This class defines 2D geometric vectors, which can be defined by their Polar or Cartesian coordinates. More...

#include <Vector.hpp>

Inheritance diagram for iSeeML::geom::Vector:

Collaboration diagram for iSeeML::geom::Vector:

[legend]

Public Member Functions
	Vector ()
	The default constructor, creating the zero vector with Cartesian coordinates (0,0).

	Vector (const double &theta)
	A simple constructor, creating the unit vector of given orientation. More...

	Vector (const double &x, const double &y)
	The main constructor, creating a vector from its Cartesian coordinates. More...

iSeeML::Object &	clone () const
	Description method, giving a copy of the current vector. More...

void	writeTo (ostream &O) const
	Description method, writing a description of the vector into a stream: Cartesian coordinate in each dimension is written, between paranthesis and separated by commas. More...

const double &	xCoord () const
	Description method, giving the vector's first Cartesian coordinate. More...

const double &	yCoord () const
	Description method, giving the vector's second Cartesian coordinate. More...

double	orientation () const
	Description method, giving the vector's orientation. More...

double	length () const
	Description method, giving the vector's length. More...

double	sqrLength () const
	Description method, giving the square of the vector's length. More...

Vector &	moveTo (const double &x, const double &y)
	Modification method, moving the point to a given position. More...

Vector &	translate (const Vector &v)
	Modification method, translating the vector along an other. More...

Vector &	rotate (const double &theta)
	Modification method, rotating the vector of a given angle. More...

Vector &	add (const Vector &v)
	Modification method, adding a vector to the current one. More...

Vector &	multiply (const double &f)
	Modification method, multiplying a vector by a real factor. More...

Vector &	divide (const double &f)
	Division method, dividing a vector by a real factor. More...

Vector &	symmetryOx ()
	Modification method, transforming a vector into its symmetric with respect to the X axis. More...

Vector &	symmetryOy ()
	Modification method, transforming a vector into its symmetric with respect to the Y axis. More...

bool	operator== (const Vector &other) const
	Equality operator between vectors (differences between both Cartesian coordinates should be zero). More...

Vector	operator+ (const Vector &v) const
	Sum operator between two vectors, giving the translation of the first one by the other. More...

Vector	operator- (const Vector &v) const
	Difference operator between two vectors, giving the sum of the first vector and of the second one's opposite. More...

Vector	operator- () const
	Opposite operator for a vector, such that the sum of the vector and of its opposite is the zero vector. More...

Vector	operator* (const double &f) const
	Multiplication operator between a vector and a real. More...

Vector	operator/ (const double &f) const
	Division operator between a vector and a real. More...

double	operator* (const Vector &v) const
	Scalar product operator between two vectors. More...

double	operator^ (const Vector &v) const
	Vectorial product operator between two vectors. More...

Public Member Functions inherited from iSeeML::geom::Object
virtual bool	operator== (const iSeeML::geom::Object &other) const
	Equality operator between geometric objects. More...

Public Member Functions inherited from iSeeML::Object
virtual	~Object ()
	This virtual class needs a virtual destructor.

virtual const string	className () const
	Description method, giving the object's class name. More...

bool	sameClass (const iSeeML::Object &other)
	Method verifying that a given object has the same type (same class name) than the current one. More...

Static Public Member Functions
static double	FresnelCos (const double &s)
	Various method, computing the Fresnel Cosine integral. More...

static double	FresnelSin (const double &s)
	Various method, computing the Fresnel Sine integral. More...

static Vector	FresnelInt (const double &s)
	Various method, computing the Fresnel integrals in a vector. More...

Static Public Member Functions inherited from iSeeML::Object
template<class T >
static const T &	min (const T &a, const T &b)
	Method giving the minimum of two elements. More...

template<class T >
static const T &	max (const T &a, const T &b)
	Method giving the maximum of two elements. More...

static double	sqr (const double &x)
	Method giving the square of a double. More...

static double	mod2pi (const double &theta)
	Method giving the angle between - $\pi$ (excluded) and $\pi$ (included), which is equal to a given angle modulo 2 $\pi$ . More...

static double	rad2deg (const double &theta)
	Method transforming an angle in radian, $x \pi$ with between -1 (excluded) and 1 (included), into its equivalent in degree, i.e. More...

static double	deg2rad (const double &theta)
	Method transforming an angle in degree, with between -1 (excluded) and 1 (included), into its equivalent in radian, i.e. More...

static bool	isPositive (const double &x)
	Method telling whether a double is strictly positive. More...

static bool	isNegative (const double &x)
	Method telling whether a double is strictly negative. More...

static bool	isZero (const double &x)
	Method comparing a double to zero. More...

static int	sign (const double &x)
	Method giving the sign of a double. More...

