A 3D vector \( \mathbf{v}\in \mathbb{R}^3 \). More...

#include <Vector3D.hpp>

Public Types
typedef Eigen::Matrix< T, 3, 1 >	EigenVector3D
	Eigen type equivalent to Vector3D.

typedef T	value_type
	Value type.

Public Member Functions
	Vector3D ()
	Creates a 3D vector initialized with 0's.

	Vector3D (T x, T y, T z)
	Creates a 3D vector. More...

	Vector3D (const Vector3D< T > &copy_vec)
	Copy constructor. More...

template<class R >
	Vector3D (const Eigen::MatrixBase< R > &r)
	Creates a 3D vector from vector_expression. More...

	Vector3D (const std::vector< T > &vec)
	construct vector from std::vector More...

size_t	size () const
	The dimension of the vector (i.e. 3). This method is provided to help support generic algorithms using size() and operator[]. More...

template<class R >
Vector3D< T >	elemDivide (const Eigen::MatrixBase< R > &rhs) const
	element wise division. More...

template<class R >
Vector3D< T >	elemMultiply (const Eigen::MatrixBase< R > &rhs) const
	Elementweise multiplication. More...

template<class R >
Vector3D< T >	operator- (const Eigen::MatrixBase< R > &rhs) const
	Vector subtraction.

template<class R >
Vector3D< T >	operator+ (const Eigen::MatrixBase< R > &rhs) const
	Vector addition.

Vector3D< T >	elemDivide (const Vector3D< T > &rhs) const
	element wise division. More...

Vector3D< T >	elemMultiply (const Vector3D< T > &rhs) const
	Elementweise multiplication. More...

Vector3D< T >	operator- (const Vector3D< T > &b) const
	Vector subtraction.

Vector3D< T >	operator+ (const Vector3D< T > &b) const
	Vector addition.

Vector3D< T >	operator- () const
	Unary minus. More...

Vector3D< T >	operator/ (T s) const
	Scalar division. More...

Vector3D< T >	operator* (T rhs) const
	Scalar multiplication. More...

template<class R >
Vector3D< T >	operator* (const Eigen::MatrixBase< R > &rhs) const
	Scalar multiplication. More...

Vector3D< T >	elemSubtract (const T rhs) const
	Scalar subtraction.

Vector3D< T >	elemAdd (const T rhs) const
	Scalar addition.

T	norm2 () const
	Returns the Euclidean norm (2-norm) of the vector. More...

T	norm1 () const
	Returns the Manhatten norm (1-norm) of the vector. More...

T	normInf () const
	Returns the infinte norm ( \(\inf\)-norm) of the vector. More...

Vector3D< T >	cross (const Vector3D &vec) const
	Calculate cross product. More...

T	dot (const Vector3D &vec) const
	calculate the dot product More...

Vector3D< T >	normalize ()
	normalize vector to get length 1 More...

EigenVector3D &	e ()
	Returns Reference to Eigen Vector. More...

const EigenVector3D	e () const
	Returns Reference to Eigen Vector. More...

const T &	operator() (size_t i) const
	Returns reference to vector element. More...

T &	operator() (size_t i)
	Returns reference to vector element. More...

const T &	operator[] (size_t i) const
	Returns reference to vector element. More...

T &	operator[] (size_t i)
	Returns reference to vector element. More...

Vector3D< T > &	operator*= (T s)
	Scalar multiplication.

Vector3D< T > &	operator/= (T s)
	Scalar division.

Vector3D< T > &	operator+= (const Vector3D< T > &v)
	Vector addition.

Vector3D< T > &	operator-= (const Vector3D< T > &v)
	Vector subtraction.

template<class R >
Vector3D< T > &	operator= (const Eigen::MatrixBase< R > &r)
	copy a vector from eigen type More...

template<class R >
Vector3D< T > &	operator+= (const Eigen::MatrixBase< R > &r)
	Vector addition.

template<class R >
Vector3D< T > &	operator-= (const Eigen::MatrixBase< R > &r)
	Vector subtraction.

bool	operator== (const Vector3D< T > &b) const
	Compare with b for equality. More...

bool	operator!= (const Vector3D< T > &b) const
	Compare with b for inequality. More...

template<class R >
bool	operator== (const Eigen::MatrixBase< R > &rhs) const
	Compare with rhs for equality. More...

template<class R >
bool	operator!= (const Eigen::MatrixBase< R > &rhs) const
	Compare with rhs for inequality. More...

	operator EigenVector3D () const
	implicit conversion to EigenVector

	operator EigenVector3D & ()
	implicit conversion to EigenVector

Static Public Member Functions
static Vector3D< T >	zero ()
	Get zero vector. More...

static Vector3D< T >	x ()
	Get x vector (1,0,0) More...

static Vector3D< T >	y ()
	Get y vector (0,1,0) More...

static Vector3D< T >	z ()
	Get z vector (0,0,1) More...

