#include <C:/Users/Andres/source/repos/casm_viewer/external/tinc/external/allolib/include/al/math/al_Quat.hpp>

Public Member Functions
	Quat (const T &w=T(1), const T &x=T(0), const T &y=T(0), const T &z=T(0))
	Default constructor creates an identity quaternion.

template<class U >
	Quat (const Quat< U > &v)

template<class U >
	Quat (const Vec< 3, U > &xyz)
	Construct 'pure imaginary' quaternion. More...

template<class U >
	Quat (const T &w, const Vec< 3, U > &xyz)
	Construct quaternion from real and imaginary parts. More...

T &	operator[] (int i)
	Set component with index.

const T &	operator[] (int i) const
	Get component with index.

bool	operator== (const Quat &v) const
	Returns true if all components are equal.

bool	operator!= (const Quat &v) const
	Returns true if any components are not equal.

Quat	operator- () const

Quat	operator+ (const Quat &v) const

Quat	operator+ (const T &v) const

Quat	operator- (const Quat &v) const

Quat	operator- (const T &v) const

Quat	operator/ (const Quat &v) const

Quat	operator/ (const T &v) const

Quat	operator* (const Quat &v) const

Quat	operator* (const T &v) const

template<class U >
Quat &	operator= (const Quat< U > &v)

Quat &	operator= (const T &v)

Quat &	operator+= (const Quat &v)

Quat &	operator+= (const T &v)

Quat &	operator-= (const Quat &v)

Quat &	operator-= (const T &v)

Quat &	*operator=** (const Quat &v)

Quat &	*operator=** (const T &v)

Quat &	operator/= (const Quat &v)

Quat &	operator/= (const T &v)

Quat	conj () const
	Returns the conjugate.

T	dot (const Quat &v) const
	Returns dot product with another quaternion.

Quat	inverse () const
	Returns inverse (same as conjugate if normalized as q^-1 = q_conj/q_mag^2)

T	mag () const
	Get magnitude.

T	magSqr () const
	Get magnitude squared.

Quat	pow (T v) const
	Return quaternion raised to a power.

Quat	recip () const
	Returns multiplicative inverse.

Quat	sgn () const
	Returns signum, q/\|q\|, the closest point on unit 3-sphere.

Quat	multiply (const Quat &q2) const

Quat	reverseMultiply (const Quat &q2) const

Quat &	normalize ()
	Normalize magnitude to one. More...

Quat &	set (const T &w, const T &x, const T &y, const T &z)
	Set components.

template<class U >
Quat &	set (const Quat< U > &q)
	Set from other quaternion.

Quat &	setIdentity ()
	Set to identity.

Quat &	fromAxisAngle (const T &angle, const T &ux, const T &uy, const T &uz)
	Set as versor rotated by angle, in radians, around unit vector (ux,uy,uz)

Quat &	fromAxisAngle (const T &angle, const Vec< 3, T > &axis)
	Set as versor rotated by angle, in radians, around unit vector.

Quat &	fromAxisX (const T &angle)
	Set as versor rotated by angle, in radians, around x-axis.

Quat &	fromAxisY (const T &angle)
	Set as versor rotated by angle, in radians, around y-axis.

Quat &	fromAxisZ (const T &angle)
	Set as versor rotated by angle, in radians, around z-axis.

Quat &	fromEuler (const Vec< 3, T > &aeb)
	Set as versor rotated by YXZ Euler angles, in radians.

Quat &	fromEuler (const T &az, const T &el, const T &ba)
	Set as versor rotated by YXZ Euler angles, in radians.

Quat &	fromMatrix (const T *matrix)

Quat &	fromMatrix (const Mat< 4, T > &v)

Quat &	fromMatrixTransposed (const T *matrix)
	Set as versor from row-major 4-by-4 projective space transformation matrix.