Static Public Attributes
static const string	ClassName
	The class name is public, as this class can be instanced. More...

Protected Member Functions
int	algDimension () const
	Description method, giving the dimension of the containing space (2) when this vector is considered as an algebraic one. More...

double	algCoord (const int i) const
	Description method, giving Cartesian coordinate of given index for the vector. More...

Protected Member Functions inherited from iSeeML::Object
virtual void	algWriteTo (ostream &O) const
	Description method for algebraic vectors, writing this vector in a given output stream: coordinates for each dimension are written, between paranthesis and separated by commas. More...

Friends
Vector	operator* (const double &f, const Vector &v)
	Multiplication operator between a real and a vector. More...

Vector	operator/ (const double &f, const Vector &v)
	Division operator between a real and a vector. More...

Additional Inherited Members
Related Functions inherited from iSeeML::Object
ostream &	operator<< (ostream &O, const iSeeML::Object &o)
	Modification method, writing a description of a ISeeML object in a given output stream. More...

Detailed Description

This class defines 2D geometric vectors, which can be defined by their Polar or Cartesian coordinates.

This class contains description methods giving Polar and Cartesian coordinates as well as the writeTo method, modification methods giving translation, rotation, scaling and symmetry of a vector, the corresponding operators as well as the equality operator, and a last method computing Cartesian coordinates of a reference clothoid (which are Fresnel integrals).

Author: Alexis Scheuer.

Version: 1.0

Examples:: wxGuiFwd.cpp.

Constructor & Destructor Documentation

iSeeML::geom::Vector::Vector ( const double & theta )

inline

A simple constructor, creating the unit vector of given orientation.

The vector of Polar coordinates (rho, theta) can thus be obtained using iSeeML::geom::Vector(theta).multiply(rho).

Parameters

theta the orientation of the vector.

See also: orientation, length, multiply.

iSeeML::geom::Vector::Vector	(	const double &	x,
		const double &	y
	)

inline

The main constructor, creating a vector from its Cartesian coordinates.

Parameters

x	the first Cartesian coordinate of the vector,
y	the second Cartesian coordinate of the vector.

See also: xCoord, yCoord.

Member Function Documentation

Vector& iSeeML::geom::Vector::add ( const Vector & v )

inline

Modification method, adding a vector to the current one.

The original vector is changed, addition without modification is obtained using operator+(const Vector&) const.

Parameters

v	the vector of the translation.

Returns: the new vector, after translation / addition.

double iSeeML::geom::Vector::algCoord ( const int i ) const

inlineprotectedvirtual

Description method, giving Cartesian coordinate of given index for the vector.

Parameters

i	the index of the searched Cartesian coordinate.

Precondition: the parameter is an index, and should be equal to one or two. If not, and if ISEEML_CHECK_GEOM_VECT_PRECOND is defined (see CompilerFlags.h), an error is generated.

Returns: the Cartesian coordinate associated to the index if this one is between 1 and dimension, or 0.

See also: xCoord, yCoord, algDimension.

Reimplemented from iSeeML::Object.

int iSeeML::geom::Vector::algDimension ( ) const

inlineprotectedvirtual

Description method, giving the dimension of the containing space (2) when this vector is considered as an algebraic one.

This representation is mainly used to define a unified writeTo. Dimension cannot be static, as it is virtual.

Reimplemented from iSeeML::Object.

iSeeML::Object& iSeeML::geom::Vector::clone ( ) const

inlinevirtual

Description method, giving a copy of the current vector.

This clone is dynamically allocated (using default copy constructor), it has to be deleted later.

Returns: a copy/clone of the current vector.

Implements iSeeML::Object.

