Class translotator::SOGroup¶

template <size_t N, typename Type>

ClassList > translotator > SOGroup

Special Orthogonal Group. More...

#include <SOGroup.hpp>

Inherits the following classes: translotator::SquareMatrix

Public Types inherited from translotator::MatrixBase¶

Type	Name
typedef Type	DATATYPE

Public Static Attributes¶

Type	Name
constexpr static ObjectType	OBJECT_TYPE = = ObjectType::SO_GROUP

Public Static Attributes inherited from translotator::SquareMatrix¶

See translotator::SquareMatrix

Type	Name
constexpr static ObjectType	OBJECT_TYPE = = ObjectType::SQUARE_MATRIX

Public Static Attributes inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
constexpr static size_t	COLS = = M
constexpr static bool	MATRIX_BASE = = true
constexpr static size_t	ROWS = = N

Public Functions¶

Type	Name
	SOGroup (const Vector< N, Type > & vec1, const Vector< N, Type > & vec2, bool col=true)
	SOGroup (const Vector< N, Type > & vec1, const Vector< N, Type > & vec2, const Vector< N, Type > & vec3, bool col=true)
	SOGroup (const Type & theta)
	SOGroup (const Vector< N, Type > & angleVector)
SOGroup< N, Type >	T () const transpose
void	inverse () inverse this matrix
SOGroup< N, Type >	inversed () const inverse is same as transpose in SOGroup __
void	normalize () normalize this matrix
SOGroup< N, Type >	normalized () const Get the orthogonalized matrix.
auto	operator* (const OtherContainer & other) const SOGroup *SOGroup =>SOGroup .
void	*operator= (const SOGroup< N, Type > & other) SOGroup** =SOGroup* .
SquareMatrix< N, Type >	operator+ (const OtherContainer & other) const SOGroup +SOGroup =>SquareMatrix .
SquareMatrix< N, Type >	operator- (const OtherContainer & other) const SOGroup -SOGroup =>SquareMatrix .
SOGroup< N, Type >	operator- () const - SOGroup __
auto	operator/ (const OtherContainer & other) const SOGroup /SOGroup =>SOGroup .
SOGroup< N, Type >	pow (const Type & t) const power of SOGroup . Using Exponential & Logarithm Map of Lie Group
AxisAngle< Type >	toAxisAngle () const convert to AxisAngle __
EulerAngle< Type, NewOrder >	toEulerAngle () const Convert to Euler Angle.
UnitComplexNum< Type >	toUnitComplexNum () const convert to UnitComplexNum . Using only z-axis
UnitQuaternion< Type >	toUnitQuaternion () const convert to UnitQuaternion __

Public Functions inherited from translotator::SquareMatrix¶

See translotator::SquareMatrix

Type	Name
Type	determinant () const determinant of a square matrix. Only 2x2, 3x3 matrices are supported
void	inverse ()
SquareMatrix< N, Type >	inversed (bool & result) const 1x1 ~ 3x3 closed form solution 4x4 ~ LU factorization with partial pivotting from PX4-Matrix Library
Type	trace () const trace of a square matrix