Friends
template<class R >
Vector3D< T >	operator- (const Eigen::MatrixBase< R > &lhs, const Vector3D< T > &rhs)
	Vector subtraction.

template<class R >
Vector3D< T >	operator+ (const Eigen::MatrixBase< R > &lhs, const Vector3D< T > &rhs)
	Vector subtraction.

Vector3D< T >	operator/ (T lhs, const Vector3D< T > &rhs)
	Scalar division. More...

Vector3D< T >	operator* (T lhs, const Vector3D< T > &rhs)
	Scalar multiplication. More...

template<class R >
Vector3D< T >	operator* (const Eigen::MatrixBase< R > &lhs, const Vector3D< T > &rhs)
	Scalar multiplication. More...

std::ostream &	operator<< (std::ostream &out, const Vector3D< T > &v)
	Streaming operator. More...

template<class R >
bool	operator== (const Eigen::MatrixBase< R > &lhs, const Vector3D< T > &rhs)
	Compare with rhs for equality. More...

template<class R >
bool	operator!= (const Eigen::MatrixBase< R > &lhs, const Vector3D< T > &rhs)
	Compare with rhs for inequality. More...

Related Functions
(Note that these are not member functions.)
template<class T >
const Vector3D< T >	cross (const Vector3D< T > &v1, const Vector3D< T > &v2)
	Calculates the 3D vector cross product \( \mathbf{v1} \times \mathbf{v2} \). More...

template<class T >
void	cross (const Vector3D< T > &v1, const Vector3D< T > &v2, Vector3D< T > &dst)
	Calculates the 3D vector cross product \( \mathbf{v1} \times \mathbf{v2} \). More...

template<class T >
T	dot (const Vector3D< T > &v1, const Vector3D< T > &v2)
	Calculates the dot product \( \mathbf{v1} . \mathbf{v2} \). More...

template<class T >
const Vector3D< T >	normalize (const Vector3D< T > &v)
	Returns the normalized vector \(\mathbf{n}=\frac{\mathbf{v}}{\\|\mathbf{v}\\|} \). In case \( \\|mathbf{v}\\| = 0\) the zero vector is returned. More...

template<class T >
double	angle (const Vector3D< T > &v1, const Vector3D< T > &v2, const Vector3D< T > &n)
	Calculates the angle from \( \mathbf{v1}\) to \( \mathbf{v2} \) around the axis defined by \( \mathbf{v1} \times \mathbf{v2} \) with n determining the sign. More...

template<class T >
double	angle (const Vector3D< T > &v1, const Vector3D< T > &v2)
	Calculates the angle from \( \mathbf{v1}\) to \( \mathbf{v2} \) around the axis defined by \( \mathbf{v1} \times \mathbf{v2} \). More...

template<class Q , class T >
const Vector3D< Q >	cast (const Vector3D< T > &v)
	Casts Vector3D<T> to Vector3D<Q> More...

template<>
void	write (const rw::math::Vector3D< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	write (const rw::math::Vector3D< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	read (rw::math::Vector3D< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<>
void	read (rw::math::Vector3D< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<class Archive , class T >
void	serialize (Archive &archive, rw::math::Vector3D< T > &vector, const unsigned int version)
	Boost serialization. More...

Detailed Description

template<class T = double>
class rw::math::Vector3D< T >

A 3D vector \( \mathbf{v}\in \mathbb{R}^3 \).

