Vectors in two dimensions. More...

#include <evector.h>

Public Member Functions
	Vector2 ()
	Empty.

	Vector2 (const double &)
	Create a vector with the same real coordinates. More...

	Vector2 (const double &, const double &)
	Create a vector with argument coordinates.

	Vector2 (const Vector &)
	Create a two dimension vector from another three dimension vector.

double &	operator[] (int)
	Gets the i-th coordinate of vector.

constexpr double	operator[] (int) const
	Returns the i-th coordinate of vector.

Vector2	Orthogonal () const
	Returns a direct orthogonal vector.

Vector2	operator+ () const
	Overloaded.

Vector2	operator- () const
	Overloaded.

Vector2 &	operator+= (const Vector2 &)
	Destructive addition.

Vector2 &	operator-= (const Vector2 &)
	Destructive subtraction.

Vector2 &	*operator=** (const Vector2 &)
	Destructively scale a vector by another vector.

Vector2 &	operator/= (const Vector2 &)
	Destructively divide the components of a vector by another vector.

Vector2 &	*operator=** (double)
	Destructive scalar multiply.

Vector2 &	operator/= (double)
	Destructive division by a scalar.

double	Max () const
	Compute the maximum component of a vector. More...

int	MaxIndex () const
	Compute the index of the maximum component of a vector. More...

int	MinIndex () const
	Compute the index of the minimum component of a vector. More...

Vector	ToVector (const double &=0.0) const
	Convert a Vector2 to a Vector. More...

Vector2	Inverse () const
	Inverse of a vector. More...

int	Quadrant (const Vector2 &) const
	Computes quadrant index of a vector with respect to the vector object. More...

QString	ToString (int=6) const
	Create a QString form a vector. More...

Vector2	Scaled (const Vector2 &) const
	Scales the vector. More...

void	Scale (const Vector2 &)
	Scales the vector. More...

Vector2	Sort () const
	Sort the terms of the vector into ascending order.

double	Angle (const Vector2 &) const
	Compute the angle between two vectors. More...

double	Angle () const
	Compute the angle of a vector. More...

Vector2	Floor () const
	Compute the numerator part of the coordinates. More...

Vector2	Fract () const
	Compute the fractional part of the coordinates. More...

Static Public Member Functions
static bool	Equal (const Vector2 &, const Vector2 &, const double &=0.0001)
	Test if two vectors are almost equal. More...

static Vector2	Min (const Vector2 &, const Vector2 &)
	Return a vector with coordinates set to the minimum coordinates of the two argument vectors.

static Vector2	Max (const Vector2 &, const Vector2 &)
	Return a vector with coordinates set to the maximum coordinates of the two argument vectors.

static void	SetMinMax (const Vector2 &, Vector2 &, Vector2 &)
	Update the minimum and maximum values given a vector. More...

static Vector2	Modulo (const Vector2 &, const Vector2 &)
	Modulo of two vectors. More...

static Vector2	Lerp (const Vector2 &, const Vector2 &, const double &)
	Linear interpolation between two vectors. More...

static Vector2	Bilinear (const Vector2 &, const Vector2 &, const Vector2 &, const Vector2 &, const double &, const double &)
	Bi-linear interpolation between four vectors. More...

static Vector2	FromString (QString)
	Creates a vector from a QString. More...

static Vector2	Polar (const double &)
	Creates a vector given polar coordinates. More...

static Vector2	Solve (const Vector2 &, const Vector2 &, const double &, const double &)
	Compute the point on a segment such that the linear function satisfies f(a)=va and f(b)=vb. More...

static bool	Clockwise (const Vector2 &, const Vector2 &, const Vector2 &)
	Returns true if the three points make a clockwise turn. More...

Static Public Attributes
static const Vector2	Null = Vector2(0.0, 0.0)
	Null vector.

static const Vector2	X = Vector2(1.0, 0.0)
	Vector2(1,0).

static const Vector2	Y = Vector2(0.0, 1.0)
	Vector2(0,1).