Public Functions inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
	MatrixBase () = default Returns the number of columns.
	MatrixBase (const MatrixBase & other) = default
	MatrixBase (const Type data)
	MatrixBase (const Type data)
	MatrixBase (const initializer_list< N M, Type > & list) Initializer list constructor.*
auto	T () const Transpose.
Matrix< P, Q, Type >	block (size_t i, size_t j) const Returns a block of the matrix.
Matrix< P, Q, Type >	block () const Returns a block of the matrix.
ComplexNum< Type >	cast2ComplexNum () const Casts the object to a complex number by copying.
ComplexNum< Type > &	cast2ComplexNumRef () Casts the object to a complex number reference without copying.
DualNumber< Type >	cast2DualNumber () const Casts the object to a dual number by copying.
DualNumber< Type > &	cast2DualNumberRef () Casts the object to a dual number reference without copying.
DualQuaternion< Type >	cast2DualQuaternion () const Casts the object to a dual quaternion by copying.
DualQuaternion< Type > &	cast2DualQuaternionRef () Casts the object to a dual quaternion reference without copying.
Matrix< N, M, Type >	cast2Matrix () const Casts the object to a different matrix type by copying.
Matrix< N, M, Type > &	cast2MatrixRef () Casts the object to a matrix reference without copying.
Quaternion< Type >	cast2Quaternion () const Casts the object to a quaternion by copying.
Quaternion< Type > &	cast2QuaternionRef () Casts the object to a quaternion reference without copying.
SOGroup< N, Type >	cast2SOGroup () const Casts the object to a special orthogonal group by copying.
SOGroup< N, Type > &	cast2SOGroupRef () Casts the object to a special orthogonal group reference without copying.
SquareMatrix< N, Type >	cast2SquareMatrix () const Casts the object to a square matrix by copying.
SquareMatrix< N, Type > &	cast2SquareMatrixRef () Casts the object to a square matrix reference without copying.
UnitComplexNum< Type >	cast2UnitComplexNum () const Casts the object to a unit complex number by copying.
UnitComplexNum< Type > &	cast2UnitComplexNumRef () Casts the object to a unit complex number reference without copying.
UnitDualQuaternion< Type >	cast2UnitDualQuaternion () const Casts the object to a unit dual quaternion by copying.
UnitDualQuaternion< Type > &	cast2UnitDualQuaternionRef () Casts the object to a unit dual quaternion reference without copying.
UnitQuaternion< Type >	cast2UnitQuaternion () const Casts the object to a unit quaternion by copying.
UnitQuaternion< Type > &	cast2UnitQuaternionRef () Casts the object to a unit quaternion reference without copying.
Vector< N, Type >	cast2Vector () const Casts the object to a vector by copying.
Vector< N, Type > &	cast2VectorRef () Casts the object to a vector reference without copying.
NewContainer	castContainer () const Casts the matrix to a different container type by copying.
NewContainer &	castContainerRef () Casts the object to a different container reference without copying.
NewDerived &	castContainerRef ()
auto	castDataType () const Returns the Frobenius norm.
Matrix< N, 1, Type >	col (size_t j) const Returns the j-th column.
void	copyTo (Type * data) const Returns the raw data pointer.
void	fill (const Type & v) Fills the matrix with a value.
Type	frobeniusNorm () const
Type	frobeniusNormSquared () const Returns the squared Frobenius norm.
Type *	getData () const
const Type &	operator() (size_t i, size_t j) const Accesses the element at (i, j)
Type &	operator() (size_t i, size_t j) Accesses the element at (i, j)
auto	operator* (const OtherDerived & other) const Matrix multiplication.
Derived	operator* (const Type & v) const Matrix multiplication by scalar.
void	*operator= (const OtherDerived & other) Matrix** multiplication by scalar.
Derived	operator+ (const OtherDerived & other) const Multiplication by scalar.
void	operator+= (const OtherDerived & other) Matrix division by scalar.
Derived	operator- (const OtherDerived & other) const Matrix subtraction.
Derived	operator- () const Matrix multiplication by scalar.
void	operator-= (const OtherDerived & other) Matrix subtraction by scalar.
Derived	operator/ (Type v) const Division by scalar.
void	operator/= (Type v) Division by scalar.
Derived &	operator= (const Derived & other) Copies the data to the given pointer.
void	print () const Prints the matrix.
Matrix< 1, M, Type >	row (size_t i) const Returns the i-th row.
Derived &	setBlock (size_t i, size_t j, const OtherDerived & block) Sets the element at (i, j)
Derived &	setBlock (const OtherDerived & block) Sets the i-th row.
Derived &	setCol (size_t j, const OtherDerived & col) Sets the j-th column.
Derived &	setCol (const OtherDerived & col) Sets the j-th column.
Derived &	setRow (size_t i, const OtherDerived & row) Sets the i-th row.
Derived &	setRow (const OtherDerived & row) Sets the i-th row.
void	swapCols (size_t j1, size_t j2) Swaps two columns.
void	swapRows (size_t i1, size_t i2) Swaps two rows.
Type	toScalar () const Casts the matrix to a scalar if it is a 1x1 matrix.

Public Static Functions¶

Type	Name
SOGroup< N, Type >	axisRotation (const Type & angle) Create a rotation matrix around the axis.
SOGroup< N, Type >	identity () identity rotation element, which is identity matrix

Public Static Functions inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
Derived	NaN () Returns a matrix filled with NaN.
constexpr static size_t	colSize () Returns the number of rows.
Derived	eye () Returns an identity matrix.
Derived	ones () Returns a matrix filled with ones.
constexpr static size_t	rowSize ()
Derived	zeros () Returns a matrix filled with zeros.

Protected Attributes inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
Type	data_

Detailed Description¶

Template parameters:

N dimension
Type data type

Special Orthogonal Group is a group of rotation in N dimension. It is a group of orthogonal matrices with determinant 1. Subgroup of SOGroup is SO(2) and SO(3). Also SOGroup is a Lie Group. Exponential and Logarithm map can be defined.

