ParameterLine2D Class Reference

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

#include <ParameterLine2D.h>

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.
	operator Line2D ()
	Downcast the line to the normal representation.
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.
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.
double	distance (const double first, const double second) const
	Calculates the signed distance of the point given by its to coordinates to the line.
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.
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.
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.
void	moveAlongSecond (const double second)
	Moves the line along the second coordinate axes in place.
void	passiveMoveBy (const Vector2D &by)
	Moves the coordinate system in the given direction in place.
void	passiveMoveAlongFirst (const double first)
	Moves the coordinate system along the first coordinate axes in place.
void	passiveMoveAlongSecond (const double second)
	Moves the coordinate system along the second coordinate axes in place.
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.
static ParameterLine2D	fromSlopeIntercept (const double slope, const double intercept, const EForwardBackward orientation)
	Constructs a line with slope and intercept.
static ParameterLine2D	throughPoints (const Vector2D &start, const Vector2D &end)
	Static constructor for a line between to points.
static ParameterLine2D	touchingCircles (const Vector2D &fromCenter, double fromSignedRadius, const Vector2D &toCenter, double toSignedRadius)
	Constructs a line touching two circles in one point each.

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 where
is the support point and is the tangential vector
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() [1/3]

ParameterLine2D ( )

inline

Default constructor for ROOT compatibility.

Definition at line 42 of file ParameterLine2D.h.

        : m_support(0.0, 0.0)
        , m_tangential(0.0, 0.0)
      {
      }

ParameterLine2D() [2/3]

ParameterLine2D ( const Vector2D &  support, const Vector2D &  tangential  )

inline

Standard constructor taking the support point and the tangential vector.

Definition at line 49 of file ParameterLine2D.h.

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

ParameterLine2D() [3/3]

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

absoluteDistance()

double absoluteDistance ( const Vector2D &  point ) const

inline

Gives the unsigned distance of a point to the line.

Definition at line 221 of file ParameterLine2D.h.

      {
        return fabs(distance(point));
      }

alignedWithFirst()

EForwardBackward alignedWithFirst ( ) const

inline

Indicates if the tangential vector point in a commmon direction with the first coordinate axes.

Definition at line 149 of file ParameterLine2D.h.

      {
        return static_cast<EForwardBackward>(sign(tangential().first()));
      }

alignedWithSecond()

EForwardBackward alignedWithSecond ( ) const

inline

Indicates if the tangential vector point in a commmon direction with the second coordinate axes.

Definition at line 156 of file ParameterLine2D.h.

      {
        return static_cast<EForwardBackward>(sign(tangential().second()));
      }

at()

Vector2D at ( const double  parameter ) const

inline

Evaluates the line formula at the parameter given.

Definition at line 142 of file ParameterLine2D.h.

      {
        return tangential() * parameter += support();
      }

closest()

Vector2D closest ( const Vector2D &  point ) const

inline

Gives the position at the closest approach on the line to point.

Definition at line 245 of file ParameterLine2D.h.

      {
        double norm_squared = tangential().normSquared();
        return Vector2D(tangential(),
                        tangential().dot(point) / norm_squared,
                        tangential().cross(support()) / norm_squared);
      }

closestAt()

double closestAt ( const Vector2D &  point ) const

inline

Gives the line parameter at the closest approach to point.

Definition at line 254 of file ParameterLine2D.h.

      {
        return (tangential().dot(point) - tangential().dot(support())) / tangential().normSquared();
      }

closestToOrigin()

Vector2D closestToOrigin ( ) const

inline

Gives the position of closest approach to the origin.

Definition at line 260 of file ParameterLine2D.h.

      {
        return tangential().orthogonal() *=
                 (tangential().cross(support()) / tangential().normSquared());
      }

closestToOriginAt()

double closestToOriginAt ( ) const

inline

Gives the line parameter at the closest approach to the origin.

Definition at line 267 of file ParameterLine2D.h.

      {
        return -tangential().dot(support()) / tangential().normSquared();
      }

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.

      {
        return distance(Vector2D(first, second));
      }

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.

      {
        return distanceToOrigin() - point.orthogonalComp(tangential());
      }

distanceToOrigin()

double distanceToOrigin ( ) const

inline

Gives the signed distance of the origin.

Definition at line 215 of file ParameterLine2D.h.

      {
        return support().orthogonalComp(tangential());
      }

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.

      {
        return ParameterLine2D(Vector2D(0.0, intercept), Vector2D(1.0, slope));
      }

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.

      {
        return ParameterLine2D(Vector2D(0.0, intercept),
                               Vector2D(orientation, static_cast<double>(orientation) * slope));
      }

intercept()

double intercept ( ) const

inline

Second coordinate for first being zero.

Definition at line 388 of file ParameterLine2D.h.

      {
        return support().second() - slope() * support().first();
      }

intersection() [1/2]

Vector2D intersection ( const Line2D &  line ) const

inline

Gives the point where the two lines meet. Infinities for parallels.

Definition at line 306 of file ParameterLine2D.h.

      {
        return at(intersectionAt(line));
      }

intersection() [2/2]

Vector2D intersection ( const ParameterLine2D &  line ) const

inline

Gives the point where the two lines meet. Infinities for parallels.

Definition at line 312 of file ParameterLine2D.h.

      {
        return at(intersectionAt(line));
      }

intersectionAt() [1/2]

double intersectionAt ( const Line2D &  line ) const

inline

Gives the line parameter where the two lines meet. Infinity for parallels.

Definition at line 279 of file ParameterLine2D.h.

      {
        return -(line.n0() + support().dot(line.normal())) / tangential().dot(line.normal());
      }

intersectionAt() [2/2]

double intersectionAt ( const ParameterLine2D &  line ) const

inline

Gives the line parameter of this line where the two lines meet. Infinity for parallels.