\( \robabx{i}{j}{\mathbf{v}} = \left[ \begin{array}{c} v_x \\ v_y \\ v_z \end{array} \right] \)

Usage example:

const Vector3D<> v1(1.0, 2.0, 3.0);
const Vector3D<> v2(6.0, 7.0, 8.0);
const Vector3D<> v3 = cross(v1, v2);
const double d = dot(v1, v2);
const Vector3D<> v4 = v2 - v1;

Constructor & Destructor Documentation

◆ Vector3D() [1/4]

Vector3D	(	T	x,
		T	y,
		T	z
	)

inline

Creates a 3D vector.

Parameters

x	[in] \( x \)
y	[in] \( y \)
z	[in] \( z \)

◆ Vector3D() [2/4]

Vector3D ( const Vector3D< T > & copy_vec )

inline

Copy constructor.

Parameters

copy_vec [in] vector to copy

◆ Vector3D() [3/4]

Vector3D ( const Eigen::MatrixBase< R > & r )

inlineexplicit

Creates a 3D vector from vector_expression.

Parameters

r	[in] an Eigen Vector

◆ Vector3D() [4/4]

Vector3D ( const std::vector< T > & vec )

inline

construct vector from std::vector

Parameters

vec	[in] the vector to construct from

Member Function Documentation

◆ cross()

Vector3D<T> cross ( const Vector3D< T > & vec ) const

inline

Calculate cross product.

Parameters

vec	[in] the vector to cross with

Returns: the cross product

◆ dot()

T dot ( const Vector3D< T > & vec ) const

inline

calculate the dot product

Parameters

vec	[in] the vecor to be dotted

Returns: the dot product

◆ e() [1/2]

EigenVector3D& e ( )

inline

Returns Reference to Eigen Vector.

Returns: reference to underling eigen

◆ e() [2/2]

const EigenVector3D e ( ) const

inline

Returns Reference to Eigen Vector.

Returns: copy of eigen vector

◆ elemDivide() [1/2]

Vector3D<T> elemDivide ( const Eigen::MatrixBase< R > & rhs ) const

inline

element wise division.

Parameters

rhs	[in] the vector being devided with

Returns: the resulting Vector3D

◆ elemDivide() [2/2]

Vector3D<T> elemDivide ( const Vector3D< T > & rhs ) const

inline

element wise division.

Parameters

rhs	[in] the vector being devided with

Returns: the resulting Vector3D

◆ elemMultiply() [1/2]

Vector3D<T> elemMultiply ( const Eigen::MatrixBase< R > & rhs ) const

inline

Elementweise multiplication.

Parameters

rhs	[in] vector

Returns: the element wise product

◆ elemMultiply() [2/2]

Vector3D<T> elemMultiply ( const Vector3D< T > & rhs ) const

inline

Elementweise multiplication.

Parameters

rhs	[in] vector

Returns: the element wise product

◆ norm1()

T norm1 ( ) const

inline

Returns the Manhatten norm (1-norm) of the vector.

Returns: the norm

◆ norm2()

T norm2 ( ) const

inline

Returns the Euclidean norm (2-norm) of the vector.

Returns: the norm

◆ normalize()

Vector3D<T> normalize ( )

inline

normalize vector to get length 1

Returns: the normalized Vector

◆ normInf()

T normInf ( ) const

inline

Returns the infinte norm ( \(\inf\)-norm) of the vector.

Returns: the norm

◆ operator!=() [1/2]

bool operator!= ( const Eigen::MatrixBase< R > & rhs ) const

inline

Compare with rhs for inequality.

Parameters

rhs	[in] other vector.

Returns: True if this object and rhs are different, false otherwise.

◆ operator!=() [2/2]

bool operator!= ( const Vector3D< T > & b ) const

inline

Compare with b for inequality.

Parameters

b	[in] other vector.

Returns: True if a and b are different, false otherwise.

◆ operator()() [1/2]

T& operator() ( size_t i )

inline

Returns reference to vector element.

Parameters

i	[in] index in the vector \(i\in \{0,1,2\} \)

Returns: reference to element

◆ operator()() [2/2]

const T& operator() ( size_t i ) const

inline

Returns reference to vector element.

Parameters

i	[in] index in the vector \(i\in \{0,1,2\} \)

Returns: const reference to element

◆ operator*() [1/2]

Vector3D<T> operator* ( const Eigen::MatrixBase< R > & rhs ) const

inline

Scalar multiplication.

