Utility functions for the rw::math module. More...

#include <Math.hpp>

Static Public Member Functions
template<class A >
static rw::math::EAA< A >	quaternionToEAA (const rw::math::Quaternion< A > &quat)
	Quaternion to equivalent angle axis conversion. More...

template<class A >
static rw::math::Quaternion< A >	eaaToQuaternion (const rw::math::EAA< A > &eaa)
	Equivalent angle axis to quaternion conversion. More...

template<class A >
static rw::math::Rotation3D< A >	zyxToRotation3D (A roll, A pitch, A yaw)
	this function converts a EAA object to a Quaternion More...

template<class R >
static Eigen::Matrix< R, 3, 3 >	skew (const rw::math::Vector3D< R > &s)
	Constructs a 3x3 skew-symmetric matrix \( S\in so(3)\). More...

static double	clamp (double val, double min, double max)
	clamp val to either min or max More...

static rw::math::Q	clampQ (const rw::math::Q &q, const rw::math::Q &min, const rw::math::Q &max)
	Clamps values of q with min and max. More...

static rw::math::Q	clampQ (const rw::math::Q &q, const std::pair< rw::math::Q, rw::math::Q > &bounds)
	Clamps values of q with bounds.first and bounds.second. More...

static rw::math::Vector3D	clamp (const rw::math::Vector3D<> &q, const rw::math::Vector3D<> &min, const rw::math::Vector3D<> &max)
	Clamps values of q with min and max. More...

static double	ran ()
	A random double in the range [0, 1[ using a uniform distribution. More...

static void	seed (unsigned seed)
	Seeds the random number generator. More...

static void	seed ()
	Seeds the random number generator with current time of day. More...

static double	ran (double from, double to)
	A random double in the range [from, to[ using a uniform distribution. More...

static int	ranI (int from, int to)
	A random integer in the range [from, to[ using a uniform distribution. More...

static double	ranNormalDist (double mean, double sigma)
	Returns a random sample around mean with standard deviation sigma using the normal distribution. More...

static rw::math::Q	ranQ (const rw::math::Q &from, const rw::math::Q &to)
	Returns a random Q between with values in the range [from, to[ using a uniform distribution. More...

static rw::math::Q	ranQ (const std::pair< rw::math::Q, rw::math::Q > &bounds)
	Returns a random Q between with values in the range [bounds.first, bounds.second[ using a uniform distribution. More...

static rw::math::Q	ranDir (size_t dim, double length=1)
	Returns a random direction in dim dimensions using the standard normal distribution. More...

static rw::math::Q	ranWeightedDir (size_t dim, const rw::math::Q &weights, double length=1)
	Returns a weighted random direction in dim dimensions using the standard normal distribution. More...

template<class T >
static rw::math::Quaternion< T >	ranQuaternion ()
	Returns a uniformly distributed random orientation. More...

template<class T >
static rw::math::Rotation3D< T >	ranRotation3D ()
	Returns a uniformly distributed random orientation. More...

template<class T >
static rw::math::Transform3D< T >	ranTransform3D (const double translationLength=1)
	Returns random Transform3D based on ranDir (using the standard normal distribution) and ranRotation3D (using a uniform distribution). More...

static double	round (double d)
	Rounds off to nearest integer. More...

template<class T >
static T	sqr (const T &d)
	The square of d. More...

static rw::math::Q	sqr (const rw::math::Q &q)
	The squares of the elements of q.

static rw::math::Q	sqrt (const rw::math::Q &q)
	The square roots of the elements of q.

static rw::math::Q	abs (const rw::math::Q &v)
	Returns vector with the absolute values. More...

static double	min (const rw::math::Q &v)
	Returns the smallest element of v. More...

static double	max (const rw::math::Q &v)
	Returns the largest element of v. More...

template<class T >
static T	min (const T &a, const T &b)
	Returns vector with the elementwise smallest elements of a and b. More...

template<class T >
static T	max (const T &a, const T &b)
	Returns vector with the elementwise largest elements of a and b. More...

template<class T >
static Vector3D< T >	abs (const Vector3D< T > &v)
	Returns vector with the absolute values. More...

template<class T >
static T	min (const Vector3D< T > &v)
	Returns the smallest element of v. More...

template<class T >
static T	max (const Vector3D< T > &v)
	Returns the largest element of v. More...

template<class T >
static Vector3D< T >	min (const Vector3D< T > &a, const Vector3D< T > &b)
	Returns vector with the elementwise smallest elements of a and b. More...

template<class T >
static Vector3D< T >	max (const Vector3D< T > &a, const Vector3D< T > &b)
	Returns vector with the elementwise largest elements of a and b. More...

static double	sign (double s)
	Returns the sign of s. More...

