rl::math Namespace Reference

Common mathematical functions. More...

Namespaces
	metrics
	spatial
	Spatial vector algebra.

Classes
class	Circular
	Circular segment function that maps from a time x to a point on a circular trajectory. More...
class	Circular< Vector2 >
	Circular segment function that maps from a time x to a point in 2D on a circular trajectory. More...
class	Circular< Vector3 >
	Circular segment function that maps from a time x to a point in 3D on a circular trajectory. More...
class	Function
	A mathematical mapping from Real -> ArrayX. More...
class	GnatNearestNeighbors
	Geometric Near-Neighbor Access Tree (GNAT). More...
class	Kalman
	Kalman filter. More...
class	KdtreeBoundingBoxNearestNeighbors
	k-d tree. More...
class	KdtreeNearestNeighbors
	k-d tree. More...
class	LinearNearestNeighbors
	Linear nearest neighbor search. More...
class	LowPass
	Low-pass filter. More...
class	NestedFunction
class	Pid
	Proportional-Integral-Derivative controller. More...
class	Polynomial
	A vector-valued polynomial function from Real -> T. More...
class	Polynomial< Quaternion >
class	Spline
	A piecewise Function of Polynomial functions. More...
class	Spline< Quaternion >
class	TrapezoidalVelocity
class	TypeTraits
class	TypeTraits< ::Eigen::Array< Scalar, Rows, Cols, Options, MaxRows, MaxCols > >
class	TypeTraits< ::Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > >

Typedefs
typedef ::Eigen::Array< Real, ::Eigen::Dynamic, 1 >	ArrayX
typedef ::Eigen::Array< Real, ::Eigen::Dynamic, ::Eigen::Dynamic >	ArrayXX
typedef ::Eigen::Matrix< Real, ::Eigen::Dynamic, ::Eigen::Dynamic >	Matrix
typedef ::Eigen::Matrix< Real, 2, 2 >	Matrix22
typedef ::Eigen::Matrix< Real, 3, 3 >	Matrix33
typedef ::Eigen::Matrix< Real, 4, 4 >	Matrix44
typedef ::Eigen::Matrix< Real, 6, 6 >	Matrix66
typedef ::Eigen::Block< Matrix >	MatrixBlock
typedef ::Eigen::Block< Matrix22 >	Matrix22Block
typedef ::Eigen::Block< Matrix33 >	Matrix33Block
typedef ::Eigen::Block< Matrix44 >	Matrix44Block
typedef ::Eigen::Block< Matrix66 >	Matrix66Block
typedef Matrix::ColXpr	MatrixColumn
typedef Matrix22::ColXpr	Matrix22Column
typedef Matrix33::ColXpr	Matrix33Column
typedef Matrix44::ColXpr	Matrix44Column
typedef Matrix66::ColXpr	Matrix66Column
typedef Matrix::RowXpr	MatrixRow
typedef Matrix22::RowXpr	Matrix22Row
typedef Matrix33::RowXpr	Matrix33Row
typedef Matrix44::RowXpr	Matrix44Row
typedef Matrix66::RowXpr	Matrix66Row
typedef ::Eigen::Block< const Matrix >	ConstMatrixBlock
typedef ::Eigen::Block< const Matrix22 >	ConstMatrix22Block
typedef ::Eigen::Block< const Matrix33 >	ConstMatrix33Block
