Rotation stored as modified Rodrigues parameters. More...

Detailed Description

Rotation stored as modified Rodrigues parameters.

The storage space is (3).

One way to define this convention is that the three parameters are the values of the vector n tan(theta/4) where n is the rotation axis and theta the rotation angle.

Note this is different from the standard Rodrigues parameters, which are defined by n tan(theta/2)

#include <Rot.h>

Inheritance diagram for Rot:

[legend]

Public Member Functions
R2	euler_rodrigues () const
	Generate a rotation matrix using the Euler-Rodrigues formula.

R3	deuler_rodrigues () const
	d(R2)/d(r) – useful in constructing other derivatives

Rot	rotate (const Rot &r) const
	Rotate.

R2	drotate (const Rot &r) const
	Derivative of the rotated Rodrigues vector w.r.t. the other Rodrigues vector.

R2	drotate_self (const Rot &r) const
	Derivative of the rotated Rodrigues vector w.r.t. this vector.

Rot	shadow () const
	Return the shadow parameter set (a set of MRPs that define the same orientation)

R2	dshadow () const
	Return the derivative of the shadow map.

Scalar	dist (const Rot &r) const
	Distance measure between two rotations, accounting for shadow mapping.

Scalar	gdist (const Rot &r) const
	Raw distance formula, not accounting for shadown mapping.

Scalar	dV () const
	Volume element at locations.

Public Member Functions inherited from VecBase< Rot >
Rot	rotate (const Rot &r) const
	Rotate using a Rodrigues vector.

Rot	rotate (const R2 &R) const
	Rotate using a rotation matrix.

R2	drotate (const Rot &r) const
	Derivative of the rotated vector w.r.t. the Rodrigues vector.

R3	drotate (const R2 &R) const
	Derivative of the rotated vector w.r.t. the rotation matrix.

Public Member Functions inherited from PrimitiveTensor< Rot, 3 >
	PrimitiveTensor ()=default
	Special member functions.

	PrimitiveTensor (const ATensor &tensor, Size intmd_dim)
	Construct from an ATensor and infer dynamic shape.

	PrimitiveTensor (const ATensor &tensor, Size dynamic_dim, Size intmd_dim)
	Construct from an ATensor and extract dynamic shape given dynamic dimension.

	PrimitiveTensor (const ATensor &tensor, const TraceableTensorShape &dynamic_shape, Size intmd_dim)
	Construct from an ATensor given dynamic shape.

	PrimitiveTensor (const TensorBase< Derived2 > &tensor)
	Copy constructor.

	operator neml2::Tensor () const
	Implicit conversion to a Tensor (discards information on the fixed base shape)

Scalar	operator() (Args... i) const
	Single-element accessor.

Public Member Functions inherited from TensorBase< Rot >
	TensorBase ()=default
	Default constructor.

	TensorBase (const ATensor &tensor, Size dynamic_dim, Size intmd_dim)
	Construct from an ATensor with given dynamic dimension.

	TensorBase (const ATensor &tensor, TraceableTensorShape dynamic_shape, Size intmd_dim)
	Construct from an ATensor with given dynamic shape.

	TensorBase (const TensorBase< Derived2 > &tensor)
	Copy constructor.

	TensorBase (double)=delete

	TensorBase (float)=delete

	TensorBase (int)=delete

Rot	variable_data () const
	Variable data without function graph.

Rot	contiguous () const

Rot	clone () const
	Clone (take ownership)

Rot	detach () const
	Discard function graph.

Rot	to (const TensorOptions &options) const
	Change tensor options.

Rot	operator- () const
	Negation.

Size	batch_dim () const

Size	base_dim () const

Size	dynamic_dim () const

Size	static_dim () const

Size	intmd_dim () const

TraceableTensorShape	batch_sizes () const

TensorShapeRef	base_sizes () const

const TraceableTensorShape &	dynamic_sizes () const

TensorShapeRef	static_sizes () const

TensorShapeRef	intmd_sizes () const

TraceableSize	batch_size (Size i) const

Size	base_size (Size i) const

const TraceableSize &	dynamic_size (Size i) const

Size	static_size (Size i) const

Size	intmd_size (Size i) const

Rot	dynamic_index (indexing::TensorIndicesRef indices) const

Rot	intmd_index (indexing::TensorIndicesRef indices) const

neml2::Tensor	base_index (indexing::TensorIndicesRef indices) const

Rot	dynamic_slice (Size d, const indexing::Slice &index) const

Rot	intmd_slice (Size d, const indexing::Slice &index) const

neml2::Tensor	base_slice (Size d, const indexing::Slice &index) const

void	dynamic_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	dynamic_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

void	intmd_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	intmd_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

void	base_index_put_ (indexing::TensorIndicesRef indices, const ATensor &other)

void	base_index_put_ (indexing::TensorIndicesRef indices, const CScalar &v)