static rw::math::Q	sign (const rw::math::Q &q)
	Returns the sign of each element. More...

static int	ceilLog2 (int n)
	Exact implementation of ceil(log_2(n)) for n > 0.

static long long	factorial (long long n)
	Factorial The method does not implement any safe guards for negative numbers of overflow of numbers.

template<class ARR >
static std::vector< double >	toStdVector (const ARR &tmp, int size)
	convert a math vector type to an vector of doubles. The input should have the index operator () in order to use this conversion More...

template<class MAT >
static std::vector< double >	toStdVector (const MAT &tmp, int size1, int size2)
	convert a math matrix type to an vector of doubles. The input should have the index operator (x,y) in order to use this conversion More...

template<class T , class ARR >
static ARR	fromStdVector (const std::vector< T > &data, ARR &tmp)

template<class T , class MAT >
static MAT	fromStdVectorToMat (const std::vector< T > &data, MAT &tmp, int size1, int size2)

static bool	isNaN (double d)
	Implements an isNaN function. More...

static double	NaN ()
	Get a value for NaN. More...

Detailed Description

Utility functions for the rw::math module.

Member Function Documentation

◆ abs() [1/2]

static rw::math::Q abs ( const rw::math::Q & v )

inlinestatic

Returns vector with the absolute values.

Given a vector \( v=[v_1,v_2,\ldots,v_n] \) then Abs(v) is defined as \( Abs(v)=[abs(v_1),abs(v_i),\ldots,abs(v_n)] \)

Parameters

v	[in] the vector \( v\)

Returns: the vector \( Abs(v)\)

◆ abs() [2/2]

static Vector3D<T> abs ( const Vector3D< T > & v )

inlinestatic

Returns vector with the absolute values.

Given a vector \(v=[v_1,v_2,\ldots,v_n]\) then Abs(v) is defined as \(Abs(v)=[abs(v_1),abs(v_i),\ldots,abs(v_n)] \)

Parameters

v	[in] the vector \(v\)

Returns: the vector \(Abs(v)\)

◆ clamp() [1/2]

static rw::math::Vector3D clamp	(	const rw::math::Vector3D<> &	q,
		const rw::math::Vector3D<> &	min,
		const rw::math::Vector3D<> &	max
	)

inlinestatic

Clamps values of q with min and max.

Parameters

q	[in] Values to clamp
min	[min] The minimum value
max	[min] The maximum value

Returns: The clamped values

◆ clamp() [2/2]

static double clamp	(	double	val,
		double	min,
		double	max
	)

inlinestatic

clamp val to either min or max

Parameters

val	[in] the value that is to be clamped
min	[in] the minimum allowed value
max	[in] the maximum allowed value

Returns: the clamped value of val

◆ clampQ() [1/2]

static rw::math::Q clampQ	(	const rw::math::Q &	q,
		const rw::math::Q &	min,
		const rw::math::Q &	max
	)

static

Clamps values of q with min and max.

Parameters

q	[in] Values to clamp
min	[min] The minimum value
max	[min] The maximum value

Returns: The clamped values

◆ clampQ() [2/2]

static rw::math::Q clampQ	(	const rw::math::Q &	q,
		const std::pair< rw::math::Q, rw::math::Q > &	bounds
	)

inlinestatic

Clamps values of q with bounds.first and bounds.second.

Parameters

q	[in] Values to clamp
bounds	[min] The pair containing minimum and maximum values as first and second element

Returns: The clamped values

◆ eaaToQuaternion()

static rw::math::Quaternion<A> eaaToQuaternion ( const rw::math::EAA< A > & eaa )

inlinestatic

Equivalent angle axis to quaternion conversion.

Parameters

eaa	[in] the EAA object that is to be converted

Returns: a Quaternion object that represents the converted EAA

◆ fromStdVector()

static ARR fromStdVector	(	const std::vector< T > &	data,
		ARR &	tmp
	)

inlinestatic

convert a vector of doubles to a vector math type. The math type should implement the operator () in order to use this function.

Parameters

data	[in] the input
tmp	[out] the output

Returns: reference to tmp

◆ fromStdVectorToMat()

static MAT fromStdVectorToMat	(	const std::vector< T > &	data,
		MAT &	tmp,
		int	size1,
		int	size2
	)

inlinestatic

convert a vector of doubles to a matrix math type. The math type should implement the operator (i,j) in order to use this function.

Parameters

data	[in] the input
tmp	[out] the output
size1	[in] the size of the first dimension of the matrix.
size2	[in] the size of the second dimension of the matrix.

Returns: reference to tmp

◆ isNaN()

static bool isNaN ( double d )

static

Implements an isNaN function.

Use to make sure code is independent of specific compile specific implementations

◆ max() [1/4]

static double max ( const rw::math::Q & v )

inlinestatic

Returns the largest element of v.