typedef ::Eigen::Block< const Matrix44 >	ConstMatrix44Block
typedef ::Eigen::Block< const Matrix66 >	ConstMatrix66Block
typedef Matrix::ConstColXpr	ConstMatrixColumn
typedef Matrix22::ConstColXpr	ConstMatrix22Column
typedef Matrix33::ConstColXpr	ConstMatrix33Column
typedef Matrix44::ConstColXpr	ConstMatrix44Column
typedef Matrix66::ConstColXpr	ConstMatrix66Column
typedef Matrix::ConstRowXpr	ConstMatrixRow
typedef Matrix22::ConstRowXpr	ConstMatrix22Row
typedef Matrix33::ConstRowXpr	ConstMatrix33Row
typedef Matrix44::ConstRowXpr	ConstMatrix44Row
typedef Matrix66::ConstRowXpr	ConstMatrix66Row
typedef ::Eigen::Ref< Matrix >	MatrixRef
typedef ::Eigen::Ref< const Matrix >	ConstMatrixRef
typedef ::Eigen::Quaternion< Real >	Quaternion
typedef double	Real
typedef Matrix33	Rotation
typedef Matrix33Block	RotationBlock
typedef Matrix33Column	RotationColumn
typedef Matrix33Row	RotationRow
typedef ConstMatrix33Block	ConstRotationBlock
typedef ConstMatrix33Column	ConstRotationColumn
typedef ConstMatrix33Row	ConstRotationRow
typedef ::Eigen::AngleAxis< Real >	AngleAxis
typedef spatial::ArticulatedBodyInertia< Real >	ArticulatedBodyInertia
typedef spatial::ForceVector< Real >	ForceVector
typedef spatial::MotionVector< Real >	MotionVector
typedef spatial::PlueckerTransform< Real >	PlueckerTransform
typedef spatial::RigidBodyInertia< Real >	RigidBodyInertia
typedef ::Eigen::Transform< Real, 3, ::Eigen::Affine >	Transform
	Rigid transformation in 3D. More...
typedef ::Eigen::Translation< Real, 3 >	Translation
	Translation in 3D. More...
typedef ::Eigen::Matrix< Real, ::Eigen::Dynamic, 1 >	Vector
typedef ::Eigen::Matrix< Real, 2, 1 >	Vector2
typedef ::Eigen::Matrix< Real, 3, 1 >	Vector3
typedef ::Eigen::Matrix< Real, 4, 1 >	Vector4
typedef ::Eigen::Matrix< Real, 6, 1 >	Vector6
typedef ::Eigen::VectorBlock< Vector, ::Eigen::Dynamic >	VectorBlock
typedef ::Eigen::VectorBlock< Vector2, ::Eigen::Dynamic >	Vector2Block
typedef ::Eigen::VectorBlock< Vector3, ::Eigen::Dynamic >	Vector3Block
typedef ::Eigen::VectorBlock< Vector4, ::Eigen::Dynamic >	Vector4Block
typedef ::Eigen::VectorBlock< Vector6, ::Eigen::Dynamic >	Vector6Block
typedef ::Eigen::VectorBlock< const Vector, ::Eigen::Dynamic >	ConstVectorBlock
typedef ::Eigen::VectorBlock< const Vector2, ::Eigen::Dynamic >	ConstVector2Block
typedef ::Eigen::VectorBlock< const Vector3, ::Eigen::Dynamic >	ConstVector3Block
typedef ::Eigen::VectorBlock< const Vector4, ::Eigen::Dynamic >	ConstVector4Block
typedef ::Eigen::VectorBlock< const Vector6, ::Eigen::Dynamic >	ConstVector6Block
typedef ::Eigen::Ref< Vector >	VectorRef
typedef ::Eigen::Ref< const Vector >	ConstVectorRef

