) / norm;
   double cokappa = sqrt(1 - kappa * kappa);
  
   Vector2D fromPos = Vector2D(connecting, kappa * fromSignedRadius, cokappa * fromSignedRadius);
   fromPos += fromCenter;
  
   Vector2D toPos = Vector2D(connecting, kappa * toSignedRadius, cokappa * toSignedRadius);
   toPos += toCenter;
  
   return ParameterLine2D::throughPoints(fromPos, toPos);
 }

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

tracking/trackFindingCDC/geometry/include/ParameterLine2D.h
tracking/trackFindingCDC/geometry/src/ParameterLine2D.cc

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ParameterLine2D()

Member Function Documentation

◆ distance() [1/2]

◆ distance() [2/2]

◆ fromSlopeIntercept() [1/2]

◆ fromSlopeIntercept() [2/2]

◆ intersectionsAt()

◆ moveAlongFirst()

◆ moveAlongSecond()

◆ normalize()

◆ operator Line2D()

◆ passiveMoveAlongFirst()

◆ passiveMoveAlongSecond()

◆ passiveMoveAtBy()

◆ passiveMoveBy()

◆ throughPoints()

◆ touchingCircles()