This class implements an infinite line in 2D space. More...

Inheritance diagram for Ocean::LineT2< T >:

Public Types
typedef T	Type
	Definition of the used data type. More...

Public Member Functions
	LineT2 ()
	Creates an invalid line. More...

	LineT2 (const VectorT2< T > &point, const VectorT2< T > &direction)
	Creates a line defined by a point on the line and a line direction. More...

	LineT2 (const VectorT3< T > &parameters)
	Creates a new line object by given (implicit) three-parameter representation of the line. More...

	LineT2 (const T angle, const T distance)
	Creates a new line object by a given angle of the line's normal and the distance of the line to the origin. More...

template<typename U >
	LineT2 (const LineT2< U > &line)
	Copies a line with different data type than T. More...

const VectorT2< T > &	point () const
	Returns a point on the line. More...

VectorT2< T >	point (const T distance) const
	Returns a point on the line that is defined by a scalar. More...

const VectorT2< T > &	direction () const
	Returns the direction of the line. More...

VectorT2< T >	normal () const
	Returns a normal to the direction of this line. More...

void	decomposeAngleDistance (T &angle, T &distance) const
	Calculates the angle of the line's normal and the corresponding distance of this line to the origin. More...

VectorT3< T >	decomposeNormalDistance (const bool forcePositiveDistance=false) const
	Calculates the (implicit) three-parameters representation of this line composed of the line's normal and a distance parameter (nx, ny, d). More...

bool	isOnLine (const VectorT2< T > &point) const
	Returns whether a given point is part of the line. More...

bool	isLeftOfLine (const VectorT2< T > &point) const
	Check if a point is in the left half-plane of the direction vector of a line A point `p` is located on the left side of a line, if the cross product of the direction of the line, `d`, and the vector pointing from starting point of the line, `s`, to the point `p` is positive: (d x (p - s)) > 0. More...

T	distance (const VectorT2< T > &point) const
	Returns the distance between the line and a given point. More...

T	sqrDistance (const VectorT2< T > &point) const
	Returns the square distance between the line and a given point. More...

VectorT2< T >	nearestPoint (const VectorT2< T > &point) const
	Returns the point on this line nearest to an arbitrary given point. More...

bool	intersection (const LineT2< T > &right, VectorT2< T > &point) const
	Returns the unique intersection point of two lines. More...

bool	isParallel (const LineT2< T > &right) const
	Returns whether two lines are parallel up to a small epsilon. More...

bool	isValid () const
	Returns whether this line has valid parameters. More...

bool	hasUnitDirection () const
	Returns whether this line has a unit vector as direction. More...

bool	operator== (const LineT2< T > &right) const
	Returns whether two line are identical up to a small epsilon. More...

bool	operator!= (const LineT2< T > &right) const
	Returns whether two line are identical up to a small epsilon. More...

	operator bool () const
	Returns whether this line is valid. More...

bool	isOnLine (const VectorT2< float > &point) const

Static Public Member Functions
static bool	fitLineLeastSquare (const VectorT2< T > *points, const size_t size, LineT2< T > &line)
	Fits a line to a set of given image points by application of the least square measure. More...

Protected Attributes
VectorT2< T >	linePoint
	Point on the line. More...

VectorT2< T >	lineDirection
	Direction of the line. More...

Friends
template<typename U >
class	LineT2

Detailed Description

template<typename T>
class Ocean::LineT2< T >

This class implements an infinite line in 2D space.

The implementation is realized by an (explicit) parametric equation using a point on the line and the direction of the line.
However, the line support conversion function to receive also an implicit equation.

Template Parameters

T	Data type used to represent lines

See also: Line2, LineF2, LineD2, FiniteLine2, FiniteLine.

Member Typedef Documentation

◆ Type

template<typename T >

typedef T Ocean::LineT2< T >::Type

Definition of the used data type.

Constructor & Destructor Documentation

◆ LineT2() [1/5]

template<typename T >

Ocean::LineT2< T >::LineT2

Creates an invalid line.

◆ LineT2() [2/5]

template<typename T >

Ocean::LineT2< T >::LineT2	(	const VectorT2< T > &	point,
		const VectorT2< T > &	direction
	)

Creates a line defined by a point on the line and a line direction.

Parameters

point	Point on the line
direction	Vector representing the direction of the line, a unit vector might be appropriate

◆ LineT2() [3/5]

template<typename T >

Ocean::LineT2< T >::LineT2 ( const VectorT3< T > & parameters )

explicit

Creates a new line object by given (implicit) three-parameter representation of the line.