Enumerations
enum	Unit {   UNIT_NONE, UNIT_METER, UNIT_KILOGRAM, UNIT_SECOND,   UNIT_AMPERE, UNIT_KELVIN, UNIT_MOLE, UNIT_CANDELA,   UNIT_RADIAN, UNIT_HERTZ, UNIT_NEWTON, UNIT_VOLT,   UNIT_CELSIUS, UNIT_METER_PER_SECOND, UNIT_METER_PER_SECOND_SQUARED, UNIT_RADIAN_PER_SECOND,   UNIT_RADIAN_PER_SECOND_SQUARED, UNIT_NEWTON_SECOND, UNIT_NEWTON_METER_SECOND, UNIT_NEWTON_METER }

Functions
template<typename T >
T	cbrt (const T &arg)
template<typename T >
T	sign (const T &arg)
void	cartesianToPolar (const Real &x, const Real &y, Real &r, Real &theta)
void	cartesianToSpherical (const Real &x, const Real &y, const Real &z, Real &rho, Real &psi, Real &theta)
void	polarToCartesian (const Real &r, const Real &theta, Real &x, Real &y)
void	sphericalToCartesian (const Real &rho, const Real &psi, const Real &theta, Real &x, Real &y, Real &z)

Variables
static const Real	FUNCTION_BOUNDARY = 1.0e-8f
static const Real	DEG2RAD = static_cast<Real>(M_PI) / 180.0f
static const Real	GIGA2UNIT = 1.0e+9f
static const Real	GRAVITY = 9.80665f
	[m · s-2] More...
static const Real	KILO2UNIT = 1.0e+3f
static const Real	MEGA2UNIT = 1.0e+6f
static const Real	MICRO2UNIT = 1.0e-6f
static const Real	MILLI2UNIT = 1.0e-3f
static const Real	NANO2UNIT = 1.0e-9f
static const Real	RAD2DEG = 180.0f / static_cast<Real>(M_PI)
static const Real	UNIT2GIGA = 1.0e-9f
static const Real	UNIT2KILO = 1.0e-3f
static const Real	UNIT2MEGA = 1.0e-6f
static const Real	UNIT2MICRO = 1.0e+6f
static const Real	UNIT2MILLI = 1.0e+3f
static const Real	UNIT2NANO = 1.0e+9f

Detailed Description

Common mathematical functions.

Typedef Documentation

AngleAxis

typedef ::Eigen::AngleAxis<Real> rl::math::AngleAxis

ArrayX

typedef ::Eigen::Array<Real, ::Eigen::Dynamic, 1> rl::math::ArrayX

ArrayXX

typedef ::Eigen::Array<Real, ::Eigen::Dynamic, ::Eigen::Dynamic> rl::math::ArrayXX

ArticulatedBodyInertia

typedef spatial::ArticulatedBodyInertia<Real> rl::math::ArticulatedBodyInertia

ConstMatrix22Block

typedef ::Eigen::Block<const Matrix22> rl::math::ConstMatrix22Block

ConstMatrix22Column

typedef Matrix22::ConstColXpr rl::math::ConstMatrix22Column

ConstMatrix22Row

typedef Matrix22::ConstRowXpr rl::math::ConstMatrix22Row

ConstMatrix33Block

typedef ::Eigen::Block<const Matrix33> rl::math::ConstMatrix33Block

ConstMatrix33Column

typedef Matrix33::ConstColXpr rl::math::ConstMatrix33Column

ConstMatrix33Row

typedef Matrix33::ConstRowXpr rl::math::ConstMatrix33Row

ConstMatrix44Block

typedef ::Eigen::Block<const Matrix44> rl::math::ConstMatrix44Block

ConstMatrix44Column

typedef Matrix44::ConstColXpr rl::math::ConstMatrix44Column

ConstMatrix44Row

typedef Matrix44::ConstRowXpr rl::math::ConstMatrix44Row

ConstMatrix66Block

typedef ::Eigen::Block<const Matrix66> rl::math::ConstMatrix66Block

ConstMatrix66Column

typedef Matrix66::ConstColXpr rl::math::ConstMatrix66Column

ConstMatrix66Row

typedef Matrix66::ConstRowXpr rl::math::ConstMatrix66Row

ConstMatrixBlock

typedef ::Eigen::Block<const Matrix> rl::math::ConstMatrixBlock

ConstMatrixColumn

typedef Matrix::ConstColXpr rl::math::ConstMatrixColumn

ConstMatrixRef

typedef ::Eigen::Ref<const Matrix> rl::math::ConstMatrixRef

ConstMatrixRow

typedef Matrix::ConstRowXpr rl::math::ConstMatrixRow

ConstRotationBlock

typedef ConstMatrix33Block rl::math::ConstRotationBlock

ConstRotationColumn

typedef ConstMatrix33Column rl::math::ConstRotationColumn

ConstRotationRow

typedef ConstMatrix33Row rl::math::ConstRotationRow

ConstVector2Block

typedef ::Eigen::VectorBlock<const Vector2, ::Eigen::Dynamic> rl::math::ConstVector2Block

ConstVector3Block

typedef ::Eigen::VectorBlock<const Vector3, ::Eigen::Dynamic> rl::math::ConstVector3Block

ConstVector4Block

typedef ::Eigen::VectorBlock<const Vector4, ::Eigen::Dynamic> rl::math::ConstVector4Block

ConstVector6Block

typedef ::Eigen::VectorBlock<const Vector6, ::Eigen::Dynamic> rl::math::ConstVector6Block

ConstVectorBlock

typedef ::Eigen::VectorBlock<const Vector, ::Eigen::Dynamic> rl::math::ConstVectorBlock

ConstVectorRef

typedef ::Eigen::Ref<const Vector> rl::math::ConstVectorRef

ForceVector

typedef spatial::ForceVector<Real> rl::math::ForceVector

Matrix

typedef ::Eigen::Matrix<Real, ::Eigen::Dynamic, ::Eigen::Dynamic> rl::math::Matrix

Matrix22

typedef ::Eigen::Matrix<Real, 2, 2> rl::math::Matrix22

Matrix22Block

typedef ::Eigen::Block<Matrix22> rl::math::Matrix22Block

Matrix22Column

typedef Matrix22::ColXpr rl::math::Matrix22Column

Matrix22Row

typedef Matrix22::RowXpr rl::math::Matrix22Row

Matrix33

typedef ::Eigen::Matrix<Real, 3, 3> rl::math::Matrix33

Matrix33Block

typedef ::Eigen::Block<Matrix33> rl::math::Matrix33Block

Matrix33Column

typedef Matrix33::ColXpr rl::math::Matrix33Column

Matrix33Row

typedef Matrix33::RowXpr rl::math::Matrix33Row

Matrix44

typedef ::Eigen::Matrix<Real, 4, 4> rl::math::Matrix44

Matrix44Block

typedef ::Eigen::Block<Matrix44> rl::math::Matrix44Block

Matrix44Column

typedef Matrix44::ColXpr rl::math::Matrix44Column

Matrix44Row

typedef Matrix44::RowXpr rl::math::Matrix44Row

Matrix66

typedef ::Eigen::Matrix<Real, 6, 6> rl::math::Matrix66

Matrix66Block

typedef ::Eigen::Block<Matrix66> rl::math::Matrix66Block

Matrix66Column

typedef Matrix66::ColXpr rl::math::Matrix66Column

Matrix66Row

typedef Matrix66::RowXpr rl::math::Matrix66Row

MatrixBlock

typedef ::Eigen::Block<Matrix> rl::math::MatrixBlock

MatrixColumn

typedef Matrix::ColXpr rl::math::MatrixColumn

MatrixRef

typedef ::Eigen::Ref<Matrix> rl::math::MatrixRef

MatrixRow

typedef Matrix::RowXpr rl::math::MatrixRow

MotionVector

typedef spatial::MotionVector<Real> rl::math::MotionVector

PlueckerTransform

typedef spatial::PlueckerTransform<Real> rl::math::PlueckerTransform

Quaternion

typedef ::Eigen::Quaternion<Real> rl::math::Quaternion

Real

typedef double rl::math::Real

RigidBodyInertia

typedef spatial::RigidBodyInertia<Real> rl::math::RigidBodyInertia

Rotation

typedef Matrix33 rl::math::Rotation

RotationBlock

typedef Matrix33Block rl::math::RotationBlock

RotationColumn

typedef Matrix33Column rl::math::RotationColumn

RotationRow

typedef Matrix33Row rl::math::RotationRow

Transform

typedef ::Eigen::Transform<Real, 3, ::Eigen::Affine> rl::math::Transform

Rigid transformation in 3D.

Translation

typedef ::Eigen::Translation<Real, 3> rl::math::Translation

Translation in 3D.

Vector

typedef ::Eigen::Matrix<Real, ::Eigen::Dynamic, 1> rl::math::Vector

Vector2

typedef ::Eigen::Matrix<Real, 2, 1> rl::math::Vector2

Vector2Block

typedef ::Eigen::VectorBlock<Vector2, ::Eigen::Dynamic> rl::math::Vector2Block

Vector3

typedef ::Eigen::Matrix<Real, 3, 1> rl::math::Vector3

Vector3Block

typedef ::Eigen::VectorBlock<Vector3, ::Eigen::Dynamic> rl::math::Vector3Block

Vector4

typedef ::Eigen::Matrix<Real, 4, 1> rl::math::Vector4

Vector4Block

typedef ::Eigen::VectorBlock<Vector4, ::Eigen::Dynamic> rl::math::Vector4Block

Vector6

typedef ::Eigen::Matrix<Real, 6, 1> rl::math::Vector6

Vector6Block

typedef ::Eigen::VectorBlock<Vector6, ::Eigen::Dynamic> rl::math::Vector6Block

VectorBlock

typedef ::Eigen::VectorBlock<Vector, ::Eigen::Dynamic> rl::math::VectorBlock

VectorRef

typedef ::Eigen::Ref<Vector> rl::math::VectorRef

Enumeration Type Documentation

Unit

enum rl::math::Unit

SI base units

Name	Symbol	Measure
meter	m	length
kilogram	kg	mass
second	s	time
ampere	A	electric current
kelvin	K	thermodynamic temperature
mole	mol	quantity of matter (mass/mass)
candela	cd	luminous intensity

SI derived units

Name	Symbol	Quantity	Expression in terms of SI base units
radian	rad	Angle
hertz	Hz	frequency	s-1
newton	N	Force, Weight	m · kg · s-2
volt	V	Electrical potential difference, Electromotive force	m2 · kg · s-3 · A-1
degree Celsius	°C	Thermodynamic temperature	TºC = TK - 273.16
meter per second	m · s-1	speed, velocity	m · s-1
meter per second squared	m · s-2	acceleration	m · s-2
radian per second	rad · s-1	angular velocity	s-1
newton second	N · s	momentum, impulse	kg · m · s-1
newton meter second	N · m · s	angular momentum	kg · m2 · s-1
newton meter	N · m	Torque, moment of force	kg · m2 · s-2

Enumerator
UNIT_NONE
UNIT_METER
UNIT_KILOGRAM
UNIT_SECOND
UNIT_AMPERE
UNIT_KELVIN
UNIT_MOLE
UNIT_CANDELA
UNIT_RADIAN
UNIT_HERTZ
UNIT_NEWTON
UNIT_VOLT
UNIT_CELSIUS
UNIT_METER_PER_SECOND
UNIT_METER_PER_SECOND_SQUARED
UNIT_RADIAN_PER_SECOND
UNIT_RADIAN_PER_SECOND_SQUARED
UNIT_NEWTON_SECOND
UNIT_NEWTON_METER_SECOND
UNIT_NEWTON_METER

Function Documentation

cartesianToPolar()

void rl::math::cartesianToPolar ( const Real &  x, const Real &  y, Real &  r, Real &  theta  )

inline

cartesianToSpherical()

void rl::math::cartesianToSpherical ( const Real &  x, const Real &  y, const Real &  z, Real &  rho, Real &  psi, Real &  theta  )

inline

cbrt()

template<typename T >

T rl::math::cbrt ( const T &  arg )

inline

polarToCartesian()

void rl::math::polarToCartesian ( const Real &  r, const Real &  theta, Real &  x, Real &  y  )

inline

sign()

template<typename T >

T rl::math::sign ( const T &  arg )

inline

sphericalToCartesian()

void rl::math::sphericalToCartesian ( const Real &  rho, const Real &  psi, const Real &  theta, Real &  x, Real &  y, Real &  z  )

inline

Variable Documentation

DEG2RAD

const Real rl::math::DEG2RAD = static_cast<Real>(M_PI) / 180.0f

static

FUNCTION_BOUNDARY

const Real rl::math::FUNCTION_BOUNDARY = 1.0e-8f

static

GIGA2UNIT

const Real rl::math::GIGA2UNIT = 1.0e+9f

static

GRAVITY

const Real rl::math::GRAVITY = 9.80665f

static

[m · s^-2]

KILO2UNIT

const Real rl::math::KILO2UNIT = 1.0e+3f

static

MEGA2UNIT

const Real rl::math::MEGA2UNIT = 1.0e+6f

static

MICRO2UNIT

const Real rl::math::MICRO2UNIT = 1.0e-6f

static

MILLI2UNIT

const Real rl::math::MILLI2UNIT = 1.0e-3f

static

NANO2UNIT

const Real rl::math::NANO2UNIT = 1.0e-9f

static

RAD2DEG

const Real rl::math::RAD2DEG = 180.0f / static_cast<Real>(M_PI)

static

UNIT2GIGA

const Real rl::math::UNIT2GIGA = 1.0e-9f

static

UNIT2KILO

const Real rl::math::UNIT2KILO = 1.0e-3f

static

UNIT2MEGA

const Real rl::math::UNIT2MEGA = 1.0e-6f

static

UNIT2MICRO

const Real rl::math::UNIT2MICRO = 1.0e+6f

static

UNIT2MILLI

const Real rl::math::UNIT2MILLI = 1.0e+3f

static

UNIT2NANO

const Real rl::math::UNIT2NANO = 1.0e+9f

static