Tensor-product non-uniform B-spline (core functionality) More...

#include </home/runner/work/iganet/iganet/include/bspline.hpp>

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

Public Types
template<typename other_t , short_t GeoDim_, short_t... Degrees_>
using	derived_self_type = NonUniformBSplineCore< 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< short_t >::type degree_elevate = 0>
using	derived_type = BSpline< real_t, GeoDim,(Degrees+degree_elevate)... >
	Deduces the type of the template 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 = NonUniformBSplineCore< other_t, GeoDim, Degrees... >
	Deduces the derived self-type when exposed to a different class template parameter `real_t`

template<std::make_signed< short_t >::type degree_elevate = 0>
using	self_type = typename Base::template derived_type< NonUniformBSplineCore, 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, 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 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
	NonUniformBSplineCore (const std::array< std::vector< typename Base::value_type >, Base::parDim_ > &kv, const utils::TensorArray< Base::geoDim_ > &coeffs, bool clone=false, Options< real_t > options=Options< real_t >{})
	Constructor for non-equidistant knot vectors.

	NonUniformBSplineCore (const std::array< std::vector< typename Base::value_type >, Base::parDim_ > &kv, enum init init=init::greville, Options< real_t > options=Options< real_t >{})
	Constructor for non-equidistant knot vectors.

template<typename BSpline >
auto &	from_gismo (BSpline &bspline, bool, bool)

NonUniformBSplineCore &	insert_knots (const utils::TensorArray< Base::parDim_ > &knots)
	Returns the B-spline object with refined knot and coefficient vectors.

NonUniformBSplineCore &	reduce_continuity (int numReduce=1, int dim=-1)
	Returns the B-spline object with updated knot and coefficient vectors with reduced continuity.

NonUniformBSplineCore &	uniform_refine (int numRefine=1, int dim=-1)
	Returns the B-spline object with uniformly refined knot and coefficient vectors.



Public Member Functions inherited from iganet::UniformBSplineCore< real_t, GeoDim, 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.

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 &	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, 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, 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, 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, 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_ > &)> transformation)
	Transforms the coefficients based on the given mapping.

UniformBSplineCore &	transform (const std::function< std::array< real_t, N >(const std::array< real_t, parDim_ > &)> transformation, 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 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 void	pretty_print (std::ostream &os=Log(log::info)) const noexcept=0
	Returns a string representation.

Static Public Member Functions
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, Degrees... >
static constexpr const 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, Degrees... >
	Base type.

Private Member Functions
void	init_knots (const std::array< std::vector< typename Base::value_type >, Base::parDim_ > &kv)
	Initializes the B-spline knots.

Additional Inherited Members
Protected Member Functions inherited from iganet::UniformBSplineCore< real_t, GeoDim, 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`

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, 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, 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::NonUniformBSplineCore< real_t, GeoDim, Degrees >

Tensor-product non-uniform B-spline (core functionality)

This class extends the base class UniformBSplineCore to non-uniform B-splines. Like its base class it only implements the core functionality of non-uniform B-splines

Member Typedef Documentation

◆ Base

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

using iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::Base = UniformBSplineCore<real_t, GeoDim, 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::NonUniformBSplineCore< real_t, GeoDim, Degrees >::derived_self_type = NonUniformBSplineCore<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< short_t >::type degree_elevate = 0>

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

Deduces the type of the template 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::NonUniformBSplineCore< real_t, GeoDim, Degrees >::real_derived_self_type = NonUniformBSplineCore<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< short_t >::type degree_elevate = 0>

using iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::self_type = typename Base::template derived_type<NonUniformBSplineCore, 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::NonUniformBSplineCore< real_t, GeoDim, Degrees >::value_type = real_t

Value type.

Constructor & Destructor Documentation

◆ NonUniformBSplineCore() [1/2]

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

iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::NonUniformBSplineCore	(	const std::array< std::vector< typename Base::value_type >, Base::parDim_ > &	kv,
		enum init	init = `init::greville`,
		Options< real_t >	options = `Options<real_t>{}`
	)

inline

Constructor for non-equidistant knot vectors.

