#include <ImathEuler.h>

Inheritance diagram for Euler< T >:

Public Member Functions
Constructors
All default to `ZYX` non-relative (ala Softimage 3D/Maya), where there is no argument to specify it. The Euler-from-matrix constructors assume that the matrix does not include shear or non-uniform scaling, but the constructors do not examine the matrix to verify this assumption. If necessary, you can adjust the matrix by calling the removeScalingAndShear() function, defined in ImathMatrixAlgo.h.
IMATH_HOSTDEVICE constexpr	Euler () IMATH_NOEXCEPT
	No initialization by default. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Euler (const Euler &) IMATH_NOEXCEPT
	Copy constructor. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Euler (Order p) IMATH_NOEXCEPT
	Construct from given Order. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Euler (const Vec3< T > &v, Order o=Default, InputLayout l=IJKLayout) IMATH_NOEXCEPT
	Construct from vector, order, layout. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Euler (T i, T j, T k, Order o=Default, InputLayout l=IJKLayout) IMATH_NOEXCEPT
	Construct from explicit axes, order, layout. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Euler (const Euler< T > &euler, Order newp) IMATH_NOEXCEPT
	Copy constructor with new Order. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Euler (const Matrix33< T > &, Order o=Default) IMATH_NOEXCEPT
	Construct from Matrix33. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Euler (const Matrix44< T > &, Order o=Default) IMATH_NOEXCEPT
	Construct from Matrix44. More...

IMATH_HOSTDEVICE	~Euler ()=default
	Destructor. More...

Set Value
IMATH_HOSTDEVICE void	setOrder (Order) IMATH_NOEXCEPT

IMATH_HOSTDEVICE void	setXYZVector (const Vec3< T > &) IMATH_NOEXCEPT

IMATH_HOSTDEVICE void	set (Axis initial, bool relative, bool parityEven, bool firstRepeats) IMATH_NOEXCEPT
	Set the value. More...

Assignments and Conversions
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Euler < T > &	operator= (const Euler< T > &) IMATH_NOEXCEPT
	Assignment. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Euler < T > &	operator= (const Vec3< T > &) IMATH_NOEXCEPT
	Assignment. More...

IMATH_HOSTDEVICE void	extract (const Matrix33< T > &) IMATH_NOEXCEPT
	Assign from Matrix33, assumed to be affine. More...

IMATH_HOSTDEVICE void	extract (const Matrix44< T > &) IMATH_NOEXCEPT
	Assign from Matrix44, assumed to be affine. More...

IMATH_HOSTDEVICE void	extract (const Quat< T > &) IMATH_NOEXCEPT
	Assign from Quaternion. More...

IMATH_HOSTDEVICE Matrix33< T >	toMatrix33 () const IMATH_NOEXCEPT
	Convert to Matrix33. More...

IMATH_HOSTDEVICE Matrix44< T >	toMatrix44 () const IMATH_NOEXCEPT
	Convert to Matrix44. More...

IMATH_HOSTDEVICE Quat< T >	toQuat () const IMATH_NOEXCEPT
	Convert to Quat. More...

IMATH_HOSTDEVICE Vec3< T >	toXYZVector () const IMATH_NOEXCEPT

Public Member Functions inherited from Vec3< T >
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T &	operator[] (int i) IMATH_NOEXCEPT
	Element access by index. More...

IMATH_HOSTDEVICE constexpr const T &	operator[] (int i) const IMATH_NOEXCEPT
	Element access by index. More...

IMATH_HOSTDEVICE	Vec3 () IMATH_NOEXCEPT
	Uninitialized by default. More...

IMATH_HOSTDEVICE constexpr	Vec3 (T a) IMATH_NOEXCEPT
	Initialize to a scalar `(a,a,a)` More...

IMATH_HOSTDEVICE constexpr	Vec3 (T a, T b, T c) IMATH_NOEXCEPT
	Initialize to given elements `(a,b,c)` More...

IMATH_HOSTDEVICE constexpr	Vec3 (const Vec3 &v) IMATH_NOEXCEPT
	Copy constructor. More...

template<class S >
IMATH_HOSTDEVICE constexpr	Vec3 (const Vec3< S > &v) IMATH_NOEXCEPT
	Construct from Vec3 of another base type. More...

template<class S >
IMATH_HOSTDEVICE constexpr	Vec3 (const Vec4< S > &v) IMATH_NOEXCEPT

template<class S >
IMATH_HOSTDEVICE IMATH_CONSTEXPR14	Vec3 (const Vec4< S > &v, InfException)

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator= (const Vec3 &v) IMATH_NOEXCEPT
	Assignment. More...