The representation is given by the normal and the distance parameter of the line so that for a point (x, y) lying on the plane the following holds: [nx, ny, d] * [x, y, 1] == 0.
The normal must be defined as unit vector.

Parameters

parameters The three parameters given as 3D vector

◆ LineT2() [4/5]

template<typename T >

Ocean::LineT2< T >::LineT2	(	const T	angle,
		const T	distance
	)

Creates a new line object by a given angle of the line's normal and the distance of the line to the origin.

The distance values is equal to the distance parameter of a (implicit) three-parameter representation of a line where the other two parameters define the normal of the plane.

Parameters

angle	The angle of the line's normal, with normal = [cos(angle), sin(angle)], in radian
distance	The signed distance of the line to the origin, with range (-infinity, infinity)

See also: decomposeAngleDistance().

◆ LineT2() [5/5]

template<typename T >

template<typename U >

Ocean::LineT2< T >::LineT2 ( const LineT2< U > & line )

inlineexplicit

Copies a line with different data type than T.

Parameters

line	The line to copy

Template Parameters

U	The data type of the second line

Member Function Documentation

◆ decomposeAngleDistance()

template<typename T >

void Ocean::LineT2< T >::decomposeAngleDistance	(	T &	angle,
		T &	distance
	)		const

inline

Calculates the angle of the line's normal and the corresponding distance of this line to the origin.

The resulting distance parameter is equivalent to the distance parameter of a (implicit) three-parameter representation of this line where the other two parameters define the normal of the plane.

Parameters

angle	Resulting angle of the line's normal which is defined by atan(normal.y() / normal.x()); with normal = [cos(angle), sin(angle)], in radian
distance	Resulting signed distance between line and origin, is positive if the normal points towards the origin and negative if the normal points away from the origin

◆ decomposeNormalDistance()

template<typename T >

VectorT3< T > Ocean::LineT2< T >::decomposeNormalDistance ( const bool forcePositiveDistance = false ) const

inline

Calculates the (implicit) three-parameters representation of this line composed of the line's normal and a distance parameter (nx, ny, d).

For a point (x, y) lying on the plane the following holds: [nx, ny, d] * [x, y, 1] == 0.

Parameters

forcePositiveDistance True, to force a positive distance values; False, to accept positive and negative distance values

Returns: The resulting three parameter representation

◆ direction()

template<typename T >

const VectorT2< T > & Ocean::LineT2< T >::direction

inline

Returns the direction of the line.

Returns: Direction vector

◆ distance()

template<typename T >

T Ocean::LineT2< T >::distance ( const VectorT2< T > & point ) const

Returns the distance between the line and a given point.

This function needs a unit vector as direction!

Parameters

point Point to return the distance for

Returns: The always positive distance between point and line, with range [0, infinity)

◆ fitLineLeastSquare()

template<typename T >

bool Ocean::LineT2< T >::fitLineLeastSquare	(	const VectorT2< T > *	points,
		const size_t	size,
		LineT2< T > &	line
	)

inlinestatic

Fits a line to a set of given image points by application of the least square measure.

Parameters

points	The points for which the best fitting line is requested, must be valid
size	The number of given points, with range [2, infinity)
line	The resulting line

Returns: True, if succeeded

◆ hasUnitDirection()

template<typename T >

bool Ocean::LineT2< T >::hasUnitDirection

inline

Returns whether this line has a unit vector as direction.

Returns: True, if so

◆ intersection()

template<typename T >

bool Ocean::LineT2< T >::intersection	(	const LineT2< T > &	right,
		VectorT2< T > &	point
	)		const

Returns the unique intersection point of two lines.

Two identical lines do not have one unique intersection point, so that this function will return 'false' in such a case. This function needs a unit vector as direction!

Parameters

right	Right line for intersection calculation
point	Resulting intersection pointer

Returns: True, if both lines are not parallel

◆ isLeftOfLine()

template<typename T >

bool Ocean::LineT2< T >::isLeftOfLine ( const VectorT2< T > & point ) const

Check if a point is in the left half-plane of the direction vector of a line A point p is located on the left side of a line, if the cross product of the direction of the line, d, and the vector pointing from starting point of the line, s, to the point p is positive: (d x (p - s)) > 0.

It's on the line the cross product is zero and in the right half-plane it is negative.