Parameters

rhs	[in] the Eigen vector^T or matrix to multiply with

Returns: the product

◆ operator*() [2/2]

Vector3D<T> operator* ( T rhs ) const

inline

Scalar multiplication.

Parameters

rhs	[in] the scalar to multiply with

Returns: the product

◆ operator-()

Vector3D<T> operator- ( ) const

inline

Unary minus.

negative version

◆ operator/()

Vector3D<T> operator/ ( T s ) const

inline

Scalar division.

Parameters

s	[in] the scalar to devide with

Returns: result of devision

◆ operator=()

Vector3D<T>& operator= ( const Eigen::MatrixBase< R > & r )

inline

copy a vector from eigen type

Parameters

r	[in] an Eigen Vector

◆ operator==() [1/2]

bool operator== ( const Eigen::MatrixBase< R > & rhs ) const

inline

Compare with rhs for equality.

Parameters

rhs	[in] other vector.

Returns: True if this equals rhs, false otherwise.

◆ operator==() [2/2]

bool operator== ( const Vector3D< T > & b ) const

inline

Compare with b for equality.

Parameters

b	[in] other vector.

Returns: True if a equals b, false otherwise.

◆ operator[]() [1/2]

T& operator[] ( size_t i )

inline

Returns reference to vector element.

Parameters

i	[in] index in the vector \(i\in \{0,1,2\} \)

Returns: reference to element

◆ operator[]() [2/2]

const T& operator[] ( size_t i ) const

inline

Returns reference to vector element.

Parameters

i	[in] index in the vector \(i\in \{0,1,2\} \)

Returns: const reference to element

◆ size()

size_t size ( ) const

inline

The dimension of the vector (i.e. 3). This method is provided to help support generic algorithms using size() and operator[].

Returns: the size

◆ x()

static Vector3D<T> x ( )

inlinestatic

Get x vector (1,0,0)

Returns: vector.

◆ y()

static Vector3D<T> y ( )

inlinestatic

Get y vector (0,1,0)

Returns: vector.

◆ z()

static Vector3D<T> z ( )

inlinestatic

Get z vector (0,0,1)

Returns: vector.

◆ zero()

static Vector3D<T> zero ( )

inlinestatic

Get zero vector.

Returns: vector.

Friends And Related Function Documentation

◆ angle() [1/2]

double angle	(	const Vector3D< T > &	v1,
		const Vector3D< T > &	v2
	)

Parameters

v1	[in] \( \mathbf{v1} \)
v2	[in] \( \mathbf{v2} \)

Returns: the angle

◆ angle() [2/2]

double angle	(	const Vector3D< T > &	v1,
		const Vector3D< T > &	v2,
		const Vector3D< T > &	n
	)

Parameters

v1	[in] \( \mathbf{v1} \)
v2	[in] \( \mathbf{v2} \)
n	[in] \( \mathbf{n} \)

Returns: the angle

◆ cast()

const Vector3D< Q > cast ( const Vector3D< T > & v )

Parameters

v	[in] Vector3D with type T

Returns: Vector3D with type Q

◆ cross() [1/2]

const Vector3D< T > cross	(	const Vector3D< T > &	v1,
		const Vector3D< T > &	v2
	)

Parameters

v1	[in] \( \mathbf{v1} \)
v2	[in] \( \mathbf{v2} \)

Returns: the 3D vector cross product \( \mathbf{v1} \times \mathbf{v2} \)

The 3D vector cross product is defined as: \( \mathbf{v1} \times \mathbf{v2} = \left[\begin{array}{c} v1_y * v2_z - v1_z * v2_y \\ v1_z * v2_x - v1_x * v2_z \\ v1_x * v2_y - v1_y * v2_x \end{array}\right] \)

◆ cross() [2/2]

void cross	(	const Vector3D< T > &	v1,
		const Vector3D< T > &	v2,
		Vector3D< T > &	dst
	)

Parameters

v1	[in] \( \mathbf{v1} \)
v2	[in] \( \mathbf{v2} \)
dst	[out] the 3D vector cross product \( \mathbf{v1} \times \mathbf{v2} \)

The 3D vector cross product is defined as: \( \mathbf{v1} \times \mathbf{v2} = \left[\begin{array}{c} v1_y * v2_z - v1_z * v2_y \\ v1_z * v2_x - v1_x * v2_z \\ v1_x * v2_y - v1_y * v2_x \end{array}\right] \)

