iganet::UniformNurbsCore< real_t, GeoDim, Degrees > Class Template Reference

Tensor-product non-uniform rational B-spline with uniform knot vector (core functionality) More...

#include </home/runner/work/iganet/iganet/include/splines/nurbs.hpp>

Inheritance diagram for iganet::UniformNurbsCore< real_t, GeoDim, Degrees >:

Public Types
template<typename other_t , short_t GeoDim_, short_t... Degrees_>
using	derived_self_type = UniformNurbsCore< other_t, GeoDim_, Degrees_... >
	Deduces the derived self-type when exposed to different class template parameters real_t and GeoDim, and the Degrees parameter pack.
template<template< typename, short_t, short_t... > class BSpline, std::make_signed_t< short_t > degree_elevate = 0>
using	derived_type = BSpline< real_t, GeoDim+1,(Degrees+degree_elevate)... >
	Deduces the type of the template parameter BSpline when exposed to the class template parameters real_t and GeoDim, and the Degrees parameter pack. The optional template parameter degree_elevate can be used to (de-)elevate the degrees by an additive constant.
template<typename other_t >
using	real_derived_self_type = UniformNurbsCore< other_t, GeoDim, Degrees... >
	Deduces the derived self-type when exposed to a different class template parameter real_t
template<std::make_signed_t< short_t > degree_elevate = 0>
using	self_type = Base::template derived_type< UniformNurbsCore, degree_elevate >
	Deduces the self-type possibly degrees (de-)elevated by the additive constant degree_elevate
using	value_type = real_t
	Value type.
Public Types inherited from iganet::UniformBSplineCore< real_t, GeoDim+1, Degrees... >
using	derived_self_type = UniformBSplineCore< other_t, GeoDim_, Degrees_... >
	Deduces the derived self-type when exposed to different class template parameters real_t and GeoDim, and the Degrees parameter pack.
using	derived_type = BSpline< real_t, GeoDim,(Degrees+degree_elevate)... >
	Deduces the type of the template parameter BSpline when exposed to the class template parameters real_t and GeoDim, and the Degrees parameter pack. The optional template parameter degree_elevate can be used to (de-)elevate the degrees by an additive constant.
using	real_derived_self_type = UniformBSplineCore< other_t, GeoDim, Degrees... >
	Deduces the derived self-type when exposed to a different class template parameter real_t
using	self_type = derived_type< UniformBSplineCore, degree_elevate >
	Deduces the self-type possibly degrees (de-)elevated by the additive constant degree_elevate
using	value_type = real_t
	Value type.