	~Vec3 () IMATH_NOEXCEPT=default
	Destructor. More...

template<typename V , IMATH_ENABLE_IF(has_xyz< V, T >::value) >
IMATH_HOSTDEVICE constexpr	Vec3 (const V &v) IMATH_NOEXCEPT

template<typename V , IMATH_ENABLE_IF(has_subscript< V, T, 3 >::value &&!has_xyz< V, T >::value) >
IMATH_HOSTDEVICE	Vec3 (const V &v)

template<typename V , IMATH_ENABLE_IF(has_xyz< V, T >::value) >
IMATH_HOSTDEVICE const Vec3 &	operator= (const V &v) IMATH_NOEXCEPT

template<typename V , IMATH_ENABLE_IF(has_subscript< V, T, 3 >::value &&!has_xyz< V, T >::value) >
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator= (const V &v)

template<class S >
IMATH_HOSTDEVICE void	setValue (S a, S b, S c) IMATH_NOEXCEPT
	Set the value. More...

template<class S >
IMATH_HOSTDEVICE void	setValue (const Vec3< S > &v) IMATH_NOEXCEPT
	Set the value. More...

template<class S >
IMATH_HOSTDEVICE void	getValue (S &a, S &b, S &c) const IMATH_NOEXCEPT
	Return the value in `a`, `b`, and `c` More...

template<class S >
IMATH_HOSTDEVICE void	getValue (Vec3< S > &v) const IMATH_NOEXCEPT
	Return the value in `v` More...

IMATH_HOSTDEVICE T *	getValue () IMATH_NOEXCEPT
	Return a raw pointer to the array of values. More...

IMATH_HOSTDEVICE const T *	getValue () const IMATH_NOEXCEPT
	Return a raw pointer to the array of values. More...

template<class S >
IMATH_HOSTDEVICE constexpr bool	operator== (const Vec3< S > &v) const IMATH_NOEXCEPT
	Equality. More...

template<class S >
IMATH_HOSTDEVICE constexpr bool	operator!= (const Vec3< S > &v) const IMATH_NOEXCEPT
	Inequality. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool	equalWithAbsError (const Vec3< T > &v, T e) const IMATH_NOEXCEPT

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool	equalWithRelError (const Vec3< T > &v, T e) const IMATH_NOEXCEPT

IMATH_HOSTDEVICE constexpr T	dot (const Vec3 &v) const IMATH_NOEXCEPT
	Dot product. More...

IMATH_HOSTDEVICE constexpr T	operator^ (const Vec3 &v) const IMATH_NOEXCEPT
	Dot product. More...

IMATH_HOSTDEVICE constexpr Vec3	cross (const Vec3 &v) const IMATH_NOEXCEPT
	Right-handed cross product. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator%= (const Vec3 &v) IMATH_NOEXCEPT
	Right-handed cross product. More...

IMATH_HOSTDEVICE constexpr Vec3	operator% (const Vec3 &v) const IMATH_NOEXCEPT
	Right-handed cross product. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator+= (const Vec3 &v) IMATH_NOEXCEPT
	Component-wise addition. More...

IMATH_HOSTDEVICE constexpr Vec3	operator+ (const Vec3 &v) const IMATH_NOEXCEPT
	Component-wise addition. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator-= (const Vec3 &v) IMATH_NOEXCEPT
	Component-wise subtraction. More...

IMATH_HOSTDEVICE constexpr Vec3	operator- (const Vec3 &v) const IMATH_NOEXCEPT
	Component-wise subtraction. More...

IMATH_HOSTDEVICE constexpr Vec3	operator- () const IMATH_NOEXCEPT
	Component-wise multiplication by -1. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	negate () IMATH_NOEXCEPT
	Component-wise multiplication by -1. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator*= (const Vec3 &v) IMATH_NOEXCEPT
	Component-wise multiplication. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator*= (T a) IMATH_NOEXCEPT
	Component-wise multiplication. More...

IMATH_HOSTDEVICE constexpr Vec3	operator* (const Vec3 &v) const IMATH_NOEXCEPT
	Component-wise multiplication. More...

IMATH_HOSTDEVICE constexpr Vec3	operator* (T a) const IMATH_NOEXCEPT
	Component-wise multiplication. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator/= (const Vec3 &v) IMATH_NOEXCEPT
	Component-wise division. More...