Rot	dynamic_expand (const TraceableTensorShape &shape) const

Rot	intmd_expand (TensorShapeRef shape) const

neml2::Tensor	base_expand (TensorShapeRef shape) const

Rot	batch_expand (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape) const

neml2::Tensor	static_expand (TensorShapeRef intmd_shape, TensorShapeRef base_shape) const

Rot	dynamic_expand (const TraceableSize &size, Size d) const

Rot	intmd_expand (Size size, Size d) const

neml2::Tensor	base_expand (Size size, Size d) const

Rot	dynamic_expand_as (const neml2::Tensor &other) const

Rot	intmd_expand_as (const neml2::Tensor &other) const

neml2::Tensor	base_expand_as (const neml2::Tensor &other) const

Rot	batch_expand_as (const neml2::Tensor &other) const

neml2::Tensor	static_expand_as (const neml2::Tensor &other) const

Rot	dynamic_reshape (const TraceableTensorShape &shape) const

Rot	intmd_reshape (TensorShapeRef shape) const

neml2::Tensor	base_reshape (TensorShapeRef shape) const

Rot	batch_reshape (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape) const

neml2::Tensor	static_reshape (TensorShapeRef intmd_shape, TensorShapeRef base_shape) const

Rot	dynamic_squeeze (Size d) const

Rot	intmd_squeeze (Size d) const

neml2::Tensor	base_squeeze (Size d) const

Rot	dynamic_unsqueeze (Size d, Size n=1) const

Rot	intmd_unsqueeze (Size d, Size n=1) const

neml2::Tensor	base_unsqueeze (Size d, Size n=1) const

Rot	dynamic_transpose (Size d1, Size d2) const

Rot	intmd_transpose (Size d1, Size d2) const

neml2::Tensor	base_transpose (Size d1, Size d2) const

Rot	dynamic_movedim (Size old_dim, Size new_dim) const

Rot	intmd_movedim (Size old_dim, Size new_dim) const

neml2::Tensor	base_movedim (Size old_dim, Size new_dim) const

Rot	dynamic_flatten () const

Rot	intmd_flatten () const

neml2::Tensor	base_flatten () const

Rot	batch_flatten () const
	Flatten batch dimensions.

neml2::Tensor	static_flatten () const
	Flatten static dimensions.

Static Public Member Functions
static Rot	identity (const TensorOptions &options=default_tensor_options())
	The identity rotation, helpfully the zero vector.

static Rot	fill_euler_angles (const Vec &v, const std::string &angle_convention, const std::string &angle_type)
	Fill from Euler angle.

static Rot	fill_matrix (const R2 &M)
	Fill from rotation matrix.

static Rot	fill_rodrigues (const Scalar &rx, const Scalar &ry, const Scalar &rz)
	Fill from standard Rodrigues parameters.

static Rot	rotation_from_to (const Vec &v1, const Vec &v2)
	Fill by forming the rotation between two vectors.

static Rot	axis_angle (const Vec &n, const Scalar &theta)
	Fill with axis/angle pairs.

static Rot	axis_angle_standard (const Vec &n, const Scalar &theta)
	Fill with axis/angle pairs as a standard Rodrigues parameter, then convert to MRP.


static Rot	rand (const TensorOptions &options=default_tensor_options())

static Rot	rand (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape, const TensorOptions &options=default_tensor_options())

Static Public Member Functions inherited from PrimitiveTensor< Rot, 3 >
static Rot	create (const TensorDataContainer &data, Size intmd_dim=0, const TensorOptions &options=default_tensor_options())
	Arbitrary tensor from a nested container with inferred batch dimension.

static Rot	einsum (c10::string_view equation, TensorList tensors)
	Einstein summation along base dimensions.

static Rot	empty (const TensorOptions &options=default_tensor_options())

static Rot	empty (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static Rot	zeros (const TensorOptions &options=default_tensor_options())

static Rot	zeros (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static Rot	ones (const TensorOptions &options=default_tensor_options())

static Rot	ones (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape={}, const TensorOptions &options=default_tensor_options())

static Rot	full (const CScalar &init, const TensorOptions &options=default_tensor_options())

static Rot	full (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape, const CScalar &init, const TensorOptions &options=default_tensor_options())

static Rot	rand (const TensorOptions &options=default_tensor_options())

static Rot	rand (const TraceableTensorShape &dynamic_shape, TensorShapeRef intmd_shape, const TensorOptions &options=default_tensor_options())

static Rot	fill (Args &&... args)