Quat &	fromMatrixTransposed (const Mat< 4, T > &v)
	Set as versor from row-major 4-by-4 projective space transformation matrix.

void	toCoordinateFrame (Vec< 3, T > &ux, Vec< 3, T > &uy, Vec< 3, T > &uz) const
	Convert to coordinate frame unit vectors.

template<typename T2 >
void	toMatrix (T2 *matrix) const
	Convert to column-major 4-by-4 projective space transformation matrix.

template<typename T2 >
void	toMatrixTransposed (T2 *matrix) const
	Convert to row-major 4-by-4 projective space transformation matrix.

void	toAxisAngle (T &angle, T &ax, T &ay, T &az) const
	Convert to axis-angle form, in radians.

void	toAxisAngle (T &angle, Vec< 3, T > &axis) const

void	toEuler (T &az, T &el, T &ba) const
	Convert to YXZ Euler angles (azimuth, elevation, bank), in radians.

void	toEuler (T *aeb) const
	Convert to YXZ Euler angle vector (azimuth, elevation, bank), in radians.

void	toEuler (Vec< 3, T > &aeb) const
	Convert to YXZ Euler angle vector (azimuth, elevation, bank), in radians.

template<typename T2 >
void	toVectorX (T2 &ax, T2 &ay, T2 &az) const
	Get local x unit vector (1,0,0) in absolute coordinates.

template<typename T2 >
void	toVectorX (Vec< 3, T2 > &v) const

template<typename T2 = T>
Vec< 3, T2 >	toVectorX () const

template<typename T2 >
void	toVectorY (T2 &ax, T2 &ay, T2 &az) const
	Get local y unit vector (0,1,0) in absolute coordinates.

template<typename T2 >
void	toVectorY (Vec< 3, T2 > &v) const

template<typename T2 = T>
Vec< 3, T2 >	toVectorY () const

template<typename T2 >
void	toVectorZ (T2 &ax, T2 &ay, T2 &az) const
	Get local z unit vector (0,0,1) in absolute coordinates.

template<typename T2 >
void	toVectorZ (Vec< 3, T2 > &v) const

template<typename T2 = T>
Vec< 3, T2 >	toVectorZ () const

Vec< 3, T >	rotate (const Vec< 3, T > &v) const

Vec< 3, T >	rotateTransposed (const Vec< 3, T > &v) const
	This is rotation by the quaternion's conjugate.

Quat	slerp (const Quat &target, T amt) const
	Spherical interpolation.

void	slerpTo (const Quat &target, T amt)
	In-place spherical interpolation.

void	towardPoint (const Vec< 3, T > &pos, const Quat< T > &q, const Vec< 3, T > &v, float amt)
	Get the quaternion from a given point and quaterion toward another point. More...

void	print (std::ostream &stream) const
	utility for debug printing:

Static Public Member Functions
static Quat	getRotationTo (const Vec< 3, T > &usrc, const Vec< 3, T > &udst)

static Quat	getBillboardRotation (const Vec< 3, T > &forward, const Vec< 3, T > &up)

static Quat	identity ()
	Returns identity.

static Quat	rotor (const Vec< 3, T > &v1, const Vec< 3, T > &v2)
	Get rotor from two unit vectors. More...

static Quat	slerp (const Quat &from, const Quat &to, T amt)
	Spherical linear interpolation of a quaternion. More...

static void	slerpBuffer (const Quat &from, const Quat &to, Quat< T > *buffer, int numFrames)
	Fill an array of Quats with a full spherical interpolation. More...

static T	accuracyMax ()

static T	accuracyMin ()

static T	eps ()

Public Attributes
union {
struct {
T w
	w component

T x
	x component

T y
	y component

T z
	z component

}

T components [4]
	component vector

};

Detailed Description

template<typename T = double>
class al::Quat< T >

Quaternion

Definition at line 63 of file al_Quat.hpp.

Constructor & Destructor Documentation

◆ Quat() [1/3]

template<typename T = double>

template<class U >

al::Quat< T >::Quat ( const Quat< U > & v )

inline

Parameters

[in] v quaternion to set values from

Definition at line 82 of file al_Quat.hpp.

◆ Quat() [2/3]

template<typename T = double>

template<class U >

al::Quat< T >::Quat ( const Vec< 3, U > & xyz )

inline

Construct 'pure imaginary' quaternion.

Parameters

[in] xyz vector to set x,y,z components from; w is set to 0

Definition at line 89 of file al_Quat.hpp.

◆ Quat() [3/3]

template<typename T = double>

template<class U >

al::Quat< T >::Quat	(	const T &	w,
		const Vec< 3, U > &	xyz
	)

inline

Construct quaternion from real and imaginary parts.

Parameters

[in]	w	real part (w)
[in]	xyz	vector to set imaginary (x,y,z) components from

Definition at line 96 of file al_Quat.hpp.

Member Function Documentation

◆ fromMatrix() [1/2]

template<typename T = double>

Quat& al::Quat< T >::fromMatrix ( const Mat< 4, T > & v )

inline

Set as versor from column-major 4-by-4 projective space transformation matrix

Definition at line 314 of file al_Quat.hpp.