Public Static Attributes Documentation¶

variable OBJECT_TYPE¶

constexpr static ObjectType translotator::SOGroup< N, Type >::OBJECT_TYPE;

Public Functions Documentation¶

function SOGroup [2/5]¶

template<size_t N_, typename>
inline translotator::SOGroup::SOGroup (
    const Vector < N, Type > & vec1,
    const Vector < N, Type > & vec2,
    bool col=true
)

constructors

function SOGroup [3/5]¶

template<size_t N_, typename>
inline translotator::SOGroup::SOGroup (
    const Vector < N, Type > & vec1,
    const Vector < N, Type > & vec2,
    const Vector < N, Type > & vec3,
    bool col=true
)

function SOGroup [4/5]¶

template<size_t N_, typename>
inline explicit translotator::SOGroup::SOGroup (
    const Type & theta
)

function SOGroup [5/5]¶

template<size_t N_, typename>
inline explicit translotator::SOGroup::SOGroup (
    const Vector < N, Type > & angleVector
)

function T¶

inline SOGroup < N, Type > translotator::SOGroup::T () const

function inverse¶

inline void translotator::SOGroup::inverse ()

function inversed¶

inline SOGroup < N, Type > translotator::SOGroup::inversed () const

function normalize¶

inline void translotator::SOGroup::normalize ()

function normalized¶

Get the orthogonalized matrix.

inline SOGroup < N, Type > translotator::SOGroup::normalized () const

utils

Returns:

SOGroup<N, Type>

Note:

This function uses UnitComplexNum & UnitQuternion internally. Not a mathmatically correct way, but it works.

function operator*¶

SOGroup *SOGroup =>SOGroup .

template<typename OtherContainer>
inline auto translotator::SOGroup::operator* (
    const OtherContainer & other
) const

Template parameters:

OtherContainer Matrix based object with same dimension SOGroup * SOGroup => SOGroup

function operator*=¶

inline void translotator::SOGroup::operator*= (
    const SOGroup < N, Type > & other
)

function operator+¶

SOGroup +SOGroup =>SquareMatrix .

template<typename OtherContainer>
inline SquareMatrix < N, Type > translotator::SOGroup::operator+ (
    const OtherContainer & other
) const

operators

Template parameters:

OtherContainer Matrix based object with same dimension

function operator-¶

SOGroup -SOGroup =>SquareMatrix .

template<typename OtherContainer>
inline SquareMatrix < N, Type > translotator::SOGroup::operator- (
    const OtherContainer & other
) const

Template parameters:

OtherContainer Matrix based object with same dimension SOGroup - SOGroup => SquareMatrix

function operator-¶

inline SOGroup < N, Type > translotator::SOGroup::operator- () const

function operator/¶

SOGroup /SOGroup =>SOGroup .

template<typename OtherContainer>
inline auto translotator::SOGroup::operator/ (
    const OtherContainer & other
) const

Template parameters:

OtherContainer Matrix based object with same dimension

function pow¶

inline SOGroup < N, Type > translotator::SOGroup::pow (
    const Type & t
) const

function toAxisAngle¶

inline AxisAngle < Type > translotator::SOGroup::toAxisAngle () const

function toEulerAngle¶

Convert to Euler Angle.

template<EULER_ORDER NewOrder>
inline EulerAngle < Type, NewOrder > translotator::SOGroup::toEulerAngle () const

Template parameters:

NewOrder New Euler Order

function toUnitComplexNum¶

convert to UnitComplexNum . Using only z-axis

inline UnitComplexNum < Type > translotator::SOGroup::toUnitComplexNum () const

casts

function toUnitQuaternion¶

inline UnitQuaternion < Type > translotator::SOGroup::toUnitQuaternion () const

Public Static Functions Documentation¶

function axisRotation¶

Create a rotation matrix around the axis.

template<AXIS Axis>
static inline SOGroup < N, Type > translotator::SOGroup::axisRotation (
    const Type & angle
)

Template parameters:

Axis Axis to rotate

Parameters:

angle angle in radian

function identity¶

identity rotation element, which is identity matrix

static inline SOGroup < N, Type > translotator::SOGroup::identity ()

static functions

Friends Documentation¶

friend operator*¶

inline SquareMatrix < N, Type > translotator::SOGroup::operator* (
    const Type & lhs,
    const SOGroup & rhs
)

The documentation for this class was generated from the following file include/translotator/objects/SOGroup.hpp