Definition at line 285 of file ParameterLine2D.h.

      {
        return (line.tangential().cross(support()) - line.tangential().cross(line.support())) /
               tangential().cross(line.tangential());
      }

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.

      {
        double a = genCircle.n3() * tangential().normSquared();
        double b = tangential().dot(genCircle.gradient(support()));
        double c = genCircle.fastDistance(support());
 
        return solveQuadraticABC(a, b, c);
      }

invalidate()

void invalidate ( )

inline

Clear all information from the line.

Definition at line 173 of file ParameterLine2D.h.

      {
        m_support.set(0, 0);
        m_tangential.set(0, 0);
      }

inverseMap()

double inverseMap ( const double  second ) const

inline

Method for the inverse mapping the second coordinate to the first according to the line.

Definition at line 412 of file ParameterLine2D.h.

      {
        return support().first() + inverseSlope() * (second - support().second());
      }

inverseSlope()

double inverseSlope ( ) const

inline

The inveres line slope.

Definition at line 382 of file ParameterLine2D.h.

      {
        return tangential().first() / tangential().second();
      }

invert()

void invert ( )

inline

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

Definition at line 418 of file ParameterLine2D.h.

      {
        m_tangential.swapCoordinates();
        m_support.swapCoordinates();
      }

inverted()

ParameterLine2D inverted ( ) const

inline

Gives the line assoziated with the inverse function as a copy.

Definition at line 425 of file ParameterLine2D.h.

      {
        return ParameterLine2D(Vector2D(support().second(), support().first()),
                               Vector2D(tangential().second(), tangential().first()));
      }

isInvalid()

bool isInvalid ( ) const

inline

Check it the line is in an invalid state.

Definition at line 180 of file ParameterLine2D.h.

      {
        return m_tangential.isNull();
      }

isLeft()

bool isLeft ( const Vector2D &  rhs ) const

inline

Return if the point given is left of the line.

Definition at line 233 of file ParameterLine2D.h.

      {
        return isRightOrLeft(rhs) == ERightLeft::c_Left;
      }

isRight()

bool isRight ( const Vector2D &  rhs ) const

inline

Return if the point given is right of the line.

Definition at line 239 of file ParameterLine2D.h.

      {
        return isRightOrLeft(rhs) == ERightLeft::c_Right;
      }

isRightOrLeft()

ERightLeft isRightOrLeft ( const Vector2D &  point ) const

inline

Return if the point given is right or left of the line.

Definition at line 227 of file ParameterLine2D.h.

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

lengthOnCurve()

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

inline

Denotes the length on the line between the two points.

Definition at line 273 of file ParameterLine2D.h.

      {
        return (to.dot(tangential()) - from.dot(tangential())) / tangential().norm();
      }

map()

double map ( const double  first ) const

inline

Method mapping the first coordinate to the second according to the line.

Definition at line 400 of file ParameterLine2D.h.

      {
        return support().second() + slope() * (first - support().first());
      }

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.

      {
        m_support.setFirst(m_support.first() + first);
      }

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.

      {
        m_support.setSecond(m_support.second() + second);
      }

moveBy()

void moveBy ( const Vector2D &  by )

inline

Moves the line in the given direction in place. Corresponds to an active transformation.

Definition at line 329 of file ParameterLine2D.h.

      {
        m_support += by;
      }

normal()

Vector2D normal ( ) const

inline

Gives the normal vector of the line.

Definition at line 130 of file ParameterLine2D.h.

      {
        return tangential().orthogonal(ERotation::c_Clockwise);
      }

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.

      {
        m_tangential.normalize();
      }

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.

      {
        return Line2D(distanceToOrigin(), normal().unit());
      } // not optimal yet. tangential.norm() is getting calculated two times.

operator()()

double operator() ( const double  first ) const

inline

Operator mapping the first coordinate to the second according to the line.

Definition at line 406 of file ParameterLine2D.h.

      {
        return map(first);
      }

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.

      {
        m_support.setFirst(m_support.first() - first);
      }

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.

      {
        m_support.setSecond(m_support.second() - second);
      }

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.

      {
        m_support += tangential() * delta;
      }

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.

      {
        m_support -= by;
      }

reverse()

void reverse ( )

inline

Reverses the tangential vector inplace.

Definition at line 186 of file ParameterLine2D.h.

      {
        m_tangential.reverse();
      }

reversed()

ParameterLine2D reversed ( ) const

inline

Makes a copy line which has the opposite tangential vector but same support point.

Definition at line 192 of file ParameterLine2D.h.

      {
        return ParameterLine2D(support(), -tangential());
      }

slope()

double slope ( ) const

inline

The line slope.

Definition at line 376 of file ParameterLine2D.h.

      {
        return tangential().second() / tangential().first();
      }

support()

const Vector2D & support ( ) const

inline

Gives the support vector of the line.

Definition at line 136 of file ParameterLine2D.h.

      {
        return m_support;
      }

tangential()

const Vector2D & tangential ( ) const

inline

Gives the tangential vector of the line.

Definition at line 125 of file ParameterLine2D.h.

      {
        return m_tangential;
      }

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.

      {
        return ParameterLine2D(start, end - start);
      }

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);
}

zero()

double zero ( ) const

inline

First coordinate for second being zero.

Definition at line 394 of file ParameterLine2D.h.

      {
        return support().first() - inverseSlope() * support().second();
      }

Member Data Documentation

m_support

Vector2D m_support

private

Support vector of the line.

Definition at line 434 of file ParameterLine2D.h.

m_tangential

Vector2D m_tangential

private

Tangential vector of the line.

Definition at line 437 of file ParameterLine2D.h.

---

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

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