◆ fromMatrix() [2/2]

template<typename T >

Quat< T > & al::Quat< T >::fromMatrix ( const T * matrix )

Set as versor from column-major 4-by-4 projective space transformation matrix

Definition at line 579 of file al_Quat.hpp.

◆ getBillboardRotation()

template<typename T >

Quat< T > al::Quat< T >::getBillboardRotation	(	const Vec< 3, T > &	forward,
		const Vec< 3, T > &	up
	)

static

Similar to getRotationTo, but this function maintains an up vector Intended for billboarding in omni

Typical use case for omni billboarding:

Vec3d forward = Vec3d(pose.pos() - src.pos()).normalize();
Quatd rot = Quatd::getBillboardRotation(forward, pose.uu());
g.rotate(rot);

Definition at line 1031 of file al_Quat.hpp.

◆ getRotationTo()

template<typename T >

Quat< T > al::Quat< T >::getRotationTo	(	const Vec< 3, T > &	usrc,
		const Vec< 3, T > &	udst
	)

static

Calculate the rotation required to move from unit vector src to unit vector dst NOTE: both arguments must be UNIT VECTORS (normalized) rotation occurs around the axis created by the cross product of src and dst if the vectors are nearly opposing, the Y axis is used instead if the Y axis isn't suitable, the Z axis is used instead

a typical use case: rotate object A to face object B:

Vec3d src = Vec3d(A.quat().toVectorZ()).normalize();
Vec3d dst = Vec3d(B.pos() - A.pos()).normalize();
Quatd rot = Quatd::getRotationTo(src, dst);
A.quat() = rot * A.quat();

Definition at line 985 of file al_Quat.hpp.

◆ normalize()

template<typename T >

Quat< T > & al::Quat< T >::normalize

inline

Normalize magnitude to one.

Implementation.

Definition at line 443 of file al_Quat.hpp.

◆ rotate()

template<typename T >

Vec< 3, T > al::Quat< T >::rotate ( const Vec< 3, T > & v ) const

inline

Rotate vector NOTE: quaternion should be normalized for accurate results.

Definition at line 841 of file al_Quat.hpp.

◆ rotor()

template<typename T >

Quat< T > al::Quat< T >::rotor	(	const Vec< 3, T > &	v1,
		const Vec< 3, T > &	v2
	)

static

Get rotor from two unit vectors.

Alternatively expressed as Q = (1+gp(v1, v2))/sqrt(2*(1+dot(b, a))).

Definition at line 1134 of file al_Quat.hpp.

◆ slerp()

template<typename T >

Quat< T > al::Quat< T >::slerp	(	const Quat< T > &	from,
		const Quat< T > &	to,
		T	amt
	)

static

Spherical linear interpolation of a quaternion.

Parameters

[in]	from	The quaternion to interpolate from
[in]	to	The quaternion to interpolate to
[in]	amt	The amount to interpolate, range [0, 1]

Returns: resulting interpolated quaternion

Definition at line 863 of file al_Quat.hpp.

◆ slerpBuffer()

template<typename T >

void al::Quat< T >::slerpBuffer	(	const Quat< T > &	from,
		const Quat< T > &	to,
		Quat< T > *	buffer,
		int	numFrames
	)

static

Fill an array of Quats with a full spherical interpolation.

Sinusoidal generator based on recursive formula x0 = c x1 - x2

Constructor

Generate next value.

< Multiplication factor. [-2, 2] range gives stable sinusoids.

Definition at line 913 of file al_Quat.hpp.

◆ towardPoint()

template<typename T >

void al::Quat< T >::towardPoint	(	const Vec< 3, T > &	pos,
		const Quat< T > &	q,
		const Vec< 3, T > &	v,
		float	amt
	)

Get the quaternion from a given point and quaterion toward another point.

Get the quaternion from a given point and quaterion toward another point

Definition at line 1088 of file al_Quat.hpp.

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

al_Quat.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

template<typename T = double> class al::Quat< T >

Constructor & Destructor Documentation

◆ Quat() [1/3]

◆ Quat() [2/3]

◆ Quat() [3/3]

Member Function Documentation

◆ fromMatrix() [1/2]

◆ fromMatrix() [2/2]

◆ getBillboardRotation()

◆ getRotationTo()

◆ normalize()

◆ rotate()

◆ rotor()

◆ slerp()

◆ slerpBuffer()

◆ towardPoint()

template<typename T = double>
class al::Quat< T >