Public Member Functions
	UniformNurbsCore (const std::array< int64_t, Base::parDim_ > &ncoeffs, const utils::TensorArray< Base::geoDim_ > &coeffs, bool clone=false, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.
	UniformNurbsCore (const std::array< int64_t, Base::parDim_ > &ncoeffs, enum init init=init::greville, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.
	UniformNurbsCore (const std::array< int64_t, Base::parDim_ > &ncoeffs, utils::TensorArray< Base::geoDim_ > &&coeffs, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.
template<typename other_t >
	UniformNurbsCore (const UniformNurbsCore< other_t, GeoDim+1, Degrees... > &other, Options< real_t > options=Options< real_t >{})
	Copy constructor.
	UniformNurbsCore (Options< real_t > options=Options< real_t >{})
	Default constructor.
const torch::Tensor &	weights () const noexcept
	Returns a constant reference to the weights.
torch::Tensor &	weights () noexcept
	Returns a non-constant reference to the weights.
Public Member Functions inherited from iganet::UniformBSplineCore< real_t, GeoDim+1, Degrees... >
	UniformBSplineCore (const std::array< int64_t, parDim_ > &ncoeffs, const utils::TensorArray< geoDim_ > &coeffs, bool clone=false, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.
	UniformBSplineCore (const std::array< int64_t, parDim_ > &ncoeffs, enum init init=init::greville, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.
	UniformBSplineCore (const std::array< int64_t, parDim_ > &ncoeffs, utils::TensorArray< geoDim_ > &&coeffs, Options< real_t > options=Options< real_t >{})
	Constructor for equidistant knot vectors.
	UniformBSplineCore (const UniformBSplineCore< other_t, GeoDim, Degrees... > &other, Options< real_t > options=Options< real_t >{})
	Copy constructor.
	UniformBSplineCore (Options< real_t > options=Options< real_t >{})
	Default constructor.
	~UniformBSplineCore () override=default
	Destructor.
torch::Tensor	as_tensor () const noexcept override
	Returns all coefficients as a single tensor.
int64_t	as_tensor_size () const noexcept override
	Returns the size of the single tensor representation of all coefficients.
const utils::TensorArray< geoDim_ > &	coeffs () const noexcept
	Returns a constant reference to the array of coefficient vectors.
utils::TensorArray< geoDim_ > &	coeffs () noexcept
	Returns a non-constant reference to the array of coefficient vectors.
const torch::Tensor &	coeffs (short_t i) const noexcept
	Returns a constant reference to the coefficient vector in the \(i\)-th dimension.
torch::Tensor &	coeffs (short_t i) noexcept
	Returns a non-constant reference to the coefficient vector in the \(i\)-th dimension.
nlohmann::json	coeffs_to_json () const
	Returns the B-spline object's coefficients as JSON object.
utils::TensorArray< geoDim_ >	coeffs_view () const noexcept
	Returns an array of views to the coefficient vectors.
const auto	coeffs_view (short_t i) const noexcept
	Returns a view to the coefficient vector in the \(i\)-th dimension.
torch::Device	device () const noexcept override
	Returns the device property.
int32_t	device_index () const noexcept override
	Returns the device_index property.
torch::Dtype	dtype () const noexcept override
	Returns the dtype property.
auto	eval (const utils::TensorArray< parDim_ > &xi, const utils::TensorArray< parDim_ > &knot_indices) const
	Returns the value of the univariate B-spline object in the points xi
auto	eval (const utils::TensorArray< parDim_ > &xi, const utils::TensorArray< parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
	Returns the value of the univariate B-spline object in the points xi
auto	eval_tr (const utils::TensorArray< parDim_ > &xi, const utils::TensorArray< parDim_ > &knot_indices) const
auto	eval_tr (const utils::TensorArray< parDim_ > &xi, const utils::TensorArray< parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const
auto &	from_gismo (BSpline &bspline, bool, bool)
UniformBSplineCore &	from_json (const nlohmann::json &json)
	Updates the B-spline object from JSON object.
UniformBSplineCore &	from_tensor (const torch::Tensor &tensor) noexcept override
	Sets all coefficients from a single tensor.
UniformBSplineCore &	from_xml (const pugi::xml_document &doc, int id=0, const std::string &label="", int index=-1)
	Updates the B-spline object from XML object.
UniformBSplineCore &	from_xml (const pugi::xml_node &root, int id=0, const std::string &label="", int index=-1)
	Updates the B-spline object from XML node.
auto	greville (bool interior=false) const
	Returns the Greville abscissae.