If the vector has zero length, the method returns 0

Parameters

v	[in] the vector v

Returns: the largest element

◆ max() [2/4]

static T max	(	const T &	a,
		const T &	b
	)

inlinestatic

Returns vector with the elementwise largest elements of a and b.

Parameters

a	[in] the vector a
b	[in] the vector b

Returns: Q with largest elements

◆ max() [3/4]

static Vector3D<T> max	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)

inlinestatic

Returns vector with the elementwise largest elements of a and b.

Parameters

a	[in] the vector a
b	[in] the vector b

Returns: Vector with largest elements

◆ max() [4/4]

static T max ( const Vector3D< T > & v )

inlinestatic

Returns the largest element of v.

Parameters

v	[in] the vector v

Returns: the largest element

◆ min() [1/4]

static double min ( const rw::math::Q & v )

inlinestatic

Returns the smallest element of v.

If the vector has zero length, the method returns 0

Parameters

v	[in] the vector v

Returns: the smallest element

◆ min() [2/4]

static T min	(	const T &	a,
		const T &	b
	)

inlinestatic

Returns vector with the elementwise smallest elements of a and b.

Parameters

a	[in] the vector a
b	[in] the vector b

Returns: Q with smallest elements

◆ min() [3/4]

static Vector3D<T> min	(	const Vector3D< T > &	a,
		const Vector3D< T > &	b
	)

inlinestatic

Returns vector with the elementwise smallest elements of a and b.

Parameters

a	[in] the vector a
b	[in] the vector b

Returns: Vector with smallest elements

◆ min() [4/4]

static T min ( const Vector3D< T > & v )

inlinestatic

Returns the smallest element of v.

Parameters

v	[in] the vector v

Returns: the smallest element

◆ NaN()

static double NaN ( )

static

Get a value for NaN.

Use to make sure code is independent of specific compile specific implementations

Returns: a double representation of NaN.

◆ quaternionToEAA()

static rw::math::EAA<A> quaternionToEAA ( const rw::math::Quaternion< A > & quat )

inlinestatic

Quaternion to equivalent angle axis conversion.

Parameters

quat	[in] the Quaternion object that is to be converted.

Returns: a EAA object that represents the converted quaternion

◆ ran() [1/2]

static double ran ( )

static

A random double in the range [0, 1[ using a uniform distribution.

Note: Uses boost::random

◆ ran() [2/2]

static double ran	(	double	from,
		double	to
	)

static

A random double in the range [from, to[ using a uniform distribution.

Note: Uses boost::random

◆ ranDir()

static rw::math::Q ranDir	(	size_t	dim,
		double	length = `1`
	)

static

Returns a random direction in dim dimensions using the standard normal distribution.

The length of the vector is given by length;

Parameters

dim	[in] Number of dimensions
length	[in] Length of return vector. Default is 1;

Returns: Random direction

Warning: Please see the warning for Math::ranNormalDist

◆ ranI()

static int ranI	(	int	from,
		int	to
	)

static

A random integer in the range [from, to[ using a uniform distribution.

Note: Uses boost::random

◆ ranNormalDist()

static double ranNormalDist	(	double	mean,
		double	sigma
	)

static

Returns a random sample around mean with standard deviation sigma using the normal distribution.

Note: Uses boost::random

Warning: The number sequence generated can vary in different Boost versions (there is a known change in Boost 1.56.0).

Parameters

mean	[in] Means value
sigma	[in] Standard deviation

Returns: Random sample

◆ ranQ() [1/2]

static rw::math::Q ranQ	(	const rw::math::Q &	from,
		const rw::math::Q &	to
	)

static

Returns a random Q between with values in the range [from, to[ using a uniform distribution.

Note: Uses boost::random

Parameters

from	[in] The lower bound
to	[in] The upper bound

Returns: Random Q

◆ ranQ() [2/2]

static rw::math::Q ranQ ( const std::pair< rw::math::Q, rw::math::Q > & bounds )

static

Returns a random Q between with values in the range [bounds.first, bounds.second[ using a uniform distribution.

Note: Uses boost::random

Parameters

bounds [in] The lower and upper bounds

Returns: Random Q

◆ ranQuaternion()

static rw::math::Quaternion<T> ranQuaternion ( )

inlinestatic

Returns a uniformly distributed random orientation.

Returns: Random orientation represented as a Quaternion

◆ ranRotation3D()

static rw::math::Rotation3D<T> ranRotation3D ( )

inlinestatic

Returns a uniformly distributed random orientation.

Returns: Random orientation represented as a Rotation3D

◆ ranTransform3D()

static rw::math::Transform3D<T> ranTransform3D ( const double translationLength = 1 )

inlinestatic

Returns random Transform3D based on ranDir (using the standard normal distribution) and ranRotation3D (using a uniform distribution).