Vector& iSeeML::geom::Vector::divide ( const double & f )

inline

Division method, dividing a vector by a real factor.

The original vector is changed, division without modification is obtained using operator/() const.

Parameters

f	a real factor.

Precondition: the dividing factor should not be zero. If it is, and ISEEML_CHECK_GEOM_VECT_PRECOND is defined (see CompilerFlags.h), an error is generated.

Returns: the new vector, after division.

See also: multiply.

static double iSeeML::geom::Vector::FresnelCos ( const double & s )

inlinestatic

Various method, computing the Fresnel Cosine integral.

Parameters

s	the integration length.

Precondition: Coordinates have only been computed for values of the arc length s smaller (in absolute value) then 2, which correspond to a deflection (change of the orientation) of $\pm$ 2 $\pi$ .

Returns: the integral, from zero to s, of cos( $\pi$ u² / 2).

See also: FresnelInt, xCoord.

static Vector iSeeML::geom::Vector::FresnelInt ( const double & s )

static

Various method, computing the Fresnel integrals in a vector.

The returned vector correspond to the Cartesian coordinates of the point of given arc length along a reference clothoid (along which curvature is equal to $\pi$ times the arc length). These coordinates have been precomputed with a precision of 1E-5, and are stored in two static arrays.

Parameters

s	the arc length along the reference clothoid of the searched position, or the integration length of the Fresnel integrals.

Precondition: Coordinates have only been computed for values of the arc length s smaller (in absolute value) then 2, which correspond to a deflection (change of the orientation) of $\pm$ 2 $\pi$ . An error message is generated if s is not correct and check flags ISEEML_CHECK_GEOM_VECT_PRECOND or ISEEML_CHECK_ARRAY_ELEMT (see CompilerFlags.h) are defined.

Returns: the vector whose Cartesian coordinates are the integral, from zero to s, of respectively cos( $\pi$ u² / 2) and sin( $\pi$ u² / 2).

static double iSeeML::geom::Vector::FresnelSin ( const double & s )

inlinestatic

Various method, computing the Fresnel Sine integral.

Parameters

s	the integration length.

Precondition: Coordinates have only been computed for values of the arc length s smaller (in absolute value) then 2, which correspond to a deflection (change of the orientation) of $\pm$ 2 $\pi$ .

Returns: the integral, from zero to s, of sin( $\pi$ u² / 2).

See also: FresnelInt, yCoord.

double iSeeML::geom::Vector::length ( ) const

inline

Description method, giving the vector's length.

The couple (length, orientation) gives Polar coordinates of the vector, while the couple (xCoord, yCoord) gives Cartesian coordinates.

Returns: the vector's length.

See also: sqrLength.

Vector& iSeeML::geom::Vector::moveTo	(	const double &	x,
		const double &	y
	)

inline

Modification method, moving the point to a given position.

The original vector is changed.

Parameters

x	the first coordinate of the new position,
y	the second coordinate of the new position.

Returns: the vector, after tranformation.

See also: xCoord, yCoord.

Vector& iSeeML::geom::Vector::multiply ( const double & f )

inline

Modification method, multiplying a vector by a real factor.

The original vector is changed, multiplication without modification is obtained using operator*() const.

Parameters

f	a real factor.

Returns: the new vector, after multiplication.

Vector iSeeML::geom::Vector::operator* ( const double & f ) const

inline

Multiplication operator between a vector and a real.

Parameters

f	a real factor.

Returns: the product of the current vector by the real factor.

See also: multiply.

double iSeeML::geom::Vector::operator* ( const Vector & v ) const

inline

Scalar product operator between two vectors.

Parameters

v	the second vector of the product.

Returns: the scalar product between the current vector and the given one.

Vector iSeeML::geom::Vector::operator+ ( const Vector & v ) const

inline

Sum operator between two vectors, giving the translation of the first one by the other.

Parameters

v	the vector of the translation.

Returns: the sum of the two vectors.

See also: add.

Vector iSeeML::geom::Vector::operator- ( const Vector & v ) const

inline

Difference operator between two vectors, giving the sum of the first vector and of the second one's opposite.

Parameters

v a vector.

Returns: the current vector minus the given one.

See also: operator-(), operator+.