Protected Attributes
double	c [2]
	Components.

Friends
bool	operator> (const Vector2 &, const Vector2 &)
	Compare two vectors.

bool	operator< (const Vector2 &, const Vector2 &)
	Compare two vectors.

bool	operator>= (const Vector2 &, const Vector2 &)
	Overloaded.

bool	operator<= (const Vector2 &, const Vector2 &)
	Overloaded.

Vector2	operator+ (const Vector2 &, const Vector2 &)
	Adds up two vectors.

Vector2	operator- (const Vector2 &, const Vector2 &)
	Difference between two vectors.

double	operator* (const Vector2 &, const Vector2 &)
	Dot product between two vectors. More...

Vector2	operator* (const Vector2 &, double)
	Right multiply by a scalar.

Vector2	operator* (double, const Vector2 &)
	Left multiply by a scalar.

Vector2	operator/ (const Vector2 &, double)
	Left divide by a scalar.

double	operator/ (const Vector2 &, const Vector2 &)
	Cross productof two vectors. Note that the derminant of a 2-square matrix is the cross product of its two colum vectors.

bool	operator== (const Vector2 &, const Vector2 &)
	Strong equality test.

bool	operator!= (const Vector2 &, const Vector2 &)
	Strong difference test.

double	Norm (const Vector2 &)
	Compute the Euclidean norm of a vector. This function involves a square root computation, it is often more efficient to rely on the squared norm of a vector instead. More...

double	SquaredNorm (const Vector2 &)
	Compute the squared Euclidean norm of a vector. More...

double	NormInfinity (const Vector2 &)
	Compute the infinity norm of a vector. More...

void	Normalize (Vector2 &)
	Normalize a two dimensional vector. More...

Vector2	Normalized (const Vector2 &)
	Return a Normalized a vector, computing the inverse of its norm and scaling the components. This function does not check if the vector is null, which might result in errors.

double	Sine (const Vector2 &, const Vector2 &)
	Returns the sine of two vectors. More...

double	Cosine (const Vector2 &, const Vector2 &)
	Returns the positive cosine of two vectors. More...

Vector2	Abs (const Vector2 &)
	Computes the absolute value of a vector.

void	Swap (Vector2 &, Vector2 &)
	Swap two vectors. More...

Vector2	Clamp (const Vector2 &, const Vector2 &, const Vector2 &)
	Clamp a Vector2 between two bounds. More...

double	WhichSide (const Vector2 &, const Vector2 &, const Vector2 &)
	Compute the position of a point with respect to a line. More...

bool	IsLeft (const Vector2 &, const Vector2 &, const Vector2 &)
	Compute the position of a point with respect to a line. More...

bool	IsRight (const Vector2 &, const Vector2 &, const Vector2 &)
	Compute the position of a point with respect to a line. More...

std::ostream &	operator<< (std::ostream &, const Vector2 &)
	Overloaded output-stream operator. More...

Detailed Description

Vectors in two dimensions.

This class implements most operators and member functions as for Vector class.

Constructor & Destructor Documentation

◆ Vector2()

Vector2::Vector2 ( const double & a )

inlineexplicit

Create a vector with the same real coordinates.

Parameters

a Real.

Member Function Documentation

◆ Angle() [1/2]

double Vector2::Angle ( ) const

Compute the angle of a vector.

The vector need not be normalized.

◆ Angle() [2/2]

double Vector2::Angle ( const Vector2 & b ) const

Compute the angle between two vectors.

Note that both vectors should be unit.

See also: Vector2::Angle() const

Parameters

b	Argument vector forming the angle.

◆ Bilinear()

Vector2 Vector2::Bilinear	(	const Vector2 &	a00,
		const Vector2 &	a10,
		const Vector2 &	a11,
		const Vector2 &	a01,
		const double &	u,
		const double &	v
	)

inlinestatic

Bi-linear interpolation between four vectors.