Parameters

translationLength [in]

Returns: Random Transform3D

◆ ranWeightedDir()

static rw::math::Q ranWeightedDir	(	size_t	dim,
		const rw::math::Q &	weights,
		double	length = `1`
	)

static

Returns a weighted random direction in dim dimensions using the standard normal distribution.

The length of the vector is given by length;

Parameters

dim	[in] Number of dimensions
weights	[in] Weights to use
length	[in] Length of return vector when weights are applied as weighted Euclidean metric. Default is 1;

Returns: Random weigthed direction

Warning: Please see the warning for Math::ranNormalDist

◆ round()

static double round ( double d )

inlinestatic

Rounds off to nearest integer.

With some compilers round can be found in math.h. This however does not appear to be ansi C/C++ standard

Parameters

d	[in] number to round

Returns: d rounded to nearest integer.

◆ seed() [1/2]

static void seed ( )

static

Seeds the random number generator with current time of day.

Note: Uses boost::random

◆ seed() [2/2]

static void seed ( unsigned seed )

static

Seeds the random number generator.

Note: Uses boost::random

◆ sign() [1/2]

static rw::math::Q sign ( const rw::math::Q & q )

inlinestatic

Returns the sign of each element.

For each element either -1 or 1 is returned depending on the sign. If q(i) equals 0 the method returns 1

Parameters

q	[in] Vector for which to get the signs

Returns: Vector of sign values

◆ sign() [2/2]

static double sign ( double s )

inlinestatic

Returns the sign of s.

If s < 0 it return 0. If s >= 0 then 1 is returned.

Parameters

s	[in] The value for which to return the sign

Returns: The sign

◆ skew()

static Eigen::Matrix<R, 3, 3> skew ( const rw::math::Vector3D< R > & s )

inlinestatic

Constructs a 3x3 skew-symmetric matrix \( S\in so(3)\).

Parameters

s	[in] the \( s_x \), \( s_y \) and \( s_z \) of the matrix

Returns: The 3x3 skew-symmetric matrix \( S\)

\( S = \left [ \begin {array}{ccc} 0 & -s_z & s_y\\ s_z & 0 & -s_x\\ -s_y & s_x & 0 \end {array} \right ] \)

◆ sqr()

static T sqr ( const T & d )

inlinestatic

The square of d.

Parameters

d	[in] Number to square

Returns: d * d

◆ toStdVector() [1/2]

static std::vector<double> toStdVector	(	const ARR &	tmp,
		int	size
	)

inlinestatic

convert a math vector type to an vector of doubles. The input should have the index operator () in order to use this conversion

Parameters

tmp	[in] input
size	[in] length of tmp

Returns: vector of doubles

◆ toStdVector() [2/2]

static std::vector<double> toStdVector	(	const MAT &	tmp,
		int	size1,
		int	size2
	)

inlinestatic

convert a math matrix type to an vector of doubles. The input should have the index operator (x,y) in order to use this conversion

Parameters

tmp	[in] input matrix type
size1	[in] width of tmp
size2	[in] height of tmp

Returns: vector of doubles

◆ zyxToRotation3D()

static rw::math::Rotation3D<A> zyxToRotation3D	(	A	roll,
		A	pitch,
		A	yaw
	)

inlinestatic

this function converts a EAA object to a Quaternion

Parameters

roll	[in] rotation around z
pitch	[in] rotation around y
yaw	[in] rotation around x

Returns: a Quaternion object that represents the converted EAA

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

Math.hpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ abs() [1/2]

◆ abs() [2/2]

◆ clamp() [1/2]

◆ clamp() [2/2]

◆ clampQ() [1/2]

◆ clampQ() [2/2]

◆ eaaToQuaternion()

◆ fromStdVector()

◆ fromStdVectorToMat()

◆ isNaN()

◆ max() [1/4]

◆ max() [2/4]

◆ max() [3/4]

◆ max() [4/4]

◆ min() [1/4]

◆ min() [2/4]

◆ min() [3/4]

◆ min() [4/4]

◆ NaN()

◆ quaternionToEAA()

◆ ran() [1/2]

◆ ran() [2/2]

◆ ranDir()

◆ ranI()

◆ ranNormalDist()

◆ ranQ() [1/2]

◆ ranQ() [2/2]

◆ ranQuaternion()

◆ ranRotation3D()

◆ ranTransform3D()

◆ ranWeightedDir()

◆ round()

◆ seed() [1/2]

◆ seed() [2/2]

◆ sign() [1/2]

◆ sign() [2/2]

◆ skew()

◆ sqr()

◆ toStdVector() [1/2]

◆ toStdVector() [2/2]

◆ zyxToRotation3D()