#include <BLI_math_quaternion_types.hh>

Public Member Functions
	QuaternionBase ()=default

	QuaternionBase (const T &new_w, const T &new_x, const T &new_y, const T &new_z)

	QuaternionBase (const VecBase< T, 4 > &vec)

	QuaternionBase (const T &real, const VecBase< T, 3 > &imaginary)

	operator VecBase< T, 4 > () const

const VecBase< T, 3 > &	imaginary_part () const

VecBase< T, 3 > &	imaginary_part ()

QuaternionBase &	operator*= (const QuaternionBase &b)

uint64_t	hash () const

Quaternion
AngleRadianBase< T >	twist_angle (const Axis axis) const

QuaternionBase	twist (const Axis axis) const

QuaternionBase	swing (const Axis axis) const

QuaternionBase	wrapped_around (const QuaternionBase &reference) const

Static Public Member Functions
static QuaternionBase	identity ()

static QuaternionBase	zero ()

Public Attributes
T	w

T	x

T	y

T	z

Friends
QuaternionBase	operator* (const QuaternionBase &a, const QuaternionBase &b)

QuaternionBase	operator* (const QuaternionBase &a, const T &b)

QuaternionBase	operator- (const QuaternionBase &a)

std::ostream &	operator<< (std::ostream &stream, const QuaternionBase &rot)

Conversion from/to Expmap
VecBase< T, 3 >	expmap () const

static QuaternionBase	expmap (const VecBase< T, 3 > &expmap)

Detailed Description

template<typename T>
struct blender::math::QuaternionBase< T >

A blender::math::QuaternionBase<T> represents either an orientation or a rotation.

Mainly used for rigging and armature deformations as they have nice mathematical properties (eg: smooth shortest path interpolation). A blender::math::QuaternionBase<T> is cheaper to combine than MatBase<T, 3, 3>. However, transforming points is slower. Consider converting to a rotation matrix if you are rotating many points.

See this for more information: https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Performance_comparisons

Definition at line 37 of file BLI_math_quaternion_types.hh.

Constructor & Destructor Documentation

◆ QuaternionBase() [1/4]

template<typename T >

blender::math::QuaternionBase< T >::QuaternionBase ( )

default

◆ QuaternionBase() [2/4]

template<typename T >

blender::math::QuaternionBase< T >::QuaternionBase	(	const T &	new_w,
		const T &	new_x,
		const T &	new_y,
		const T &	new_z )

inline

Definition at line 42 of file BLI_math_quaternion_types.hh.

◆ QuaternionBase() [3/4]

template<typename T >

blender::math::QuaternionBase< T >::QuaternionBase ( const VecBase< T, 4 > & vec )

inlineexplicit

Creates a quaternion from an vector without reordering the components.

Note: Component order must follow the scalar constructor (w, x, y, z).

Definition at line 49 of file BLI_math_quaternion_types.hh.

◆ QuaternionBase() [4/4]

template<typename T >

blender::math::QuaternionBase< T >::QuaternionBase	(	const T &	real,
		const VecBase< T, 3 > &	imaginary )

inline

Creates a quaternion from real (w) and imaginary parts (x, y, z).

Definition at line 54 of file BLI_math_quaternion_types.hh.

Member Function Documentation

◆ expmap() [1/2]

template<typename T >

VecBase< T, 3 > blender::math::QuaternionBase< T >::expmap ( ) const

Create an exponential map representation of this quaternion. An exponential map is basically the rotation axis multiplied by the rotation angle.

Definition at line 692 of file BLI_math_quaternion.hh.

References BLI_assert, blender::math::is_unit_scale(), and blender::math::to_axis_angle().

Referenced by blender::bke::attribute_math::DefaultMixerStruct< math::Quaternion >::expmap_to_quat(), blender::bke::attribute_math::float4x4Mixer::finalize(), blender::bke::attribute_math::mix3(), blender::bke::attribute_math::mix4(), and blender::tests::TEST().

◆ expmap() [2/2]

template<typename T >

QuaternionBase< T > blender::math::QuaternionBase< T >::expmap ( const VecBase< T, 3 > & expmap )

static

Create a quaternion from an exponential map representation. An exponential map is basically the rotation axis multiplied by the rotation angle.

Definition at line 680 of file BLI_math_quaternion.hh.

References angle(), LIKELY, blender::math::normalize_and_get_length(), T, and blender::math::to_quaternion().