The vectors are given in trigonometric order.

Parameters

a00,a10,a11,a01	Interpolated vectors.
u,v	Interpolation coefficients.

See also: Math::Bilinear

◆ Clockwise()

bool Vector2::Clockwise	(	const Vector2 &	a,
		const Vector2 &	b,
		const Vector2 &	c
	)

inlinestatic

Returns true if the three points make a clockwise turn.

Parameters

a,b,c Points.

See also: WhichSide

◆ Equal()

bool Vector2::Equal	(	const Vector2 &	a,
		const Vector2 &	b,
		const double &	epsilon = `0.0001`
	)

static

Test if two vectors are almost equal.

See also: Vector::Equal

◆ Floor()

Vector2 Vector2::Floor ( ) const

inline

Compute the numerator part of the coordinates.

See also: Math::Floor

◆ Fract()

Vector2 Vector2::Fract ( ) const

inline

Compute the fractional part of the coordinates.

See also: Math::Fract

◆ FromString()

Vector2 Vector2::FromString ( QString n )

static

Creates a vector from a QString.

Parameters

n String.

◆ Inverse()

Vector2 Vector2::Inverse ( ) const

inline

Inverse of a vector.

This function inverses the components of the vector.

See also: Vector::Inverse()

◆ Lerp()

Vector2 Vector2::Lerp	(	const Vector2 &	a,
		const Vector2 &	b,
		const double &	t
	)

inlinestatic

Linear interpolation between two vectors.

Parameters

a,b	Interpolated points.
t	Interpolant.

◆ Max()

double Vector2::Max ( ) const

inline

Compute the maximum component of a vector.

See also: NormInfinity

◆ MaxIndex()

int Vector2::MaxIndex ( ) const

inline

Compute the index of the maximum component of a vector.

Vector2 a(-1.0,-3.0);

int i=MaxIndex(Abs(a)); // Should be 1

Vector2

Vectors in two dimensions.

Definition: evector.h:617

Vector2::MaxIndex

int MaxIndex() const

Compute the index of the maximum component of a vector.

Definition: evector.h:1001

Vector2::Abs

friend Vector2 Abs(const Vector2 &)

Computes the absolute value of a vector.

Definition: evector.h:975

See also: Vector::MaxIndex

◆ MinIndex()

int Vector2::MinIndex ( ) const

inline

Compute the index of the minimum component of a vector.

See also: Vector::MinIndex

◆ Modulo()

Vector2 Vector2::Modulo	(	const Vector2 &	a,
		const Vector2 &	b
	)

inlinestatic

Modulo of two vectors.

Parameters

a,b	Two vectors.

◆ Polar()

Vector2 Vector2::Polar ( const double & t )

inlinestatic

Creates a vector given polar coordinates.

Parameters

t Theta.

◆ Quadrant()

int Vector2::Quadrant ( const Vector2 & p ) const

Computes quadrant index of a vector with respect to the vector object.

See also: Box2::Quadrant(const Vector&)

Parameters

p Vector.

◆ Scale()

void Vector2::Scale ( const Vector2 & a )

inline

Scales the vector.

Parameters

a	Scaling vector.

◆ Scaled()

Vector2 Vector2::Scaled ( const Vector2 & a ) const

inline

Scales the vector.

Parameters

a	Scaling vector.

◆ SetMinMax()

void Vector2::SetMinMax	(	const Vector2 &	x,
		Vector2 &	a,
		Vector2 &	b
	)

static

Update the minimum and maximum values given a vector.

Parameters

x	Input vector.
a,b	Lower and upper vectors that will be updated.

◆ Solve()

Vector2 Vector2::Solve	(	const Vector2 &	a,
		const Vector2 &	b,
		const double &	va,
		const double &	vb
	)

inlinestatic

Compute the point on a segment such that the linear function satisfies f(a)=va and f(b)=vb.