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Vec3 &	operator/= (T a) IMATH_NOEXCEPT
	Component-wise division. More...

IMATH_HOSTDEVICE constexpr Vec3	operator/ (const Vec3 &v) const IMATH_NOEXCEPT
	Component-wise division. More...

IMATH_HOSTDEVICE constexpr Vec3	operator/ (T a) const IMATH_NOEXCEPT
	Component-wise division. More...

IMATH_HOSTDEVICE T	length () const IMATH_NOEXCEPT
	Return the Euclidean norm. More...

IMATH_HOSTDEVICE constexpr T	length2 () const IMATH_NOEXCEPT

IMATH_HOSTDEVICE const Vec3 &	normalize () IMATH_NOEXCEPT
	Normalize in place. If length()==0, return a null vector. More...

const Vec3 &	normalizeExc ()
	Normalize in place. If length()==0, throw an exception. More...

IMATH_HOSTDEVICE const Vec3 &	normalizeNonNull () IMATH_NOEXCEPT

IMATH_HOSTDEVICE Vec3< T >	normalized () const IMATH_NOEXCEPT
	Return a normalized vector. Does not modify *this. More...

Vec3< T >	normalizedExc () const

IMATH_HOSTDEVICE Vec3< T >	normalizedNonNull () const IMATH_NOEXCEPT

Protected Attributes
bool	_frameStatic: 1
	relative or static rotations More...

bool	_initialRepeated: 1
	init axis repeated as last More...

bool	_parityEven: 1
	"parity of axis permutation" More...

Axis	_initialAxis: 2
	First axis of rotation. More...

Query
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Order	order () const IMATH_NOEXCEPT
	Return the order. More...

IMATH_HOSTDEVICE constexpr bool	frameStatic () const
	Return frameStatic. More...

IMATH_HOSTDEVICE constexpr bool	initialRepeated () const
	Return intialRepeated. More...

IMATH_HOSTDEVICE constexpr bool	parityEven () const
	Return partityEven. More...

IMATH_HOSTDEVICE constexpr Axis	initialAxis () const
	Return initialAxis. More...

IMATH_HOSTDEVICE void	angleOrder (int &i, int &j, int &k) const IMATH_NOEXCEPT
	Unpack angles from ijk form. More...

IMATH_HOSTDEVICE void	angleMapping (int &i, int &j, int &k) const IMATH_NOEXCEPT
	Determine mapping from xyz to ijk (reshuffle the xyz to match the order) More...

IMATH_HOSTDEVICE static constexpr bool	legal (Order) IMATH_NOEXCEPT
	Return whether the given value is a legal Order. More...

Utility Methods
Utility methods for getting continuous rotations. None of these methods change the orientation given by its inputs (or at least that is the intent).
IMATH_HOSTDEVICE void	makeNear (const Euler< T > &target) IMATH_NOEXCEPT

IMATH_HOSTDEVICE static IMATH_CONSTEXPR14 float	angleMod (T angle) IMATH_NOEXCEPT
	Convert an angle to its equivalent in [-PI, PI]. More...

static IMATH_HOSTDEVICE void	simpleXYZRotation (Vec3< T > &xyzRot, const Vec3< T > &targetXyzRot) IMATH_NOEXCEPT
	Adjust xyzRot so that its components differ from targetXyzRot by no more than +/-PI. More...

static IMATH_HOSTDEVICE void	nearestRotation (Vec3< T > &xyzRot, const Vec3< T > &targetXyzRot, Order order=XYZ) IMATH_NOEXCEPT

Additional Inherited Members
Public Types inherited from Vec3< T >
typedef T	BaseType

Static Public Member Functions inherited from Vec3< T >
IMATH_HOSTDEVICE static constexpr unsigned int	dimensions () IMATH_NOEXCEPT
	Return the number of dimensions, i.e. 3. More...

IMATH_HOSTDEVICE static constexpr T	baseTypeLowest () IMATH_NOEXCEPT
	Largest possible negative value. More...

IMATH_HOSTDEVICE static constexpr T	baseTypeMax () IMATH_NOEXCEPT
	Largest possible positive value. More...

IMATH_HOSTDEVICE static constexpr T	baseTypeSmallest () IMATH_NOEXCEPT
	Smallest possible positive value. More...

IMATH_HOSTDEVICE static constexpr T	baseTypeEpsilon () IMATH_NOEXCEPT
	Smallest possible e for which 1+e != 1. More...