◆ dot()

T dot	(	const Vector3D< T > &	v1,
		const Vector3D< T > &	v2
	)

Parameters

v1	[in] \( \mathbf{v1} \)
v2	[in] \( \mathbf{v2} \)

Returns: the dot product \( \mathbf{v1} . \mathbf{v2} \)

◆ normalize()

const Vector3D< T > normalize ( const Vector3D< T > & v )

Parameters

v	[in] \( \mathbf{v} \) which should be normalized

Returns: the normalized vector \( \mathbf{n} \)

◆ operator!=

bool operator!=	(	const Eigen::MatrixBase< R > &	lhs,
		const Vector3D< T > &	rhs
	)

friend

Compare with rhs for inequality.

Parameters

lhs	[in] first vector.
rhs	[in] other vector.

Returns: True if lhs and rhs are different, false otherwise.

◆ operator* [1/2]

Vector3D<T> operator*	(	const Eigen::MatrixBase< R > &	lhs,
		const Vector3D< T > &	rhs
	)

friend

Scalar multiplication.

Parameters

lhs	[in] the Eigen vector^T or matrix to multiply with
rhs	[in] the Vector to be multiplied

Returns: the product

◆ operator* [2/2]

Vector3D<T> operator*	(	T	lhs,
		const Vector3D< T > &	rhs
	)

friend

Scalar multiplication.

Parameters

lhs	[in] the scalar to multiply with
rhs	[in] the Vector to be multiplied

Returns: the product

◆ operator/

Vector3D<T> operator/	(	T	lhs,
		const Vector3D< T > &	rhs
	)

friend

Scalar division.

Parameters

lhs	[in] the scalar to devide with
rhs	[out] the vector beind devided

Returns: result of devision

◆ operator<<

std::ostream& operator<<	(	std::ostream &	out,
		const Vector3D< T > &	v
	)

friend

Streaming operator.

Parameters

out	[in/out] the stream to continue
v	[in] the vector to stream

Returns: reference to out

◆ operator==

bool operator==	(	const Eigen::MatrixBase< R > &	lhs,
		const Vector3D< T > &	rhs
	)

friend

Compare with rhs for equality.

Parameters

lhs	[in] first vector.
rhs	[in] other vector.

Returns: True if lhs equals rhs, false otherwise.

◆ read() [1/2]

void read	(	rw::math::Vector3D< double > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ read() [2/2]

void read	(	rw::math::Vector3D< float > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ serialize()

void serialize	(	Archive &	archive,
		rw::math::Vector3D< T > &	vector,
		const unsigned int	version
	)

Parameters

archive	[in] the boost archive to read from or write to.
vector	[in/out] the vector to read/write.
version	[in] class version (currently version 0).

◆ write() [1/2]

void write	(	const rw::math::Vector3D< double > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ write() [2/2]

void write	(	const rw::math::Vector3D< float > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

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

core/math_fwd.hpp
Vector3D.hpp

Public Types

Public Member Functions

Static Public Member Functions

Friends

Related Functions

Detailed Description

template<class T = double> class rw::math::Vector3D< T >

Constructor & Destructor Documentation

◆ Vector3D() [1/4]

◆ Vector3D() [2/4]

◆ Vector3D() [3/4]

◆ Vector3D() [4/4]

Member Function Documentation

◆ cross()

◆ dot()

◆ e() [1/2]

◆ e() [2/2]

◆ elemDivide() [1/2]

◆ elemDivide() [2/2]

◆ elemMultiply() [1/2]

◆ elemMultiply() [2/2]

◆ norm1()

◆ norm2()

◆ normalize()

◆ normInf()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator-()

◆ operator/()

◆ operator=()

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ size()

◆ x()

◆ y()

◆ z()

◆ zero()

Friends And Related Function Documentation

◆ angle() [1/2]

◆ angle() [2/2]

◆ cast()

◆ cross() [1/2]

◆ cross() [2/2]

◆ dot()

◆ normalize()

◆ operator!=

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator/

◆ operator<<

◆ operator==

◆ read() [1/2]

◆ read() [2/2]

◆ serialize()

◆ write() [1/2]

◆ write() [2/2]

template<class T = double>
class rw::math::Vector3D< T >