The aim of this class is to compute the measure in the Lebesgues sense of the set of straight lines associated to domains defined as polygons in the (a,b)-parameter space. This parameter space maps the line $ax-y+b=0$ to the point $(a,b)$. More...

#include <DGtal/math/MeasureOfStraightLines.h>

Public Member Functions
	MeasureOfStraightLines ()

	~MeasureOfStraightLines ()

void	selfDisplay (std::ostream &out) const

bool	isValid () const

double	computeMeasure (const std::vector< double > &a, const std::vector< double > &b)

double	computeCentroidA (const std::vector< double > &a, const std::vector< double > &b)

double	computeCentroidB (const std::vector< double > &a, const std::vector< double > &b)

void	setEpsilon (const double aValue)

Private Member Functions
	MeasureOfStraightLines (const MeasureOfStraightLines &other)

MeasureOfStraightLines &	operator= (const MeasureOfStraightLines &other)

double	computeMeasureEdge (double a0, double b0, double a1, double b1)

double	computeCentroidEdge_a (double a0, double b0, double a1, double b1)

double	computeCentroidEdge_b (double a0, double b0, double a1, double b1)

double	__computeCentroidTriApprox_b (double a0, double b0, double a1, double b1)

double	__computeCentroidEdgeApprox_b (double a0, double b0, double a1, double b1)

double	__computeCentroidSquare_b (double x1, double y1, double x2, double y2)

int	sign (const double a)

Private Attributes
double	myEpsilon

Detailed Description

The aim of this class is to compute the measure in the Lebesgues sense of the set of straight lines associated to domains defined as polygons in the (a,b)-parameter space. This parameter space maps the line $ax-y+b=0$ to the point $(a,b)$.

Description of class 'MeasureOfStraightLines'

Aim:

* @inproceedings{COEURJOLLY:2009:HAL-00432711:1,
*   title = { {M}easure of {S}traight {L}ines and its {A}pplications in {D}igital {G}eometry},
*   author = {{C}oeurjolly, {D}avid and {S}ivignon, {I}sabelle},
*   booktitle = {13th {I}nternational {W}orkshop on {C}ombinatorial {I}mage {A}nalysis 13th {I}nternational {W}orkshop on {C}ombinatorial {I}mage {A}nalysis },
*   publisher = {{R}esearch {P}ublishing {S}ervices },
*   pages = {1-12 },
*   address = {{C}ancun {M}exique },
*   audience = {internationale },
*   year = {2009},
*   URL = {http://hal.archives-ouvertes.fr/hal-00432711/PDF/mesure.pdf},
* }
*

See also: testMeasure.cpp

Todo:: Create a vector<Point> interface

Definition at line 79 of file MeasureOfStraightLines.h.

Constructor & Destructor Documentation

◆ MeasureOfStraightLines() [1/2]

DGtal::MeasureOfStraightLines::MeasureOfStraightLines ( )

Constructor.

◆ ~MeasureOfStraightLines()

DGtal::MeasureOfStraightLines::~MeasureOfStraightLines ( )

Destructor.

◆ MeasureOfStraightLines() [2/2]

DGtal::MeasureOfStraightLines::MeasureOfStraightLines ( const MeasureOfStraightLines & other )

private

Copy constructor.

Parameters

other the object to clone. Forbidden by default.

Member Function Documentation

◆ __computeCentroidEdgeApprox_b()

double DGtal::MeasureOfStraightLines::__computeCentroidEdgeApprox_b	(	double	a0,
		double	b0,
		double	a1,
		double	b1
	)

private

Approximate the centroid on 'b' on the trapezioid (a0,0)-(a0,b0)-(a1,b1)-(a1,0) (internal function)

Parameters

a0	abscissa first point.
b0	ordinate of the first point.
a1	abscissa of the second point.
b1	ordinate of the second point.

◆ __computeCentroidSquare_b()

double DGtal::MeasureOfStraightLines::__computeCentroidSquare_b	(	double	x1,
		double	y1,
		double	x2,
		double	y2
	)

private

Compute the centroid on 'b' on the rectangular domain with vertices (x1,,y1) - (x2,y2)

Precondition: y1<y2

Parameters

x1	abscissa first point.
y1	ordinate of the first point.
x2	abscissa of the second point.
y2	ordinate of the second point.

◆ __computeCentroidTriApprox_b()

double DGtal::MeasureOfStraightLines::__computeCentroidTriApprox_b	(	double	a0,
		double	b0,
		double	a1,
		double	b1
	)

private

Approximate the centroid on 'b' on the triangle (0,0)-(a0,b0)-(a1,b1) (internal function)

Parameters

a0	abscissa first point.
b0	ordinate of the first point.
a1	abscissa of the second point.
b1	ordinate of the second point.