See also: Vector::Solve(const double& a, const double& b, const Vector&, const Vector&);

◆ ToString()

QString Vector2::ToString ( int n = 6 ) const

Create a QString form a vector.

Parameters

n	Number of digits.

◆ ToVector()

Vector Vector2::ToVector ( const double & z = 0.0 ) const

inline

Convert a Vector2 to a Vector.

Parameters

z	Extra coordinate.

Friends And Related Function Documentation

◆ Clamp

Vector2 Clamp	(	const Vector2 &	x,
		const Vector2 &	a,
		const Vector2 &	b
	)

friend

Clamp a Vector2 between two bounds.

Parameters

x	Input vector
a,b	Vector bounds.

◆ Cosine

double Cosine	(	const Vector2 &	u,
		const Vector2 &	v
	)

friend

Returns the positive cosine of two vectors.

Computes the dot product of the normalized vectors.

Parameters

u,v Vectors.

◆ IsLeft

bool IsLeft	(	const Vector2 &	p,
		const Vector2 &	a,
		const Vector2 &	b
	)

friend

Compute the position of a point with respect to a line.

Parameters

p	Point
a,b	Vertices of the line.

◆ IsRight

bool IsRight	(	const Vector2 &	p,
		const Vector2 &	a,
		const Vector2 &	b
	)

friend

Compute the position of a point with respect to a line.

Parameters

p	Point
a,b	Vertices of the line.

◆ Norm

double Norm ( const Vector2 & u )

friend

Compute the Euclidean norm of a vector. This function involves a square root computation, it is often more efficient to rely on the squared norm of a vector instead.

See also: SquaredNorm

◆ Normalize

void Normalize ( Vector2 & u )

friend

Normalize a two dimensional vector.

It computes the inverse of its norm and scaling the components. This function does not check if the vector is null, which might yield errors.

Parameters

u Vector.

◆ NormInfinity

double NormInfinity ( const Vector2 & u )

friend

Compute the infinity norm of a vector.

See also: Norm, SquaredNorm

◆ operator*

double operator*	(	const Vector2 &	u,
		const Vector2 &	v
	)

friend

Dot product between two vectors.

Parameters

u,v	Argument vectors.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const Vector2 &	u
	)

friend

Overloaded output-stream operator.

Parameters

u	Vector.
s	Stream.

◆ Sine

double Sine	(	const Vector2 &	u,
		const Vector2 &	v
	)

friend

Returns the sine of two vectors.

Computes the cross product of the vectors and normalizes the result.

Parameters

u,v Vectors.

◆ SquaredNorm

double SquaredNorm ( const Vector2 & u )

friend

Compute the squared Euclidean norm of a vector.

See also: Norm

◆ Swap

void Swap	(	Vector2 &	a,
		Vector2 &	b
	)

friend

Swap two vectors.

Parameters

a,b Vectors.

◆ WhichSide

double WhichSide	(	const Vector2 &	p,
		const Vector2 &	a,
		const Vector2 &	b
	)

friend

Compute the position of a point with respect to a line.

Parameters

p	Point
a,b	Vertices of the line.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Vector2()

Member Function Documentation

◆ Angle() [1/2]

◆ Angle() [2/2]

◆ Bilinear()

◆ Clockwise()

◆ Equal()

◆ Floor()

◆ Fract()

◆ FromString()

◆ Inverse()

◆ Lerp()

◆ Max()

◆ MaxIndex()

◆ MinIndex()

◆ Modulo()

◆ Polar()

◆ Quadrant()

◆ Scale()

◆ Scaled()

◆ SetMinMax()

◆ Solve()

◆ ToString()

◆ ToVector()

Friends And Related Function Documentation

◆ Clamp

◆ Cosine

◆ IsLeft

◆ IsRight

◆ Norm

◆ Normalize

◆ NormInfinity

◆ operator*

◆ operator<<

◆ Sine

◆ SquaredNorm

◆ Swap

◆ WhichSide