Vector3 Class Reference

Class representing 3D Euclidean space. More...

Inheritance diagram for Vector3:

Public Member Functions
	Vector3 (double_t x=0, double_t y=0, double_t z=0)
double_t	x () const
double_t	y () const
double_t	z () const
double_t	r () const
double_t	theta () const
double_t	phi () const
Vector3	rXY () const
void	setX (double_t scalar)
void	setY (double_t scalar)
void	setZ (double_t scalar)
void	setR (double_t scalar)
void	setTheta (double_t scalar)
void	setPhi (double_t scalar)
void	setXYZ (double_t x, double_t y, double_t z)
void	setRThetaZ (double_t r, double_t theta, double_t z)
void	setRThetaPhi (double_t r, double_t theta, double_t phi)
Vector3 &	operator^= (const Vector3 &u)
Public Member Functions inherited from NVector< double_t >
	NVector (const std::vector< double_t > &data)
	Construct a vector using a std::vector. \( x_k \) represents data[k]. More...
	NVector (std::initializer_list< double_t > list)
	Construct a vector using an initializer list {}. More...
	NVector (size_t dim=0)
	Construct a vector of a given size. More...
	NVector (const NVector< double_t > &u)
	Construct a vector by using copy() method. More...
virtual	~NVector ()=default
virtual std::string	str () const
	Creates a string representing the vector. More...
size_t	dim () const
	Dimension of the vector. More...
std::vector< double_t >	array () const
	Creates an array with this vector. More...
NVector< double_t > &	operator+= (const NVector< double_t > &u)
NVector< double_t > &	operator-= (const NVector< double_t > &u)
virtual NVector< double_t > &	operator*= (double_ts)
virtual NVector< double_t > &	operator/= (double_ts)
NVector< double_t > &	operator= (const NVector< double_t > &u)
	Copy source object on this object using copy(). More...
double_t	max () const
	Maximum of the coordinates of the vector \( (x_0, x_1, .. x_{(n-1)}) \). More...
double_t	min () const
	Minimum of the coordinates of the vector \( (x_0, x_1, .. x_{(n-1)}) \). More...
size_t	maxIndex () const
	Index of maximum of the coordinates of vector \( (x_0, x_1, ..., x_{(n-1)}) \). More...
size_t	minIndex () const
	Index of minimum of the coordinates of vector \( (x_0, x_1, ..., x_{(n-1)}) \). More...
double_t	maxAbs () const
	Maximum of the coordinates of the vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \). More...
double_t	minAbs () const
	Minimum of the coordinates of the vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \). More...
size_t	maxAbsIndex () const
	Index of maximum of the coordinates of vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \). More...
size_t	minAbsIndex () const
	Index of minimum of the coordinates of vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \). More...
NVector< double_t > &	swap (size_t k1, size_t k2)
	Permutation of two elements. More...
NVector< double_t > &	shift (long iterations)
	Shifts this vector iterations times. More...
NVector< double_t > &	fill (double_ts)
	Fill vector with a scalar. For example fill(3) will set \( (3, 3, 3, ..., 3) \). More...
double_t &	operator() (long k)
	Simple access operator. More...
double_t	operator() (long k) const
NVector< double_t >	operator() (size_t k1, size_t k2) const
	Manipulate sub-vector. More...
NVector< double_t > &	operator() (size_t k1, size_t k2)
	Manipulate sub-vector. More...
iterator	begin ()
const_iterator	begin () const
iterator	end ()
const_iterator	end () const

Static Public Member Functions
static Vector3	zeros ()
static Vector3	ones ()
static Vector3	scalar (double_t scalar)
static Vector3	cano (size_t k)
Static Public Member Functions inherited from NVector< double_t >
static NVector< double_t >	zeros (size_t dim)
static NVector< double_t >	ones (size_t dim)
static NVector< double_t >	scalar (double_ts, size_t dim)
static NVector< double_t >	cano (size_t k, size_t dim)
static NVector< double_t >	sum (const std::vector< NVector > &vectors)
	Sum of multiples vectors. More...
static NVector< double_t >	sumProd (const std::vector< double_t > &scalars, const std::vector< NVector > &vectors)
	Linear combination of scalars and vectors. More...

Protected Member Functions
Vector3 &	cross (const Vector3 &u)
double_t	angle (const Vector3 &u) const
double_t	pCos (const Vector3 &u) const
double_t	pSin (const Vector3 &u) const
double_t	pTan (const Vector3 &u) const
Protected Member Functions inherited from NVector< double_t >
	NVector (const std::vector< double_t > &data, size_t k1, size_t k2)
	Vector with regularly spaced components. More...
NVector< double_t > &	add (const NVector< double_t > &u)
NVector< double_t > &	sub (const NVector< double_t > &u)
virtual NVector< double_t > &	opp ()
virtual NVector< double_t > &	prod (double_ts)
virtual NVector< double_t > &	div (double_ts)
double_t	dotProduct (const NVector< double_t > &u) const
double_t	distance (const NVector< double_t > &u) const
bool	isValidIndex (size_t k) const
bool	isBetweenK12 (size_t k) const
bool	isNull () const
bool	isEqual (const NVector< double_t > &u) const
bool	hasSameSize (const NVector< double_t > &u) const
virtual bool	hasDefaultBrowseIndices () const
virtual void	setDefaultBrowseIndices () const
NVector< double_t > &	forEach (const NVector< double_t > &u, const std::function< void(double_t &, const double_t &)> &binary_op)
virtual NVector< double_t > &	forEach (double_ts, const std::function< void(double_t &, double_t)> &binary_op)
NVector< double_t > &	copy (const NVector< double_t > &u)
NVector< double_t >	subVector (size_t k1, size_t k2) const
void	setSubVector (const NVector< double_t > &u)
double_t	norm () const