Vector iSeeML::geom::Vector::operator- ( ) const

inline

Opposite operator for a vector, such that the sum of the vector and of its opposite is the zero vector.

Returns: the opposite of the current vector.

See also: multiply.

Vector iSeeML::geom::Vector::operator/ ( const double & f ) const

inline

Division operator between a vector and a real.

Parameters

f	a real factor.

Precondition: the dividing factor should not be zero.

Returns: the division of the current vector by the real factor.

See also: operator*(const double&), divide.

bool iSeeML::geom::Vector::operator== ( const Vector & other ) const

inline

Equality operator between vectors (differences between both Cartesian coordinates should be zero).

Parameters

other another vector.

Returns: whether the two vectors are equal.

See also: xCoord, yCoord, iSeeML::Object::isZero.

double iSeeML::geom::Vector::operator^ ( const Vector & v ) const

inline

Vectorial product operator between two vectors.

Parameters

v	the second vector of the product.

Returns: the vectorial product between the current vector and the given one.

double iSeeML::geom::Vector::orientation ( ) const

inline

Description method, giving the vector's orientation.

The couple (length, orientation) gives Polar coordinates of the vector, while the couple (xCoord, yCoord) gives Cartesian coordinates. Orientation is always uniquely defined, except for zero vector. In that case, we choose to return 0.

Returns: the vector's orientation, between - $\pi$ (excluded) and $\pi$ (included), if vector is not zero, or zero.

See also: iSeeML::Object::isPositive, iSeeML::Object::isNegative, iSeeML::Object::sign, atan.

Vector& iSeeML::geom::Vector::rotate ( const double & theta )

inline

Modification method, rotating the vector of a given angle.

The original vector is changed.

Parameters

theta the angle of the rotation.

Returns: the new vector, after rotation.

double iSeeML::geom::Vector::sqrLength ( ) const

inline

Description method, giving the square of the vector's length.

Uses the scalar product.

Returns: the square of the vector's length.

See also: operator*(const iSeeML::geom::Vector&).

Vector& iSeeML::geom::Vector::symmetryOx ( )

inline

Modification method, transforming a vector into its symmetric with respect to the X axis.

Returns: the new vector, after transformation.

Vector& iSeeML::geom::Vector::symmetryOy ( )

inline

Modification method, transforming a vector into its symmetric with respect to the Y axis.

Returns: the new vector, after transformation.

Vector& iSeeML::geom::Vector::translate ( const Vector & v )

inlinevirtual

Modification method, translating the vector along an other.

The original vector is changed, addition without modification is obtained using operator+(const Vector&) const.

Parameters

v	the vector of the translation.

Returns: the new vector, after translation.

See also: add.

Implements iSeeML::geom::Object.

void iSeeML::geom::Vector::writeTo ( ostream & O ) const

inlinevirtual

Description method, writing a description of the vector into a stream: Cartesian coordinate in each dimension is written, between paranthesis and separated by commas.

Parameters

O	the output stream in which description is written.

Implements iSeeML::Object.

const double& iSeeML::geom::Vector::xCoord ( ) const

inline

Description method, giving the vector's first Cartesian coordinate.

Returns: the vector's first Cartesian coordinate.

const double& iSeeML::geom::Vector::yCoord ( ) const

inline

Description method, giving the vector's second Cartesian coordinate.

Returns: the vector's second Cartesian coordinate.

Friends And Related Function Documentation

Vector operator*	(	const double &	f,
		const Vector &	v
	)

friend

Multiplication operator between a real and a vector.

Parameters

f	the real factor,
v	the vector.

Returns: the product between the factor and the vector.

See also: const operator*(const double&).

Vector operator/	(	const double &	f,
		const Vector &	v
	)

friend

Division operator between a real and a vector.

Parameters

f	the real factor,
v	the vector.

Precondition: the dividing factor should not be zero.

Returns: the division between the factor and the vector.

See also: const operator/(const double&).

Member Data Documentation

const string iSeeML::geom::Vector::ClassName

static

The class name is public, as this class can be instanced.

See also: className.

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

/home/ajs/Loria/Local/Compte/Recherche/Prog/C++/ISeeML/include/iSeeML/geom/Vector.hpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation