For detailed information see Math. More...

Collaboration diagram for Math Module:

Classes
class	SignedDegree< T >
	Signed angle that is represented using degrees. More...

class	Degree< T >
	Unsigned angle that is represented using degrees. More...

class	SignedRadian< T >
	Signed angle that is represented using radians. More...

class	Radian< T >
	Unsigned angle that is represented using radians. More...

class	SignedAngle< T >
	Signed angle that is represented using radians. More...

class	Angle< T >
	Unsigned angle that is represented using radians. More...

class	CRSplineInterpolator
	1D cubic Hermite spline interpolator. More...

class	IntervalFilter
	Concept and base class for all Interpolators and Filters. More...

class	LinearInterpolator
	1D linear interpolator. More...

class	LinearInterpolatorNoExtrapolation
	1D linear interpolator. More...

class	LinearInterpolatorNearestNeighbourExtrapolator
	1D linear interpolator. More...

class	LinearInterpolatorExtrapolationLimit
	1D linear interpolator. More...

class	NearestNeighborInterpolator
	1D nearest neighbor interpolator. More...

class	NormalRandomDistribution< D, T >
	Random distribution for drawing samples from univariate or multivariate normal distributions. More...

class	NormalRandomGenerator< D, T >
	Random generator for drawing samples from univariate or multivariate normal distributions. More...

struct	TPower< base, exponent >
	Computes the power base^exponent at compile time. More...

class	RandomGeneratorSingleton
	Singleton class for generating random numbers. More...

class	RandomGenerator< Distribution, Engine >
	Template class to easily generate random generators using the boost::random distributions and generators. More...

class	SchmittTriggerHysteresis< T >
	Class realizing a Schmitt trigger. More...

class	UniformRandomGenerator< T >
	A random generator that samples random numbers within the interval that is passed to the constructor. More...

Typedefs
typedef SignedDegree< int >	SignedDegreei
	Integer precision signed angle. More...

typedef SignedDegree< float >	SignedDegreef
	Float precision signed angle. More...

typedef SignedDegree< double >	SignedDegreed
	Double precision signed angle. More...

typedef Degree< int >	Degreei
	Integer precision angle. More...

typedef Degree< float >	Degreef
	Float precision angle. More...

typedef Degree< double >	Degreed
	Double precision angle. More...

typedef SignedRadian< float >	SignedRadianf
	Float precision signed angle. More...

typedef SignedRadian< double >	SignedRadiand
	Double precision signed angle. More...

typedef Radian< float >	Radianf
	Float precision angle. More...

typedef Radian< double >	Radiand
	Double precision angle. More...

typedef SignedAngle< float >	SignedAnglef
	Float precision signed angle. More...

typedef SignedAngle< double >	SignedAngled
	Double precision signed angle. More...

typedef Angle< float >	Anglef
	Float precision angle. More...

typedef Angle< double >	Angled
	Double precision angle. More...

Functions
template<typename T >
T	smallestAngleDifference (const T &a, const T &b)
	Returns the signed difference angle between the specified angles (in radian) that has the smallest absolute value. More...

template<typename T >
bool	isInAngleInterval (T value, T min, T max)
	Returns true, if the given angle (in radian) is in the given interval [min,max]. More...

template<typename T >
Getter< T >	rad2degGetter (const T &cref)
	Create a getter for serializing radians as degrees. More...

template<typename T >
Setter< T >	deg2radSetter (T &ref)
	Create setter for deserializing radians from degrees. See rad2degGetter. More...

template<typename T >
Setter< T >	deg2radSetter (T &ref, Deg2RadNonNegativeType)
	Create a setter for deserializing radians from degrees. More...

template<typename T >
Accessor< Getter< T >, Setter< T > >	radAsDegAccessor (T &ref)
	Create an accessor consisting of getter + setter for serializing radians as degrees. More...

template<typename T >
Accessor< Getter< T >, Setter< T > >	radAsDegAccessor (T &ref, Deg2RadNonNegativeType)
	Create a complete accessor consisting of getter + setter for serializing radians as degrees. More...

template<typename Derived >
TEigenFormat< Derived >	format (Eigen::MatrixBase< Derived > &matrix, Eigen::IOFormat format=EigenFormat::matlab())
	Function for formatting an Eigen matrix using a special format. More...

template<typename T , typename U >
bool	isApprox (const T &a, const T &b, const U &tol)
	Returns true, if the value a has approximately the same value as b. More...

template<typename T , typename S >
T	lerp (const T &a, const T &b, S alpha)
	Linear interpolation of different types like scalars, angles and rotations, vectors, etc. More...

template<typename T >
T	modulo (T x, T y)
	Computes x modulo y, i.e. More...

float	normcdf (float x, float mu=0.0, float sigma=1.0)
	Computes the normal cumulative distribution function at the value x using the specified mean mu and standard deviation sigma. More...

template<int exponent, typename T >
T	pow (T base)
	Computes the power of 'base' with a constant integral exponent. More...

template<typename T >
T	pow2 (T base)
	Computes base^2. More...

template<typename T >
T	pow3 (T base)
	Computes base^3. More...

template<typename T >
const T &	saturate (const T &value, const T &minValue, const T &maxValue)
	Saturate a value by limiting it to a certain interval. More...

template<typename T >
T	truncate (T value, uint32 decimals)
	Truncates a floating point value to a given number of decimals. More...

template<typename T >
Eigen::Quaternion< T >	quaternionFromYawPitchRoll (T yaw, T pitch, T roll)
	Converts yaw, pitch and roll angles to a quaternion. More...

template<typename T >
void	quaternionCovFromYawPitchRollCov (const Eigen::Matrix< T, 6, 6 > &eulerCovariance, float yaw, float pitch, float roll, Eigen::Quaternion< T > &oOrientation, Eigen::Matrix< T, 7, 7 > &oCovariance)
	Converts 6x6 dimensional covariance matrix (3D + yaw, pitch and roll) angles to a 7x7 dimensional quaternion covariance matrix (3D + Quaternion) Our convention for the order of rotations is as follows: yaw around the Z-Axis (pointing upwards) pitch around the Y-Axis (pointing left) roll around the X-Axis (pointing forward) More...

template<typename T >
Eigen::Matrix< T, 7, 7 >	quaternionCovFromYawPitchRollCov (const Eigen::Matrix< T, 6, 6 > &eulerCovariance, float yaw, float pitch, float roll)
	Converts 6x6 dimensional covariance matrix (3D + yaw, pitch and roll) angles to a 7x7 dimensional quaternion covariance matrix (3D + Quaternion) Our convention for the order of rotations is as follows: yaw around the Z-Axis (pointing upwards) pitch around the Y-Axis (pointing left) roll around the X-Axis (pointing forward) More...

template<typename T >
boost::tuples::tuple< T, T, T >	quaternionToYawPitchRoll (const Eigen::Quaternion< T > &q)
	Converts a quaternion back to yaw, pitch, roll angles. More...

template<typename T >
Eigen::Matrix< T, 6, 6 >	quaternionCovToYawPitchRollCov (const Eigen::Matrix< T, 7, 7 > &covariance, const Eigen::Quaternion< T > &q)
	Converts a 7x7 dimensional quaternion covariance (3D + Quaternion) back to a 6x6 dimensional euler covariance (3D + Yaw, Pitch, Roll). More...

template<typename T >
Eigen::Matrix< T, 3, 3 >	matrixFromYawPitchRoll (T yaw, T pitch, T roll)
	Converts yaw, pitch and roll angles to a rotation matrix. More...

template<typename T >
Eigen::Matrix< T, 3, 3 >	matrixFromYawPitchRoll (const boost::tuples::tuple< T, T, T > &ypr)
	Same as the above method, that takes the yaw,pitch,roll angles as 3-tuple. More...

template<typename T >
boost::tuples::tuple< T, T, T >	matrixToYawPitchRoll (const Eigen::Matrix< T, 3, 3 > &r)
	Converts a rotation matrix back to yaw, pitch, roll angles. More...

template<typename T >
void	derivMatricesFromYawPitchRoll (T yaw, T pitch, T roll, Eigen::Matrix< T, 3, 3 > &oR_dyaw, Eigen::Matrix< T, 3, 3 > &oR_dpitch, Eigen::Matrix< T, 3, 3 > &oR_droll)
	Returns the 3 derivates of the above rotation matrix, i.e. More...

Detailed Description

For detailed information see Math.

Typedef Documentation

◆ SignedDegreei

typedef SignedDegree<int> SignedDegreei

Integer precision signed angle.

See also: SignedDegree

◆ SignedDegreef

typedef SignedDegree<float> SignedDegreef

Float precision signed angle.

See also: SignedDegree

◆ SignedDegreed

typedef SignedDegree<double> SignedDegreed

Double precision signed angle.

See also: SignedDegree

◆ Degreei

typedef Degree<int> Degreei

Integer precision angle.

See also: Degree

◆ Degreef

typedef Degree<float> Degreef

Float precision angle.

See also: Degree

◆ Degreed

typedef Degree<double> Degreed

Double precision angle.

See also: Degree

◆ SignedRadianf

typedef SignedRadian<float> SignedRadianf

Float precision signed angle.

See also: SignedRadian

◆ SignedRadiand

typedef SignedRadian<double> SignedRadiand

Double precision signed angle.

See also: SignedRadian

◆ Radianf

typedef Radian<float> Radianf

Float precision angle.

See also: Radian

◆ Radiand

typedef Radian<double> Radiand

Double precision angle.

See also: Radian

◆ SignedAnglef

typedef SignedAngle<float> SignedAnglef

Float precision signed angle.

See also: SignedAngle

◆ SignedAngled

typedef SignedAngle<double> SignedAngled

Double precision signed angle.

See also: SignedAngle

◆ Anglef

typedef Angle<float> Anglef

Float precision angle.

See also: Angle

◆ Angled

typedef Angle<double> Angled

Double precision angle.

See also: Angle

Function Documentation

◆ smallestAngleDifference()

T mira::smallestAngleDifference	(	const T &	a,
		const T &	b
	)

inline

Returns the signed difference angle between the specified angles (in radian) that has the smallest absolute value.

◆ isInAngleInterval()

bool mira::isInAngleInterval	(	T	value,
		T	min,
		T	max
	)

inline

Returns true, if the given angle (in radian) is in the given interval [min,max].

◆ rad2degGetter()

Getter<T> mira::rad2degGetter ( const T & cref )

Create a getter for serializing radians as degrees.

Usage:

r.property("Phi",
           rad2degGetter(mPhi),
           deg2radSetter(mPhi),
           "phi internally stored in radians, serialized in degrees",
           90.f);

rad2degGetter/deg2radSetter must be used together for symmetric serialization/deserialization

◆ deg2radSetter() [1/2]

Setter<T> mira::deg2radSetter ( T & ref )

Create setter for deserializing radians from degrees. See rad2degGetter.

◆ deg2radSetter() [2/2]

Setter<T> mira::deg2radSetter	(	T &	ref,
		Deg2RadNonNegativeType
	)

Create a setter for deserializing radians from degrees.

This setter variant throws XInvalidParameter when trying to set a negative value.

Usage:

r.property("Phi",
           rad2degGetter(mPhi),
           deg2radSetter(mPhi, Deg2RadNonNegative),
           "phi internally stored in radians, serialized in degrees",
           90.f);

◆ radAsDegAccessor() [1/2]

Accessor<Getter<T>, Setter<T> > mira::radAsDegAccessor ( T & ref )

Create an accessor consisting of getter + setter for serializing radians as degrees.

Usage:

auto acc = radAsDegAccessor(mPhi);

r.property("Phi", acc, "phi internally stored in radians, serialized in degrees", 90.f);

◆ radAsDegAccessor() [2/2]

Accessor<Getter<T>, Setter<T> > mira::radAsDegAccessor	(	T &	ref,
		Deg2RadNonNegativeType
	)

Create a complete accessor consisting of getter + setter for serializing radians as degrees.

The setter from this variant throws XInvalidParameter when trying to set a negative value

Usage:

auto acc = radAsDegAccessor(mPhi, Deg2RadNonNegative);

r.property("Phi", acc, "phi internally stored in radians, serialized in degrees", 90.f);

◆ format()

TEigenFormat<Derived> mira::format	(	Eigen::MatrixBase< Derived > &	matrix,
		Eigen::IOFormat	format = `EigenFormat::matlab()`
	)

inline

Function for formatting an Eigen matrix using a special format.

This function can be used for writing and even reading a matrix to or from a stream in the given format.

Predefined formats are:

Usage:

Matrix... m
// read a matrix from the stream in Matlab format:
cin >> format(m,EigenFormat::matlab());
// write a matrix to the given stream in Matlab format using
// a precision of 9 significant digits.
cout << format(m,EigenFormat::matlab(9));

Parameters

matrix	The matrix that gets serialized.
format	The format to use.

◆ isApprox()

bool mira::isApprox	(	const T &	a,
		const T &	b,
		const U &	tol
	)

inline

Returns true, if the value a has approximately the same value as b.

The tolerance is given as third parameter. More precisely, the method returns true, if b is in the interval [a-tol,a+tol).

◆ lerp()

T mira::lerp	(	const T &	a,
		const T &	b,
		S	alpha
	)

inline

Linear interpolation of different types like scalars, angles and rotations, vectors, etc.

Rotations are interpolated via spherical linear interpolation (slerp).

The parameter alpha can vary between 0 and 1, where alpha=0 will return a and alpha=1 will return b. For values between 0 and 1 an interpolated value is returned. For some types alpha is allowed to be <0 or >1. In this case the method will extrapolate.

◆ modulo()

T mira::modulo	(	T	x,
		T	y
	)

inline

Computes x modulo y, i.e.

the remainder of the division operation x/y. This function is specialized for integral and floating point types. For integral types, the built in % operator is used. For floating point types the std::fmod() method is used.

◆ normcdf()

float mira::normcdf	(	float	x,
		float	mu = `0.0`,
		float	sigma = `1.0`
	)

inline

Computes the normal cumulative distribution function at the value x using the specified mean mu and standard deviation sigma.

Note: sigma must be > 0.

◆ pow()

T mira::pow ( T base )

inline

Computes the power of 'base' with a constant integral exponent.

Instead of:

float result = 0.4f*0.4f*0.4f*0.4f*0.4f*0.4f*0.4f*0.4f*0.4f*0.4f;

you can now write:

float result = pow<10>(0.4f);

which is much better to read and produces exactly the same code. Hence, the second variant is exactly as fast as the first one.

◆ pow2()

T mira::pow2 ( T base )

inline

Computes base^2.

◆ pow3()

T mira::pow3 ( T base )

inline

Computes base^3.

◆ saturate()

const T& mira::saturate	(	const T &	value,
		const T &	minValue,
		const T &	maxValue
	)

inline

Saturate a value by limiting it to a certain interval.

Parameters

[in]	value	The value to saturate
[in]	minValue	The minimum value of the interval
[in]	maxValue	The maximum value of the interval

Returns: The value clamped to the interval

◆ truncate()

T mira::truncate	(	T	value,
		uint32	decimals
	)

Truncates a floating point value to a given number of decimals.

truncate(3.141f,1) will give 3.1f

Parameters

value	Value to truncate
decimals	Decimals that should be kept

Returns: Truncated value

◆ quaternionFromYawPitchRoll()

Eigen::Quaternion<T> mira::quaternionFromYawPitchRoll	(	T	yaw,
		T	pitch,
		T	roll
	)

inline

Converts yaw, pitch and roll angles to a quaternion.

Our convention for the order of rotations is as follows:

yaw around the Z-Axis (pointing upwards)
pitch around the Y-Axis (pointing left)
roll around the X-Axis (pointing forward)

Parameters

[in]	yaw	The yaw angle
[in]	pitch	The pitch angle
[in]	roll	The roll angle

Returns: The yaw, pitch and roll angles as a quaternion

◆ quaternionCovFromYawPitchRollCov() [1/2]

void mira::quaternionCovFromYawPitchRollCov	(	const Eigen::Matrix< T, 6, 6 > &	eulerCovariance,
		float	yaw,
		float	pitch,
		float	roll,
		Eigen::Quaternion< T > &	oOrientation,
		Eigen::Matrix< T, 7, 7 > &	oCovariance
	)

inline

Converts 6x6 dimensional covariance matrix (3D + yaw, pitch and roll) angles to a 7x7 dimensional quaternion covariance matrix (3D + Quaternion) Our convention for the order of rotations is as follows:

yaw around the Z-Axis (pointing upwards)
pitch around the Y-Axis (pointing left)
roll around the X-Axis (pointing forward)

Our convention for the order of the quaternion is

qw
qx
qy
qz

Parameters

[in]	eulerCovariance	The 3D+Yaw,Pitch,Roll covaraiance matrix
[in]	yaw	The covariance matrix's orientation
[in]	pitch	The covariance matrix's orientation
[in]	roll	The covariance matrix's orientation
[out]	oOrientation	The computed quaternion from euler angles
[out]	oCovariance	The computed 7x7 covariance matrix in quaternion space

◆ quaternionCovFromYawPitchRollCov() [2/2]

Eigen::Matrix<T,7,7> mira::quaternionCovFromYawPitchRollCov	(	const Eigen::Matrix< T, 6, 6 > &	eulerCovariance,
		float	yaw,
		float	pitch,
		float	roll
	)

inline

Converts 6x6 dimensional covariance matrix (3D + yaw, pitch and roll) angles to a 7x7 dimensional quaternion covariance matrix (3D + Quaternion) Our convention for the order of rotations is as follows:

yaw around the Z-Axis (pointing upwards)
pitch around the Y-Axis (pointing left)
roll around the X-Axis (pointing forward)

Our convention for the order of the quaternion is

qw
qx
qy
qz

Parameters

[in]	eulerCovariance	The 3D+Yaw,Pitch,Roll covaraiance matrix
[in]	yaw	The covariance matrix's orientation
[in]	pitch	The covariance matrix's orientation
[in]	roll	The covariance matrix's orientation

Returns: The 7x7 dimensional covariance matrix in quaternion space.

◆ quaternionToYawPitchRoll()

boost::tuples::tuple<T,T,T> mira::quaternionToYawPitchRoll ( const Eigen::Quaternion< T > & q )

inline

Converts a quaternion back to yaw, pitch, roll angles.

This operation is the opposite of quaternionFromYawPitchRoll().

Please note: If a quaternion was created using quaternionFromYawPitchRoll() this method may return yaw,pitch,roll angles that may differ from the values used in the quaternionFromYawPitchRoll() call. The reason is that a single rotation can be described by different combinations of yaw, pitch and roll angles.

For details see quaternionFromYawPitchRoll().

Parameters

[in] q The quaternion with yaw, pitch and roll angles.

Returns: Returns the yaw, pitch and roll angle as 3-tuple.

◆ quaternionCovToYawPitchRollCov()

Eigen::Matrix<T,6,6> mira::quaternionCovToYawPitchRollCov	(	const Eigen::Matrix< T, 7, 7 > &	covariance,
		const Eigen::Quaternion< T > &	q
	)

inline

Converts a 7x7 dimensional quaternion covariance (3D + Quaternion) back to a 6x6 dimensional euler covariance (3D + Yaw, Pitch, Roll).

This operation is the opposite of quaternionCovFromYawPitchRollCov().