Friends
Vector3	operator+ (Vector3 u, const Vector3 &v)
Vector3	operator- (Vector3 u, const Vector3 &v)
Vector3	operator- (Vector3 u)
Vector3	operator* (double_t s, Vector3 u)
Vector3	operator* (const Vector3 &u, double_t s)
Vector3	operator/ (Vector3 u, double_t s)
double_t	operator| (const Vector3 &u, const Vector3 &v)
double_t	operator! (const Vector3 &u)
double_t	operator/ (const Vector3 &u, const Vector3 &v)
Vector3	operator^ (Vector3 u, const Vector3 &v)
	Vector product between two us. More...
double_t	operator% (const Vector3 &u, const Vector3 &v)
	Angle between two us. More...

Additional Inherited Members
Protected Attributes inherited from NVector< double_t >
size_t	_k1
size_t	_k2

Detailed Description

Class representing 3D Euclidean space.

Copyright

Dahoux Sami 2018 All rights reserved.

Date

04/05/2018

Author

samiBendou

Featuring cross product, coordinate transforms and rotations. We will use the following 3D systems of coordinates :

       -  \form#114 Cartesian coordinates.

       -  \form#115 Cylindrical coordinates. We have the following transformations :

\[ \begin{align*} & r_{xy} & = & \sqrt{x^2 + y^2} \\ & \theta & = & atan(y / x) \\ & z & = & z \\ \end{align*} \]

      -  \form#117 Spherical coordinates. We have the following transformations :

\[ \begin{align*} & r & = & \sqrt{x^2 + y^2 + z^2} \\ & \theta & = & atan(y / x) \\ & \phi & = & atan(r_{xy} / z) \\ \end{align*} \]

      The u is stored in cartesian coordinates. Getting and
      setting components generally implies a constant time calculation to translate between cartesian
      and other formats.

      The `Vector3` class doesn't support function operator `NVector::operator()()`.

Constructor & Destructor Documentation

Vector3::Vector3 ( double_t  x = 0, double_t  y = 0, double_t  z = 0  )

inlineexplicit

Member Function Documentation

double_t Vector3::x ( ) const

inline

double_t Vector3::y ( ) const

inline

double_t Vector3::z ( ) const

inline

double_t Vector3::r ( ) const

inline

double_t Vector3::theta ( ) const

inline

double_t Vector3::phi ( ) const

inline

Vector3 Vector3::rXY ( ) const

inline

void Vector3::setX ( double_t  scalar )

inline

void Vector3::setY ( double_t  scalar )

inline

void Vector3::setZ ( double_t  scalar )

inline

void Vector3::setR ( double_t  scalar )

inline

void Vector3::setTheta ( double_t  scalar )

inline

void Vector3::setPhi ( double_t  scalar )

inline

void Vector3::setXYZ ( double_t  x, double_t  y, double_t  z  )

inline

void Vector3::setRThetaZ ( double_t  r, double_t  theta, double_t  z  )

inline

void Vector3::setRThetaPhi ( double_t  r, double_t  theta, double_t  phi  )

inline

Vector3& Vector3::operator^= ( const Vector3 &  u )

inline

static Vector3 Vector3::zeros ( )

inlinestatic

static Vector3 Vector3::ones ( )

inlinestatic

static Vector3 Vector3::scalar ( double_t  scalar )

inlinestatic

static Vector3 Vector3::cano ( size_t  k )

inlinestatic

Vector3& Vector3::cross ( const Vector3 &  u )

inlineprotected

double_t Vector3::angle ( const Vector3 &  u ) const

inlineprotected

double_t Vector3::pCos ( const Vector3 &  u ) const

inlineprotected

double_t Vector3::pSin ( const Vector3 &  u ) const

inlineprotected

double_t Vector3::pTan ( const Vector3 &  u ) const

inlineprotected

Friends And Related Function Documentation

Vector3 operator+ ( Vector3  u, const Vector3 &  v  )

friend

Vector3 operator- ( Vector3  u, const Vector3 &  v  )

friend

Vector3 operator- ( Vector3  u )

friend

Vector3 operator* ( double_t  s, Vector3  u  )

friend

Vector3 operator* ( const Vector3 &  u, double_t  s  )

friend

Vector3 operator/ ( Vector3  u, double_t  s  )

friend

double_t operator| ( const Vector3 &  u, const Vector3 &  v  )

friend

double_t operator! ( const Vector3 &  u )

friend

double_t operator/ ( const Vector3 &  u, const Vector3 &  v  )

friend

Vector3 operator^ ( Vector3  u, const Vector3 &  v  )

friend

Vector product between two us.

usual u product given by :

\[ \begin{align*} & u_y v_z - u_z v_y \\ & u_z v_x - u_x v_z \\ & u_x v_y - u_y v_x \\ \end{align*} \]

Returns

value of \( \vec{u} \times \vec{v} \).

double_t operator% ( const Vector3 &  u, const Vector3 &  v  )

friend

Angle between two us.

Returns

value of the angle.