void	init_coeffs (enum init init)
	Initializes the B-spline coefficients.
void	init_knots ()
	Initializes the B-spline knots.
bool	is_sparse () const noexcept override
	Returns true if the layout is sparse.
bool	isclose (const UniformBSplineCore< other_t, GeoDim_, Degrees_... > &other, real_t rtol=real_t{1e-5}, real_t atol=real_t{1e-8}) const
	Returns true if both B-spline objects are close up to the given tolerances.
const utils::TensorArray< parDim_ > &	knots () const noexcept
	Returns a constant reference to the array of knot vectors.
utils::TensorArray< parDim_ > &	knots () noexcept
	Returns a non-constant reference to the array of knot vectors.
const torch::Tensor &	knots (short_t i) const noexcept
	Returns a constant reference to the knot vector in the \(i\)-th dimension.
torch::Tensor &	knots (short_t i) noexcept
	Returns a non-constant reference to the knot vector in the \(i\)-th dimension.
nlohmann::json	knots_to_json () const
	Returns the B-spline object's knots as JSON object.
torch::Layout	layout () const noexcept override
	Returns the layout property.
void	load (const std::string &filename, const std::string &key="bspline")
	Loads the B-spline from file.
const std::array< int64_t, parDim_ > &	ncoeffs () const noexcept
	Returns a constant reference to the array of coefficient vector dimensions.
int64_t	ncoeffs (short_t i) const noexcept
	Returns the total number of coefficients in the \(i\)-th direction.
int64_t	ncumcoeffs () const noexcept
	Returns the total number of coefficients.
const std::array< int64_t, parDim_ > &	nknots () const noexcept
	Returns a constant reference to the array of knot vector dimensions.
int64_t	nknots (short_t i) const noexcept
	Returns the dimension of the knot vector in the \(i\)-th dimension.
bool	operator!= (const UniformBSplineCore< other_t, GeoDim_, Degrees_... > &other) const
	Returns true if both B-spline objects are different.
bool	operator== (const UniformBSplineCore< other_t, GeoDim_, Degrees_... > &other) const
	Returns true if both B-spline objects are the same.
const Options< real_t > &	options () const noexcept
	Returns a constant reference to the B-spline object's options.
bool	pinned_memory () const noexcept override
	Returns the pinned_memory property.
torch::serialize::InputArchive &	read (torch::serialize::InputArchive &archive, const std::string &key="bspline")
	Reads the B-spline from a torch::serialize::InputArchive object.
bool	requires_grad () const noexcept override
	Returns the requires_grad property.
void	save (const std::string &filename, const std::string &key="bspline") const
	Saves the B-spline to file.
UniformBSplineCore &	set_requires_grad (bool requires_grad) noexcept override
	Sets the B-spline object's requires_grad property.
auto	to_gismo () const
	Converts the B-spline object into a gsBSpline object of the parametric dimension is one and a gsTensorBSpline object otherwise.
BSpline &	to_gismo (BSpline &bspline, bool, bool) const
nlohmann::json	to_json () const override
	Returns the B-spline object as JSON object.
pugi::xml_document	to_xml (int id=0, const std::string &label="", int index=-1) const
	Returns the B-spline object as XML object.
pugi::xml_node &	to_xml (pugi::xml_node &root, int id=0, const std::string &label="", int index=-1) const
	Returns the B-spline object as XML node.
UniformBSplineCore &	transform (const std::function< std::array< real_t, geoDim_ >(const std::array< real_t, parDim_ > &)> mapping)
	Transforms the coefficients based on the given mapping.
UniformBSplineCore &	transform (const std::function< std::array< real_t, N >(const std::array< real_t, parDim_ > &)> mapping, std::array< short_t, N > dims)
	Transforms the coefficients based on the given mapping.
UniformBSplineCore &	uniform_refine (int numRefine=1, int dim=-1)
	Returns the B-spline object with uniformly refined knot and coefficient vectors.
torch::serialize::OutputArchive &	write (torch::serialize::OutputArchive &archive, const std::string &key="bspline") const
	Writes the B-spline into a torch::serialize::OutputArchive object.
Public Member Functions inherited from iganet::utils::Serializable
virtual	~Serializable ()=default
	Destructor.
virtual void	pretty_print (std::ostream &os=Log(log::info)) const =0
	Returns a string representation of the object.
Public Member Functions inherited from iganet::BSplinePatch< real_t, GeoDim, sizeof...(Degrees)>
virtual	~BSplinePatch ()=default
	Destructor.
virtual void	pretty_print (std::ostream &os=Log(log::info)) const noexcept=0
	Returns a string representation.