Public Attributes inherited from Vec3< T >
T	x

T	y

T	z

Detailed Description

template<class T>
class Euler< T >

Template class Euler<T>

The Euler class represents euler angle orientations. The class inherits from Vec3 to it can be freely cast. The additional information is the euler priorities rep. This class is essentially a rip off of Ken Shoemake's GemsIV code. It has been modified minimally to make it more understandable, but hardly enough to make it easy to grok completely.

There are 24 possible combonations of Euler angle representations of which 12 are common in CG and you will probably only use 6 of these which in this scheme are the non-relative-non-repeating types.

The representations can be partitioned according to two criteria:

1) Are the angles measured relative to a set of fixed axis or relative to each other (the latter being what happens when rotation matrices are multiplied together and is almost ubiquitous in the cg community)

2) Is one of the rotations repeated (ala XYX rotation)

When you construct a given representation from scratch you must order the angles according to their priorities. So, the easiest is a softimage or aerospace (yaw/pitch/roll) ordering of ZYX.

float x_rot = 1;
float y_rot = 2;
float z_rot = 3;

Eulerf angles(z_rot, y_rot, x_rot, Eulerf::ZYX);

or:

Eulerf angles( V3f(z_rot,y_rot,z_rot), Eulerf::ZYX );

If instead, the order was YXZ for instance you would have to do this:

float x_rot = 1;
float y_rot = 2;
float z_rot = 3;

Eulerf angles(y_rot, x_rot, z_rot, Eulerf::YXZ);

or:

Eulerf angles( V3f(y_rot,x_rot,z_rot), Eulerf::YXZ );

Notice how the order you put the angles into the three slots should correspond to the enum (YXZ) ordering. The input angle vector is called the "ijk" vector – not an "xyz" vector. The ijk vector order is the same as the enum. If you treat the Euler as a Vec3 (which it inherts from) you will find the angles are ordered in the same way, i.e.:

V3f v = angles;
v.x == y_rot, v.y == x_rot, v.z == z_rot

If you just want the x, y, and z angles stored in a vector in that order, you can do this:

V3f v = angles.toXYZVector()
v.x == x_rot, v.y == y_rot, v.z == z_rot

If you want to set the Euler with an XYZVector use the optional layout argument:

Eulerf angles(x_rot, y_rot, z_rot, Eulerf::YXZ, Eulerf::XYZLayout);

This is the same as:

Eulerf angles(y_rot, x_rot, z_rot, Eulerf::YXZ);

Note that this won't do anything intelligent if you have a repeated axis in the euler angles (e.g. XYX)

If you need to use the "relative" versions of these, you will need to use the "r" enums.

The units of the rotation angles are assumed to be radians.

Definition at line 120 of file ImathEuler.h.

Constructor & Destructor Documentation

template<class T>

IMATH_HOSTDEVICE constexpr Euler< T >::Euler ( )

No initialization by default.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Euler< T >::Euler ( const Euler< T > & )

Copy constructor.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Euler< T >::Euler ( Order p )

Construct from given Order.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Euler< T >::Euler	(	const Vec3< T > &	v,
		Order	o = `Default`,
		InputLayout	l = `IJKLayout`
	)

Construct from vector, order, layout.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Euler< T >::Euler	(	T	i,
		T	j,
		T	k,
		Order	o = `Default`,
		InputLayout	l = `IJKLayout`
	)

Construct from explicit axes, order, layout.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Euler< T >::Euler	(	const Euler< T > &	euler,
		Order	newp
	)

Copy constructor with new Order.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Euler< T >::Euler	(	const Matrix33< T > &	,
		Order	o = `Default`
	)

Construct from Matrix33.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Euler< T >::Euler	(	const Matrix44< T > &	,
		Order	o = `Default`
	)

Construct from Matrix44.

template<class T>

IMATH_HOSTDEVICE Euler< T >::~Euler ( )

default

Destructor.

Member Function Documentation

template<class T>

IMATH_HOSTDEVICE void Euler< T >::angleMapping	(	int &	i,
		int &	j,
		int &	k
	)		const

Determine mapping from xyz to ijk (reshuffle the xyz to match the order)

template<class T>

IMATH_HOSTDEVICE static IMATH_CONSTEXPR14 float Euler< T >::angleMod ( T angle )

static

Convert an angle to its equivalent in [-PI, PI].

template<class T>

IMATH_HOSTDEVICE void Euler< T >::angleOrder	(	int &	i,
		int &	j,
		int &	k
	)		const

Unpack angles from ijk form.

template<class T>

IMATH_HOSTDEVICE void Euler< T >::extract ( const Matrix33< T > & )

Assign from Matrix33, assumed to be affine.

template<class T>

IMATH_HOSTDEVICE void Euler< T >::extract ( const Matrix44< T > & )

Assign from Matrix44, assumed to be affine.

template<class T>

IMATH_HOSTDEVICE void Euler< T >::extract ( const Quat< T > & )

Assign from Quaternion.

template<class T>

IMATH_HOSTDEVICE constexpr bool Euler< T >::frameStatic ( ) const

inline

Return frameStatic.

