Class translotator::Quaternion

template <typename Type>

ClassList > translotator > Quaternion

Representing a quaternion. More...

• #include <Quaternion.hpp>

Inherits the following classes: translotator::MatrixBase

Public Types inherited from translotator::MatrixBase

See translotator::MatrixBase

Type	Name
typedef Type	DATATYPE

Public Static Attributes

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

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
const Vector< 3, Type >	Im () const
Vector< 3, Type > &	Im ()
	Quaternion ()
	Quaternion (Type w, Type x, Type y, Type z)
	Quaternion (Type w, const Vector< 3, Type > & v)
	Quaternion (const ComplexNum< Type > & cplx)
const Type	Re () const
Type &	Re ()
void	canonicalize ()
Quaternion< Type >	canonicalized () const normalize the quaternion
void	conjugate () get the conjugated quaternion
Quaternion< Type >	conjugated () const canonicalize the quaternion
void	inverse () get the inversed quaternion
Quaternion< Type >	inversed () const conjugate the quaternion
Type	norm () const get the squared norm of the quaternion
Type	normSquared () const
void	normalize () get the normalized quaternion
Quaternion< Type >	normalized () const get the norm of the quaternion
Quaternion< Type >	operator* (const Quaternion< Type > & q) const quaternion multiplication
void	operator*= (const Quaternion< Type > & q) quaternion division
Quaternion< Type >	operator/ (const Quaternion< Type > & q) const
void	operator/= (const Quaternion< Type > & q) quaternion multiplication
Type	operator[] (size_t i) const
Type &	operator[] (size_t i)
Quaternion< Type >	quatNumDiv (const Quaternion< Type > & q) const
void	quatNumDivEq (const Quaternion< Type > & q)
Quaternion< Type >	quatNumMul (const Quaternion< Type > & q) const quaternion division
void	quatNumMulEq (const Quaternion< Type > & q)
SquareMatrix< 4, Type >	toMulMatrix () const get the matrix that represents the quaternion multiplication
SquareMatrix< 4, Type >	toRightMulMatrix () const get the matrix that represents the quaternion multiplication from the right
Type	w () const
Type &	w ()
Type	x () const
Type &	x ()
Type	y () const
Type &	y ()
Type	z () const
Type &	z ()

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 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:

• Type floating point type

A quaternion is a hypercomplex number that extends the complex numbers. It can be represented as a 4-dimensional vector. The quaternion is defined as q = w + xi + yj + zk, where w, x, y, and z are real numbers, and i, j, and k are the fundamental quaternion units. The quaternion has the following properties: i^2 = j^2 = k^2 = ijk = -1. (Hamillton representation) This can be used to represent rotations in 3D space. Also can be used to represent rotations in 3D space.

Public Static Attributes Documentation

variable OBJECT_TYPE

constexpr static ObjectType translotator::Quaternion< Type >::OBJECT_TYPE;

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Public Functions Documentation

function Im [1/2]

inline const Vector < 3, Type > translotator::Quaternion::Im () const

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function Im [2/2]

inline Vector < 3, Type > & translotator::Quaternion::Im () 

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function Quaternion [1/4]

inline translotator::Quaternion::Quaternion () 

constructors

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function Quaternion [2/4]

inline explicit translotator::Quaternion::Quaternion (
    Type w,
    Type x,
    Type y,
    Type z
) 

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function Quaternion [3/4]

inline explicit translotator::Quaternion::Quaternion (
    Type w,
    const Vector < 3, Type > & v
) 

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function Quaternion [4/4]

inline explicit translotator::Quaternion::Quaternion (
    const ComplexNum < Type > & cplx
) 

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function Re [1/2]

inline const Type translotator::Quaternion::Re () const

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function Re [2/2]

inline Type & translotator::Quaternion::Re () 

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function canonicalize

inline void translotator::Quaternion::canonicalize () 

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function canonicalized

normalize the quaternion

inline Quaternion < Type > translotator::Quaternion::canonicalized () const

get the canonicalized quaternion

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function conjugate

inline void translotator::Quaternion::conjugate () 

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function conjugated

inline Quaternion < Type > translotator::Quaternion::conjugated () const

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function inverse

inline void translotator::Quaternion::inverse () 

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function inversed

inline Quaternion < Type > translotator::Quaternion::inversed () const

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function norm

inline Type translotator::Quaternion::norm () const

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function normSquared

inline Type translotator::Quaternion::normSquared () const

utils

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function normalize

inline void translotator::Quaternion::normalize () 

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function normalized

inline Quaternion < Type > translotator::Quaternion::normalized () const

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function operator*

inline Quaternion < Type > translotator::Quaternion::operator* (
    const Quaternion < Type > & q
) const

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function operator*=

inline void translotator::Quaternion::operator*= (
    const Quaternion < Type > & q
) 

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function operator/

inline Quaternion < Type > translotator::Quaternion::operator/ (
    const Quaternion < Type > & q
) const

---

function operator/=

inline void translotator::Quaternion::operator/= (
    const Quaternion < Type > & q
) 

---

function operator[]

inline Type translotator::Quaternion::operator[] (
    size_t i
) const

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function operator[]

inline Type & translotator::Quaternion::operator[] (
    size_t i
) 

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function quatNumDiv

inline Quaternion < Type > translotator::Quaternion::quatNumDiv (
    const Quaternion < Type > & q
) const

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function quatNumDivEq

inline void translotator::Quaternion::quatNumDivEq (
    const Quaternion < Type > & q
) 

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function quatNumMul

inline Quaternion < Type > translotator::Quaternion::quatNumMul (
    const Quaternion < Type > & q
) const

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function quatNumMulEq

inline void translotator::Quaternion::quatNumMulEq (
    const Quaternion < Type > & q
) 

---

function toMulMatrix

get the matrix that represents the quaternion multiplication

inline SquareMatrix < 4, Type > translotator::Quaternion::toMulMatrix () const

casting

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function toRightMulMatrix

inline SquareMatrix < 4, Type > translotator::Quaternion::toRightMulMatrix () const

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function w [1/2]

inline Type translotator::Quaternion::w () const

accessors

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function w [2/2]

inline Type & translotator::Quaternion::w () 

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function x [1/2]

inline Type translotator::Quaternion::x () const

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function x [2/2]

inline Type & translotator::Quaternion::x () 

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function y [1/2]

inline Type translotator::Quaternion::y () const

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function y [2/2]

inline Type & translotator::Quaternion::y () 

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function z [1/2]

inline Type translotator::Quaternion::z () const

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function z [2/2]

inline Type & translotator::Quaternion::z () 

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