Parameters

[in]	covariance	The 3D+Quaternion covariance matrix
[in]	q	The covariance matrix's orientation

Returns: Returns the 6x6 dimensional covariance matrix (x,y,z,yaw,pitch,roll)

◆ matrixFromYawPitchRoll() [1/2]

Eigen::Matrix<T,3,3> mira::matrixFromYawPitchRoll	(	T	yaw,
		T	pitch,
		T	roll
	)

inline

Converts yaw, pitch and roll angles to a rotation matrix.

Our convention for the order of rotations is as follows:

yaw around the Z-Axis (pointing upwards)
pitch around the Y-Axis (pointing left)
roll around the X-Axis (pointing forward)

Parameters

[in]	yaw	The yaw angle
[in]	pitch	The pitch angle
[in]	roll	The roll angle

Returns: A rotation matrix for yaw, pitch and roll.

◆ matrixFromYawPitchRoll() [2/2]

Eigen::Matrix<T,3,3> mira::matrixFromYawPitchRoll ( const boost::tuples::tuple< T, T, T > & ypr )

inline

Same as the above method, that takes the yaw,pitch,roll angles as 3-tuple.

◆ matrixToYawPitchRoll()

boost::tuples::tuple<T,T,T> mira::matrixToYawPitchRoll ( const Eigen::Matrix< T, 3, 3 > & r )

inline

Converts a rotation matrix back to yaw, pitch, roll angles.

This is operation is the opposite of matrixFromYawPitchRoll().

Our convention for the order of rotations is as follows:

yaw around the Z-Axis (pointing upwards)
pitch around the Y-Axis (pointing left)
roll around the X-Axis (pointing forward)

Parameters

[in] r The rotation matrix.

Returns: Returns the yaw, pitch and roll angle as 3-tuple.

◆ derivMatricesFromYawPitchRoll()

void mira::derivMatricesFromYawPitchRoll	(	T	yaw,
		T	pitch,
		T	roll,
		Eigen::Matrix< T, 3, 3 > &	oR_dyaw,
		Eigen::Matrix< T, 3, 3 > &	oR_dpitch,
		Eigen::Matrix< T, 3, 3 > &	oR_droll
	)

inline

Returns the 3 derivates of the above rotation matrix, i.e.

3 matrices that are derived to yaw, pitch and roll respectively.

Our convention for the order of rotations is as follows:

yaw around the Z-Axis (pointing upwards)
pitch around the Y-Axis (pointing left)
roll around the X-Axis (pointing forward)

Parameters

[in]	yaw	The yaw angle
[in]	pitch	The pitch angle
[in]	roll	The roll angle
[out]	oR_dyaw	The matrixe derivated to yaw
[out]	oR_dpitch	The matrixe derivated to pitch
[out]	oR_droll	The matrixe derivated to roll

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ SignedDegreei

◆ SignedDegreef

◆ SignedDegreed

◆ Degreei

◆ Degreef

◆ Degreed

◆ SignedRadianf

◆ SignedRadiand

◆ Radianf

◆ Radiand

◆ SignedAnglef

◆ SignedAngled

◆ Anglef

◆ Angled

Function Documentation

◆ smallestAngleDifference()

◆ isInAngleInterval()

◆ rad2degGetter()

◆ deg2radSetter() [1/2]

◆ deg2radSetter() [2/2]

◆ radAsDegAccessor() [1/2]

◆ radAsDegAccessor() [2/2]

◆ format()

◆ isApprox()

◆ lerp()

◆ modulo()

◆ normcdf()

◆ pow()

◆ pow2()

◆ pow3()

◆ saturate()

◆ truncate()

◆ quaternionFromYawPitchRoll()

◆ quaternionCovFromYawPitchRollCov() [1/2]

◆ quaternionCovFromYawPitchRollCov() [2/2]

◆ quaternionToYawPitchRoll()

◆ quaternionCovToYawPitchRollCov()

◆ matrixFromYawPitchRoll() [1/2]

◆ matrixFromYawPitchRoll() [2/2]

◆ matrixToYawPitchRoll()

◆ derivMatricesFromYawPitchRoll()