Static Public Member Functions
static constexpr short_t	geoDim () noexcept
static constexpr bool	is_nonuniform ()
	Returns true if the B-spline is non-uniform.
static constexpr bool	is_uniform ()
	Returns true if the B-spline is uniform.
Static Public Member Functions inherited from iganet::UniformBSplineCore< real_t, GeoDim+1, Degrees... >
static constexpr short_t	degree (short_t i) noexcept
	Returns a constant reference to the degree in the \(i\)-th dimension.
static constexpr const std::array< short_t, parDim_ > &	degrees () noexcept
	Returns a constant reference to the array of degrees.
static constexpr short_t	geoDim () noexcept
	Returns the geometric dimension.
static constexpr bool	is_nonuniform () noexcept
	Returns true if the B-spline is non-uniform.
static constexpr bool	is_uniform () noexcept
	Returns true if the B-spline is uniform.
static constexpr short_t	parDim () noexcept
	Returns the parametric dimension.

Private Types
using	Base = UniformBSplineCore< real_t, GeoDim+1, Degrees... >
	Base type.

Additional Inherited Members
Protected Member Functions inherited from iganet::UniformBSplineCore< real_t, GeoDim+1, Degrees... >
auto	eval_basfunc_univariate (const torch::Tensor &xi, const torch::Tensor &knot_indices) const
	Returns the vector of univariate B-spline basis functions (or their derivatives) evaluated in the point xi
auto	eval_basfunc_univariate_tr (const torch::Tensor &xi, const torch::Tensor &knot_indices) const
void	update_coeffs (const utils::TensorArray< parDim_ > &knots, const utils::TensorArray< parDim_ > &knot_indices)
	Updates the B-spline coefficients after knot insertion.
auto	update_coeffs_univariate (const torch::Tensor &knots, const torch::Tensor &knot_indices) const
	Returns the knot insertion matrix.
Protected Attributes inherited from iganet::UniformBSplineCore< real_t, GeoDim+1, Degrees... >
utils::TensorArray< geoDim_ >	coeffs_
	Array storing the coefficients of the control net \(\left(\mathbf{c}_{i_d}\right)_{i_d=1}^{n_d}\), \(\mathbf{c}_{i_d}\in\mathbb{R}^{d_\text{geo}}\).
utils::TensorArray< parDim_ >	knots_
	Array storing the knot vectors \(\left(\left(t_{i_d}\right)_{i_d=1}^{n_d+p_d+1}\right)_{d=1}^{d_\text{par}}\).
std::array< int64_t, parDim_ >	ncoeffs_
	Array storing the sizes of the coefficients of the control net \(\left(n_d\right)_{d=1}^{d_\text{par}}\).
std::array< int64_t, parDim_ >	ncoeffs_reverse_
	Array storing the sizes of the coefficients of the control net \(\left(n_d\right)_{d=1}^{d_\text{par}}\) in reverse order (needed for coeffs_view)
std::array< int64_t, parDim_ >	nknots_
	Array storing the sizes of the knot vectors \(\left(n_d+p_d+1\right)_{d=1}^{d_\text{par}}\).
Options< real_t >	options_
	Options.
Static Protected Attributes inherited from iganet::UniformBSplineCore< real_t, GeoDim+1, Degrees... >
static constexpr const std::array< short_t, parDim_ >	degrees_
	Array storing the degrees \(\left(p_d\right)_{d=1}^{d_\text{par}}\).
static constexpr const short_t	geoDim_
	Dimension of the geometric space \(\Omega\subset\mathbb{R}^{d_\text{geo}}\).
static constexpr const short_t	parDim_
	Dimension of the parametric space \(\hat\Omega=[0,1]^{d_\text{par}}\).

Detailed Description

template<typename real_t, short_t GeoDim, short_t... Degrees>
class iganet::UniformNurbsCore< real_t, GeoDim, Degrees >

Tensor-product non-uniform rational B-spline with uniform knot vector (core functionality)

This class extends the base class UniformBSplineCore to non-uniform rational B-splines (NURBS) with uniform knot vectors. Like its base class it only implements the core functionality of non-uniform rational B-splines.

This implementation exploits the fact that NURBS in \(d\) space dimensions can be realized through perspective projection from B-splines in \(d+1\) space dimensions. That is, a NURBS object with control points

\[ \mathbf{c}_i = \left(x_i, y_i, z_i\right) \]

is extended to a B-spline object with homogeneous coordinates

\[ \mathbf{c}_i = \left(w_i x_i, w_i y_i, w_i z_i, w_i\right) \]

with non-negative weights \(w_i\). All operations are performed on the B-spline object which is afterward converted to a NURBS object through perspective projection onto the coordinates \(\left(x/w, y/w, z/w\right)\).

Member Typedef Documentation

Base

template<typename real_t , short_t GeoDim, short_t... Degrees>

using iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::Base = UniformBSplineCore<real_t, GeoDim + 1, Degrees...>

private

Base type.

derived_self_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t , short_t GeoDim_, short_t... Degrees_>

using iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::derived_self_type = UniformNurbsCore<other_t, GeoDim_, Degrees_...>

Deduces the derived self-type when exposed to different class template parameters real_t and GeoDim, and the Degrees parameter pack.

derived_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<template< typename, short_t, short_t... > class BSpline, std::make_signed_t< short_t > degree_elevate = 0>

using iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::derived_type = BSpline<real_t, GeoDim + 1, (Degrees + degree_elevate)...>

Deduces the type of the template parameter BSpline when exposed to the class template parameters real_t and GeoDim, and the Degrees parameter pack. The optional template parameter degree_elevate can be used to (de-)elevate the degrees by an additive constant.

