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:

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Public Member Functions
	Rot (const Vec &v)

Rot	inverse () const
	Inversion.

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 >
Scalar	operator() (Size i) const
	Accessor.

Scalar	norm_sq () const
	Norm squared.

Scalar	norm () const
	Norm.

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 batch_dim)
	Construct from another ATensor given batch dimension.

	PrimitiveTensor (const ATensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another ATensor given batch shape.

	PrimitiveTensor (const Tensor &tensor)
	Copy constructor.

	PrimitiveTensor (const ATensor &tensor)
	Construct from another ATensor and infer batch dimension.

	operator Tensor () const
	Implicit conversion to a Tensor and loses information on the fixed base shape.

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

	TensorBase (const ATensor &tensor, Size batch_dim)
	Construct from another ATensor with given batch dimension.

	TensorBase (const ATensor &tensor, const TraceableTensorShape &batch_shape)
	Construct from another ATensor with given batch shape.

	TensorBase (const neml2::Tensor &tensor)
	Copy constructor.

	TensorBase (Real)=delete

Rot	variable_data () const

Rot	clone () const

Rot	detach () const
	Discard function graph.

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

Rot	operator- () const
	Negation.

bool	batched () const
	Whether the tensor is batched.

Size	batch_dim () const
	Return the number of batch dimensions.

Size	base_dim () const
	Return the number of base dimensions.

const TraceableTensorShape &	batch_sizes () const
	Return the batch size.

TraceableSize	batch_size (Size index) const
	Return the size of a batch axis.

TensorShapeRef	base_sizes () const
	Return the base size.

Size	base_size (Size index) const
	Return the size of a base axis.

Size	base_storage () const
	Return the flattened storage needed just for the base indices.

Rot	batch_index (indexing::TensorIndicesRef indices) const
	Get a tensor by slicing on the batch dimensions.

neml2::Tensor	base_index (indexing::TensorIndicesRef indices) const
	Get a tensor by slicing on the base dimensions.

Rot	batch_slice (Size dim, const indexing::Slice &index) const
	Get a tensor by slicing along a batch dimension.

neml2::Tensor	base_slice (Size dim, const indexing::Slice &index) const
	Get a tensor by slicing along a base dimension.

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

void	batch_index_put_ (indexing::TensorIndicesRef indices, Real v)

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

void	base_index_put_ (indexing::TensorIndicesRef indices, Real v)

Rot	batch_expand (const TraceableTensorShape &batch_shape) const

Rot	batch_expand (const TraceableSize &batch_size, Size dim) const
	Return a new view of the tensor with values broadcast along a given batch dimension.

neml2::Tensor	base_expand (TensorShapeRef base_shape) const
	Return a new view of the tensor with values broadcast along the base dimensions.

neml2::Tensor	base_expand (Size base_size, Size dim) const
	Return a new view of the tensor with values broadcast along a given base dimension.

Rot	batch_expand_as (const neml2::Tensor &other) const
	Expand the batch to have the same shape as another tensor.

neml2::Tensor	base_expand_as (const neml2::Tensor &other) const
	Expand the base to have the same shape as another tensor.

Rot	batch_expand_copy (const TraceableTensorShape &batch_shape) const
	Return a new tensor with values broadcast along the batch dimensions.

neml2::Tensor	base_expand_copy (TensorShapeRef base_shape) const
	Return a new tensor with values broadcast along the base dimensions.

Rot	batch_reshape (const TraceableTensorShape &batch_shape) const
	Reshape batch dimensions.

neml2::Tensor	base_reshape (TensorShapeRef base_shape) const
	Reshape base dimensions.

Rot	batch_unsqueeze (Size d) const
	Unsqueeze a batch dimension.

neml2::Tensor	base_unsqueeze (Size d) const
	Unsqueeze a base dimension.

Rot	batch_transpose (Size d1, Size d2) const
	Transpose two batch dimensions.

neml2::Tensor	base_transpose (Size d1, Size d2) const
	Transpose two base dimensions.

neml2::Tensor	base_flatten () const
	Flatten base 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 an array of Euler angles.

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

static Rot	fill_random (unsigned int n)
	Fill some number of random orientations.

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

Static Public Member Functions inherited from VecBase< Rot >
static Rot	fill (const Real &v1, const Real &v2, const Real &v3, const TensorOptions &options=default_tensor_options())

static Rot	fill (const Scalar &v1, const Scalar &v2, const Scalar &v3)

static R2	identity_map (const TensorOptions &options=default_tensor_options())
	The derivative of a vector with respect to itself.

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

static Rot	empty (const TensorOptions &options=default_tensor_options())
	Unbatched empty tensor.

static Rot	empty (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Empty tensor given batch shape.

static Rot	zeros (const TensorOptions &options=default_tensor_options())
	Unbatched zero tensor.

static Rot	zeros (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Zero tensor given batch shape.

static Rot	ones (const TensorOptions &options=default_tensor_options())
	Unbatched unit tensor.

static Rot	ones (const TraceableTensorShape &batch_shape, const TensorOptions &options=default_tensor_options())
	Unit tensor given batch shape.

static Rot	full (Real init, const TensorOptions &options=default_tensor_options())
	Unbatched tensor filled with a given value given base shape.

static Rot	full (const TraceableTensorShape &batch_shape, Real init, const TensorOptions &options=default_tensor_options())
	Full tensor given batch shape.

static Tensor	identity_map (const TensorOptions &)
	Derived tensor classes should define identity_map where appropriate.

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, Real init)

static Rot	linspace (const Rot &start, const Rot &end, Size nstep, Size dim=0)
	Create a new tensor by adding a new batch dimension with linear spacing between `start` and `end`.

static Rot	logspace (const Rot &start, const Rot &end, Size nstep, Size dim=0, Real base=10)
	log-space equivalent of the linspace named constructor

Additional Inherited Members
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 const Size	const_base_storage
	The base storage.

Constructor & Destructor Documentation

◆ Rot()

Rot ( const Vec & v )

Member Function Documentation

◆ 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 )

static

Fill from an array of Euler angles.

◆ fill_matrix()

Rot fill_matrix ( const R2 & M )

static

Fill from rotation matrices.

◆ fill_random()

Rot fill_random ( unsigned int n )

static

Fill some number of random orientations.

◆ fill_rodrigues()

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

static

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.

◆ inverse()

Rot inverse ( ) const

Inversion.

◆ rotate()

Rot rotate ( const Rot & r ) const

Rotate.

◆ 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

Constructor & Destructor Documentation

◆ Rot()

Member Function Documentation

◆ deuler_rodrigues()

◆ dist()

◆ drotate()

◆ drotate_self()

◆ dshadow()

◆ dV()

◆ euler_rodrigues()

◆ fill_euler_angles()

◆ fill_matrix()

◆ fill_random()

◆ fill_rodrigues()

◆ gdist()

◆ identity()

◆ inverse()

◆ rotate()

◆ shadow()