Referenced by blender::bke::attribute_math::mix3(), and blender::bke::attribute_math::mix4().

◆ hash()

template<typename T >

uint64_t blender::math::QuaternionBase< T >::hash ( ) const

inline

Definition at line 163 of file BLI_math_quaternion_types.hh.

◆ identity()

template<typename T >

static QuaternionBase blender::math::QuaternionBase< T >::identity ( )

inlinestatic

Static functions.

Definition at line 59 of file BLI_math_quaternion_types.hh.

Referenced by blender::nodes::node_fn_axes_to_rotation_cc::AxesToRotationFunction::call(), blender::math::from_vector(), blender::math::invert(), make_socket_type_rotation(), blender::nodes::node_fn_axis_angle_to_rotation_cc::node_build_multi_function(), blender::nodes::node_fn_rotation_to_axis_angle_cc::node_eval_inverse(), blender::nodes::node_geo_bounding_box_cc::node_geo_exec(), blender::math::normalize_and_get_length(), blender::math::detail::normalized_to_quat_with_checks(), blender::draw::overlay::LightProbes::object_sync(), blender::io::usd::USDPointInstancerReader::read_object_data(), blender::imbuf::tests::TEST(), blender::math::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::draw::test_eevee_shadow_tag_update(), and blender::math::to_quaternion().

◆ imaginary_part() [1/2]

template<typename T >

VecBase< T, 3 > & blender::math::QuaternionBase< T >::imaginary_part ( )

inline

Definition at line 115 of file BLI_math_quaternion_types.hh.

References blender::math::QuaternionBase< T >::x.

◆ imaginary_part() [2/2]

template<typename T >

const VecBase< T, 3 > & blender::math::QuaternionBase< T >::imaginary_part ( ) const

inline

Returns the imaginary part of this quaternion (x, y, z).

Definition at line 111 of file BLI_math_quaternion_types.hh.

References blender::math::QuaternionBase< T >::x.

Referenced by blender::math::pow().

◆ operator VecBase< T, 4 >()

template<typename T >

blender::math::QuaternionBase< T >::operator VecBase< T, 4 > ( ) const

inlineexplicit

Conversions.

Definition at line 78 of file BLI_math_quaternion_types.hh.

References blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, and blender::math::QuaternionBase< T >::y.

◆ operator*=()

template<typename T >

QuaternionBase & blender::math::QuaternionBase< T >::operator*= ( const QuaternionBase< T > & b )

inline

Definition at line 143 of file BLI_math_quaternion_types.hh.

References b.

◆ swing()

template<typename T >

QuaternionBase< T > blender::math::QuaternionBase< T >::swing ( const Axis axis ) const

Returns the swing part of this quaternion for the basis axis direction. The swing is the original quaternion minus the twist around axis. So we have the following identity : q = q.swing(axis) * q.twist(axis)

Definition at line 149 of file BLI_math_quaternion.hh.

References blender::math::abs(), BLI_assert, blender::math::canonicalize(), and blender::math::invert_normalized().

Referenced by blender::tests::TEST().

◆ twist()

template<typename T >

QuaternionBase< T > blender::math::QuaternionBase< T >::twist ( const Axis axis ) const

Returns the twist part of this quaternion for the axis direction. The twist is the isolated rotation in the plane whose axis is normal to.

Definition at line 161 of file BLI_math_quaternion.hh.

References blender::math::canonicalize(), blender::math::AngleCartesianBase< T >::cos(), blender::math::AngleCartesianBase< T >::from_point(), blender::math::AngleCartesianBase< T >::sin(), T, and blender::VecBase< T, Size >::yzw().

Referenced by blender::tests::TEST().

◆ twist_angle()

template<typename T >

AngleRadianBase< T > blender::math::QuaternionBase< T >::twist_angle ( const Axis axis ) const

Returns the full twist angle for a given axis direction. The twist is the isolated rotation in the plane whose axis is normal to.

Definition at line 141 of file BLI_math_quaternion.hh.

References blender::math::canonicalize(), T, and blender::VecBase< T, Size >::yzw().

Referenced by blender::tests::TEST().

◆ wrapped_around()

template<typename T >

QuaternionBase< T > blender::math::QuaternionBase< T >::wrapped_around ( const QuaternionBase< T > & reference ) const

Methods. Return this quaternions orientation but wrapped around reference.

This means the interpolation between the returned value and reference will always take the shortest path. The angle between them will not be more than pi.