Static Public Member Functions inherited from TensorBase< Rot >
static Rot	empty_like (const Rot &other)

static Rot	zeros_like (const Rot &other)
	Zero tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static Rot	ones_like (const Rot &other)
	Unit tensor like another, i.e. same batch and base shapes, same tensor options, etc.

static Rot	full_like (const Rot &other, const CScalar &init)

static Rot	rand_like (const Rot &other)

Additional Inherited Members
Public Types inherited from PrimitiveTensor< Rot, 3 >
using	base_sizes_sequence
	Base shape sequence.

Static Public Attributes inherited from PrimitiveTensor< Rot, 3 >
static const TensorShape	const_base_sizes
	The base shape.

static constexpr Size	const_base_dim
	The base dim.

static constexpr Size	const_base_numel
	The base numel.

Protected Member Functions inherited from PrimitiveTensor< Rot, 3 >
void	validate_shapes_and_dims () const
	Validate shapes and dimensions.

Protected Member Functions inherited from TensorBase< Rot >
void	validate_shapes_and_dims () const
	Validate shapes and dimensions.

Member Function Documentation

◆ axis_angle()

Rot axis_angle	(	const Vec &	n,
		const Scalar &	theta )

staticnodiscard

Fill with axis/angle pairs.

◆ axis_angle_standard()

Rot axis_angle_standard	(	const Vec &	n,
		const Scalar &	theta )

staticnodiscard

Fill with axis/angle pairs as a standard Rodrigues parameter, then convert to MRP.

◆ deuler_rodrigues()

R3 deuler_rodrigues ( ) const

d(R2)/d(r) – useful in constructing other derivatives

◆ dist()

Scalar dist ( const Rot & r ) const

Distance measure between two rotations, accounting for shadow mapping.

◆ drotate()

R2 drotate ( const Rot & r ) const

Derivative of the rotated Rodrigues vector w.r.t. the other Rodrigues vector.

◆ drotate_self()

R2 drotate_self ( const Rot & r ) const

Derivative of the rotated Rodrigues vector w.r.t. this vector.

◆ dshadow()

R2 dshadow ( ) const

Return the derivative of the shadow map.

◆ dV()

Scalar dV ( ) const

Volume element at locations.

◆ euler_rodrigues()

R2 euler_rodrigues ( ) const

Generate a rotation matrix using the Euler-Rodrigues formula.

◆ fill_euler_angles()

Rot fill_euler_angles	(	const Vec &	v,
		const std::string &	angle_convention,
		const std::string &	angle_type )

staticnodiscard

Fill from Euler angle.

◆ fill_matrix()

Rot fill_matrix ( const R2 & M )

staticnodiscard

Fill from rotation matrix.

◆ fill_rodrigues()

Rot fill_rodrigues	(	const Scalar &	rx,
		const Scalar &	ry,
		const Scalar &	rz )

staticnodiscard

Fill from standard Rodrigues parameters.

◆ gdist()

Scalar gdist ( const Rot & r ) const

Raw distance formula, not accounting for shadown mapping.

◆ identity()

Rot identity ( const TensorOptions & options = default_tensor_options() )

staticnodiscard

The identity rotation, helpfully the zero vector.

◆ rand() [1/2]

Rot rand ( const TensorOptions & options = default_tensor_options() )

staticnodiscard

Fill random orientations following uniform distribution in SO(3)

◆ rand() [2/2]

Rot rand	(	const TraceableTensorShape &	dynamic_shape,
		TensorShapeRef	intmd_shape,
		const TensorOptions &	options = default_tensor_options() )

staticnodiscard

◆ rotate()

Rot rotate ( const Rot & r ) const

Rotate.

◆ rotation_from_to()

Rot rotation_from_to	(	const Vec &	v1,
		const Vec &	v2 )

staticnodiscard

Fill by forming the rotation between two vectors.

◆ shadow()

Rot shadow ( ) const

Return the shadow parameter set (a set of MRPs that define the same orientation)

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ axis_angle()

◆ axis_angle_standard()

◆ deuler_rodrigues()

◆ dist()

◆ drotate()

◆ drotate_self()

◆ dshadow()

◆ dV()

◆ euler_rodrigues()

◆ fill_euler_angles()

◆ fill_matrix()

◆ fill_rodrigues()

◆ gdist()

◆ identity()

◆ rand() [1/2]

◆ rand() [2/2]

◆ rotate()

◆ rotation_from_to()

◆ shadow()