theoretica::quat< Type > Class Template Reference

Quaternion class in the form \(a + bi + cj + dk\). More...

#include <quat.h>

Public Member Functions
	quat ()
	Construct a quaternion with all zero components.
	quat (Type r)
	Construct a quaternion from a real number.
	quat (Type a, Type b, Type c, Type d)
	Construct a quaternion from its components.
	quat (const quat &q)
	Copy constructor.
quat &	operator= (const quat &q)
	Assignment operator.
template<typename T >
quat &	operator= (const std::array< T, 4 > &v)
	Assignment operator from a 4D array.
Type	Re () const
	Get the real part of the quaternion.
Type	Im1 () const
	Get the first imaginary part of the quaternion.
Type	Im2 () const
	Get the second imaginary part of the quaternion.
Type	Im3 () const
	Get the third imaginary part of the quaternion.
quat	conjugate () const
	Compute the conjugate of the quaternion.
Type	sqr_norm () const
	Compute the square norm of the quaternion.
Type	norm () const
	Compute the norm of the quaternion.
quat	inverse () const
	Compute the inverse of the quaternion.
quat &	invert ()
	Invert the quaternion.
quat	operator+ () const
	Identity (for consistency)
quat	operator- () const
	Get the opposite of the quaternion.
quat	operator+ (Type k) const
	Sum a quaternion and a scalar value.
quat	operator- (Type k) const
	Subtract a quaternion and a scalar value.
quat	operator* (Type k) const
	Multiply a quaternion by a scalar value.
quat	operator/ (Type k) const
	Divide a quaternion by a scalar value.
quat	operator+ (const quat &other) const
	Add two quaternions.
quat	operator- (const quat &other) const
	Subtract two quaternions.
quat	operator* (const quat &q) const
	Multiply two quaternions.
quat	operator/ (const quat &other) const
	Divide two quaternions.
quat &	operator*= (Type k)
	Multiply this quaternion by a scalar value.
quat &	operator/= (Type k)
	Divide this quaternion by a scalar value.
quat &	operator+= (const quat &other)
	Add a quaternion to this one.
quat &	operator-= (const quat &other)
	Subtract a quaternion to this one.
quat &	operator*= (const quat &other)
	Multiply this quaternion by another one.
quat &	operator/= (const quat &other)
	Divide this quaternion by another one.
template<typename Vector >
Vector	transform (const Vector &v) const
	Transform a 3D vector.
std::string	to_string () const
	Convert the quaternion to string representation.
	operator std::string ()
	Convert the quaternion to string representation.

Static Public Member Functions
template<typename Vector >
static quat	rotation (Type rad, const Vector &axis)
	Construct a quaternion which represents a rotation of <rad> radians around the <axis> arbitrary axis.
template<typename Vector >
static Vector	rotate (const Vector &v, Type rad, const Vector &axis)
	Rotate a 3D vector <v> by <rad> radians around the <axis> arbitrary axis.

Public Attributes
Type	a
	Real part.
Type	b
	Imaginary parts.
Type	c
Type	d

Friends
Type	Re (const quat &q)
	Extract the real part of the quaternion.
Type	Im1 (const quat &q)
	Extract the first imaginary part of the quaternion.
Type	Im2 (const quat &q)
	Extract the second imaginary part of the quaternion.
Type	Im3 (const quat &q)
	Extract the third imaginary part of the quaternion.
quat	operator+ (Type r, const quat &z)
quat	operator- (Type r, const quat &z)
quat	operator* (Type r, const quat &z)
quat	operator/ (Type r, const quat &z)
std::ostream &	operator<< (std::ostream &out, const quat &obj)
	Stream the quaternion in string representation to an output stream (std::ostream)

Detailed Description

template<typename Type = real>
class theoretica::quat< Type >

Quaternion class in the form \(a + bi + cj + dk\).

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

• complex/quat.h