real_derived_self_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t >

using iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::real_derived_self_type = UniformNurbsCore<other_t, GeoDim, Degrees...>

Deduces the derived self-type when exposed to a different class template parameter real_t

self_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<std::make_signed_t< short_t > degree_elevate = 0>

using iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::self_type = Base::template derived_type<UniformNurbsCore, degree_elevate>

Deduces the self-type possibly degrees (de-)elevated by the additive constant degree_elevate

value_type

template<typename real_t , short_t GeoDim, short_t... Degrees>

using iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::value_type = real_t

Value type.

Constructor & Destructor Documentation

UniformNurbsCore() [1/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::UniformNurbsCore ( Options< real_t >  options = Options<real_t>{} )

inlineexplicit

Default constructor.

Parameters

[in]

options

Options configuration

UniformNurbsCore() [2/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::UniformNurbsCore ( const std::array< int64_t, Base::parDim_ > &  ncoeffs, enum init  init = init::greville, Options< real_t >  options = Options<real_t>{}  )

inlineexplicit

Constructor for equidistant knot vectors.

Parameters

[in]	ncoeffs	Number of coefficients per parametric dimension
[in]	init	Type of initialization
[in]	options	Options configuration

UniformNurbsCore() [3/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::UniformNurbsCore ( const std::array< int64_t, Base::parDim_ > &  ncoeffs, const utils::TensorArray< Base::geoDim_ > &  coeffs, bool  clone = false, Options< real_t >  options = Options<real_t>{}  )

inline

Constructor for equidistant knot vectors.

Parameters

[in]	ncoeffs	Number of coefficients per parametric dimension
[in]	coeffs	Vectors of coefficients per parametric dimension
[in]	clone	If true, coefficients will be cloned. Otherwise, coefficients will be aliased
[in]	options	Options configuration

Note

It is not checked whether vectors of coefficients are compatible with the given Options object if clone is false.

UniformNurbsCore() [4/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::UniformNurbsCore ( const std::array< int64_t, Base::parDim_ > &  ncoeffs, utils::TensorArray< Base::geoDim_ > &&  coeffs, Options< real_t >  options = Options<real_t>{}  )

inline

Constructor for equidistant knot vectors.

Parameters

[in]	ncoeffs	Number of coefficients per parametric dimension
[in]	coeffs	Vectors of coefficients per parametric dimension
[in]	options	Options configuration

Note

It is not checked whether vectors of coefficients are compatible with the given Options object if clone is false.

UniformNurbsCore() [5/5]

template<typename real_t , short_t GeoDim, short_t... Degrees>

template<typename other_t >

iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::UniformNurbsCore ( const UniformNurbsCore< other_t, GeoDim+1, Degrees... > &  other, Options< real_t >  options = Options<real_t>{}  )

inlineexplicit

Copy constructor.

Parameters

[in]	other	Uniform Nurbs object to copy
[in]	options	Options configuration

Member Function Documentation

geoDim()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr short_t iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::geoDim ( )

inlinestaticconstexprnoexcept

Returns

Number of geometric dimensions

Note

This override of the geoDim() function makes sure that the geometric dimension is reported correctly with respect to the NURBS object

is_nonuniform()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr bool iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::is_nonuniform ( )

inlinestaticconstexpr

Returns true if the B-spline is non-uniform.

is_uniform()

template<typename real_t , short_t GeoDim, short_t... Degrees>

static constexpr bool iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::is_uniform ( )

inlinestaticconstexpr

Returns true if the B-spline is uniform.

weights() [1/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

const torch::Tensor & iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::weights ( ) const

inlinenoexcept

Returns a constant reference to the weights.

Note

Since the weights are the entry of the homogeneous coordinates which are stored in coeff one can likewise retrieve them using coeffs(GeoDim)

weights() [2/2]

template<typename real_t , short_t GeoDim, short_t... Degrees>

torch::Tensor & iganet::UniformNurbsCore< real_t, GeoDim, Degrees >::weights ( )

inlinenoexcept

Returns a non-constant reference to the weights.

Note

Since the weights are the entry of the homogeneous coordinates which are stored in coeff one can likewise retrieve them using coeffs(GeoDim)

---

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

• include/splines/nurbs.hpp