Definition at line 251 of file ImathEuler.h.

template<class T>

IMATH_HOSTDEVICE constexpr Axis Euler< T >::initialAxis ( ) const

inline

Return initialAxis.

Definition at line 260 of file ImathEuler.h.

template<class T>

IMATH_HOSTDEVICE constexpr bool Euler< T >::initialRepeated ( ) const

inline

Return intialRepeated.

Definition at line 254 of file ImathEuler.h.

template<class T>

IMATH_HOSTDEVICE static constexpr bool Euler< T >::legal ( Order )

static

Return whether the given value is a legal Order.

template<class T>

IMATH_HOSTDEVICE void Euler< T >::makeNear ( const Euler< T > & target )

Adjusts "this" Euler so that its components differ from target by as little as possible. This method might not make sense for Eulers with different order and it probably doesn't work for repeated axis and relative orderings (TODO).

template<class T>

static IMATH_HOSTDEVICE void Euler< T >::nearestRotation	(	Vec3< T > &	xyzRot,
		const Vec3< T > &	targetXyzRot,
		Order	order = `XYZ`
	)

static

Adjust xyzRot so that its components differ from targetXyzRot by as little as possible. Note that xyz here really means ijk, because the order must be provided.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Euler<T>& Euler< T >::operator= ( const Euler< T > & )

Assignment.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 const Euler<T>& Euler< T >::operator= ( const Vec3< T > & )

Assignment.

template<class T>

IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Order Euler< T >::order ( ) const

Return the order.

template<class T>

IMATH_HOSTDEVICE constexpr bool Euler< T >::parityEven ( ) const

inline

Return partityEven.

Definition at line 257 of file ImathEuler.h.

template<class T>

IMATH_HOSTDEVICE void Euler< T >::set	(	Axis	initial,
		bool	relative,
		bool	parityEven,
		bool	firstRepeats
	)

Set the value.

template<class T>

IMATH_HOSTDEVICE void Euler< T >::setOrder ( Order )

Set the order. This does NOT convert the angles, but it does reorder the input vector.

template<class T>

IMATH_HOSTDEVICE void Euler< T >::setXYZVector ( const Vec3< T > & )

Set the euler value: set the first angle to v[0], the second to v[1], the third to v[2].

template<class T>

static IMATH_HOSTDEVICE void Euler< T >::simpleXYZRotation	(	Vec3< T > &	xyzRot,
		const Vec3< T > &	targetXyzRot
	)

static

Adjust xyzRot so that its components differ from targetXyzRot by no more than +/-PI.

template<class T>

IMATH_HOSTDEVICE Matrix33<T> Euler< T >::toMatrix33 ( ) const

Convert to Matrix33.

template<class T>

IMATH_HOSTDEVICE Matrix44<T> Euler< T >::toMatrix44 ( ) const

Convert to Matrix44.

template<class T>

IMATH_HOSTDEVICE Quat<T> Euler< T >::toQuat ( ) const

Convert to Quat.

template<class T>

IMATH_HOSTDEVICE Vec3<T> Euler< T >::toXYZVector ( ) const

Reorder the angles so that the X rotation comes first, followed by the Y and Z in cases like XYX ordering, the repeated angle will be in the "z" component

Member Data Documentation

template<class T>

bool Euler< T >::_frameStatic

protected

relative or static rotations

Definition at line 350 of file ImathEuler.h.

template<class T>

Axis Euler< T >::_initialAxis

protected

First axis of rotation.

Definition at line 363 of file ImathEuler.h.

template<class T>

bool Euler< T >::_initialRepeated

protected

init axis repeated as last

Definition at line 353 of file ImathEuler.h.

template<class T>

bool Euler< T >::_parityEven

protected

"parity of axis permutation"

Definition at line 356 of file ImathEuler.h.

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

Imath/ImathEuler.h

Public Member Functions

Protected Attributes

Query

Utility Methods

Additional Inherited Members

Detailed Description

template<class T> class Euler< T >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class T>
class Euler< T >