Note: Keep in mind that if the point is not in the left half-plane, it doesn't necessarily mean that it's in the right half-plane because it could just as well be located on the line.

Parameters

point Point to check

Returns: True, if the point is in the left half-plane

◆ isOnLine() [1/2]

bool Ocean::LineT2< float >::isOnLine ( const VectorT2< float > & point ) const

inline

◆ isOnLine() [2/2]

template<typename T >

bool Ocean::LineT2< T >::isOnLine ( const VectorT2< T > & point ) const

Returns whether a given point is part of the line.

This function needs a unit vector as direction!

Parameters

point Point to check

Returns: True, if so

◆ isParallel()

template<typename T >

bool Ocean::LineT2< T >::isParallel ( const LineT2< T > & right ) const

Returns whether two lines are parallel up to a small epsilon.

This function needs a unit vector as direction!

Parameters

right Second line

Returns: True, if so

◆ isValid()

template<typename T >

bool Ocean::LineT2< T >::isValid

inline

Returns whether this line has valid parameters.

Returns: True, if so

◆ nearestPoint()

template<typename T >

VectorT2< T > Ocean::LineT2< T >::nearestPoint ( const VectorT2< T > & point ) const

Returns the point on this line nearest to an arbitrary given point.

This function needs a unit vector as direction!

Parameters

point Arbitrary point outside the line

Returns: Nearest point on the line

◆ normal()

template<typename T >

VectorT2< T > Ocean::LineT2< T >::normal

inline

Returns a normal to the direction of this line.

The 2D cross product between the resulting normal and the direction of this line will be positive.

Returns: The resulting normal

◆ operator bool()

template<typename T >

Ocean::LineT2< T >::operator bool

inlineexplicit

Returns whether this line is valid.

Returns: True, if so

◆ operator!=()

template<typename T >

bool Ocean::LineT2< T >::operator!= ( const LineT2< T > & right ) const

inline

Returns whether two line are identical up to a small epsilon.

Parameters

right Right line

Returns: True, if so

◆ operator==()

template<typename T >

bool Ocean::LineT2< T >::operator== ( const LineT2< T > & right ) const

Returns whether two line are identical up to a small epsilon.

Parameters

right Right line

Returns: True, if so

◆ point() [1/2]

template<typename T >

const VectorT2< T > & Ocean::LineT2< T >::point

inline

Returns a point on the line.

Returns: Point on line

◆ point() [2/2]

template<typename T >

VectorT2< T > Ocean::LineT2< T >::point ( const T distance ) const

inline

Returns a point on the line that is defined by a scalar.

The result is determined by point() + direction() * distance;

Parameters

distance Distance to determine the line point for

Returns: Point on line

◆ sqrDistance()

template<typename T >

T Ocean::LineT2< T >::sqrDistance ( const VectorT2< T > & point ) const

Returns the square distance between the line and a given point.

Parameters

point Point to return the distance for

Returns: Square distance between point and line

Friends And Related Function Documentation

◆ LineT2

template<typename T >

template<typename U >

friend class LineT2

friend

Field Documentation

◆ lineDirection

template<typename T >

VectorT2<T> Ocean::LineT2< T >::lineDirection

protected

Direction of the line.

◆ linePoint

template<typename T >

VectorT2<T> Ocean::LineT2< T >::linePoint

protected

Point on the line.

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

Line2.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

template<typename T> class Ocean::LineT2< T >

Member Typedef Documentation

◆ Type

Constructor & Destructor Documentation

◆ LineT2() [1/5]

◆ LineT2() [2/5]

◆ LineT2() [3/5]

◆ LineT2() [4/5]

◆ LineT2() [5/5]

Member Function Documentation

◆ decomposeAngleDistance()

◆ decomposeNormalDistance()

◆ direction()

◆ distance()

◆ fitLineLeastSquare()

◆ hasUnitDirection()

◆ intersection()

◆ isLeftOfLine()

◆ isOnLine() [1/2]

◆ isOnLine() [2/2]

◆ isParallel()

◆ isValid()

◆ nearestPoint()

◆ normal()

◆ operator bool()

◆ operator!=()

◆ operator==()

◆ point() [1/2]

◆ point() [2/2]

◆ sqrDistance()

Friends And Related Function Documentation

◆ LineT2

Field Documentation

◆ lineDirection

◆ linePoint

template<typename T>
class Ocean::LineT2< T >