◆ computeCentroidA()

double DGtal::MeasureOfStraightLines::computeCentroidA	(	const std::vector< double > &	a,
		const std::vector< double > &	b
	)

Compute the abscissa of the centroid of the polygon {(a_i,b_i)} in the (a,b)-parameter space with respect to the measure of lines.

REQUIREMENTS:

The polygon is given counter-clockwise
a_i > 0

Parameters

a	the a-value of polygon vertices
b	the b-value of polygon vertices

Returns: the measure value (positive value)

Referenced by testUnitSquareCentroid().

◆ computeCentroidB()

double DGtal::MeasureOfStraightLines::computeCentroidB	(	const std::vector< double > &	a,
		const std::vector< double > &	b
	)

Compute the ordinate of the centroid of the polygon {(a_i,b_i)} in the (a,b)-parameter space with respect to the measure of lines. Note that there is a numerical approximation is performed.

REQUIREMENTS:

The polygon is given counter-clockwise
a_i > 0

Parameters

a	the a-value of polygon vertices
b	the b-value of polygon vertices

Returns: the measure value (positive value)

Referenced by testUnitSquareCentroid().

◆ computeCentroidEdge_a()

double DGtal::MeasureOfStraightLines::computeCentroidEdge_a	(	double	a0,
		double	b0,
		double	a1,
		double	b1
	)

private

Compute the abscissa of the centroid associated to an edge (a0,b0)-(a1,b1) It returns the measure of the triangle defined by the origin and the edge.

Parameters

a0	abscissa first point.
b0	ordinate of the first point.
a1	abscissa of the second point.
b1	ordinate of the second point.

Returns: the measure

◆ computeCentroidEdge_b()

double DGtal::MeasureOfStraightLines::computeCentroidEdge_b	(	double	a0,
		double	b0,
		double	a1,
		double	b1
	)

private

Compute the ordinate of the centroid associated to an edge (a0,b0)-(a1,b1) It returns the measure of the triangle defined by the origin and the edge.

Parameters

a0	abscissa first point.
b0	ordinate of the first point.
a1	abscissa of the second point.
b1	ordinate of the second point.

Returns: the measure

◆ computeMeasure()

double DGtal::MeasureOfStraightLines::computeMeasure	(	const std::vector< double > &	a,
		const std::vector< double > &	b
	)

Compute the measure of the polygon {(a_i,b_i)} in the (a,b)-parameter space

REQUIREMENTS:

The polygon is given counter-clockwise
a_i > 0

Parameters

a	the a-value of polygon vertices
b	the b-value of polygon vertices

Returns: the measure value (positive value)

Referenced by testUnitSquare().

◆ computeMeasureEdge()

double DGtal::MeasureOfStraightLines::computeMeasureEdge	(	double	a0,
		double	b0,
		double	a1,
		double	b1
	)

private

Compute the measure associated to an edge (a0,b0)-(a1,b1) It returns the measure of the triangle defined by the origin and the edge.

Parameters

a0	abscissa first point.
b0	ordinate of the first point.
a1	abscissa of the second point.
b1	ordinate of the second point.

Returns: the measure

◆ isValid()

bool DGtal::MeasureOfStraightLines::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ operator=()

MeasureOfStraightLines & DGtal::MeasureOfStraightLines::operator= ( const MeasureOfStraightLines & other )

private

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'. Forbidden by default.

◆ selfDisplay()

void DGtal::MeasureOfStraightLines::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ setEpsilon()

void DGtal::MeasureOfStraightLines::setEpsilon ( const double aValue )

Set the internal Epsilon threshold for the numerical approximation.

Parameters

aValue the new epsilon value

◆ sign()

int DGtal::MeasureOfStraightLines::sign ( const double a )

private

Parameters

a a value

Returns: the sign of a number (1 or -1)

Field Documentation

◆ myEpsilon

double DGtal::MeasureOfStraightLines::myEpsilon

private

Definition at line 171 of file MeasureOfStraightLines.h.

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

MeasureOfStraightLines.h

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MeasureOfStraightLines() [1/2]

◆ ~MeasureOfStraightLines()

◆ MeasureOfStraightLines() [2/2]

Member Function Documentation

◆ __computeCentroidEdgeApprox_b()

◆ __computeCentroidSquare_b()

◆ __computeCentroidTriApprox_b()

◆ computeCentroidA()

◆ computeCentroidB()

◆ computeCentroidEdge_a()

◆ computeCentroidEdge_b()

◆ computeMeasure()

◆ computeMeasureEdge()

◆ isValid()

◆ operator=()

◆ selfDisplay()

◆ setEpsilon()

◆ sign()

Field Documentation

◆ myEpsilon