Parameters

[in]	kv	Knot vectors
[in]	init	Type of initialization
[in]	options	Options configuration

◆ NonUniformBSplineCore() [2/2]

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

iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::NonUniformBSplineCore	(	const std::array< std::vector< typename Base::value_type >, Base::parDim_ > &	kv,
		const utils::TensorArray< Base::geoDim_ > &	coeffs,
		bool	clone = `false`,
		Options< real_t >	options = `Options<real_t>{}`
	)

inline

Constructor for non-equidistant knot vectors.

Parameters

[in]	kv	Knot vectors
[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.

Member Function Documentation

◆ eval() [1/4]

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

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::eval ( const torch::Tensor & xi ) const

inline

Returns the value of the multivariate B-spline object in the point xi

◆ eval() [2/4]

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

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::eval ( const utils::TensorArray< Base::parDim_ > & xi ) const

inline

Returns the value of the multivariate B-spline object in the point xi

◆ eval() [3/4]

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

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::eval	(	const utils::TensorArray< Base::parDim_ > &	xi,
		const utils::TensorArray< Base::parDim_ > &	knot_indices
	)		const

inline

Returns the value of the multivariate B-spline object in the point xi

◆ eval() [4/4]

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

template<deriv deriv = deriv::func, bool memory_optimized = false>

auto iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::eval	(	const utils::TensorArray< Base::parDim_ > &	xi,
		const utils::TensorArray< Base::parDim_ > &	knot_indices,
		const torch::Tensor &	coeff_indices
	)		const

inline

Returns the value of the multivariate B-spline object in the point xi

◆ find_knot_indices() [1/2]

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

auto iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::find_knot_indices ( const torch::Tensor & xi ) const

inline

Returns the indices of knot spans containing xi

This function returns the indices \((i_d)_{d=1}^{d_\text{par}}\) of the knot spans such that

\[ \boldsymbol{\xi} \in [t_{i_1}, t_{i_1+1}) \times [t_{i_2}, t_{i_2+1}) \times \dots \times [t_{i_{d_\text{par}}}, t_{i_{d_\text{par}}+1}). \]

The indices are returned as utils::TensorArray<parDim_> in the same order as provided in xi

◆ find_knot_indices() [2/2]

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

auto iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::find_knot_indices ( const utils::TensorArray< Base::parDim_ > & xi ) const

inline

Returns the indices of knot spans containing xi

This function returns the indices \((i_d)_{d=1}^{d_\text{par}}\) of the knot spans such that

\[ \boldsymbol{\xi} \in [t_{i_1}, t_{i_1+1}) \times [t_{i_2}, t_{i_2+1}) \times \dots \times [t_{i_{d_\text{par}}}, t_{i_{d_\text{par}}+1}). \]

The indices are returned as utils::TensorArray<parDim_> in the same order as provided in xi

◆ from_gismo()

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

template<typename BSpline >

auto & iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::from_gismo	(	BSpline &	bspline,
		bool	,
		bool
	)

inline

◆ init_knots()

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

void iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::init_knots ( const std::array< std::vector< typename Base::value_type >, Base::parDim_ > & kv )

inlineprivate

Initializes the B-spline knots.

◆ insert_knots()

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

NonUniformBSplineCore & iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::insert_knots ( const utils::TensorArray< Base::parDim_ > & knots )

inline

Returns the B-spline object with refined knot and coefficient vectors.

◆ is_nonuniform()

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

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

inlinestaticconstexpr

Returns true if the B-spline is uniform.

◆ reduce_continuity()

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

NonUniformBSplineCore & iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::reduce_continuity	(	int	numReduce = `1`,
		int	dim = `-1`
	)

inline

Returns the B-spline object with updated knot and coefficient vectors with reduced continuity.

◆ uniform_refine()

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

NonUniformBSplineCore & iganet::NonUniformBSplineCore< real_t, GeoDim, Degrees >::uniform_refine	(	int	numRefine = `1`,
		int	dim = `-1`
	)

inline

Returns the B-spline object with uniformly refined knot and coefficient vectors.

If dim = -1, new knot values are inserted uniformly in each knot span in all spatial dimensions. Otherwise, i.e., dim != -1 new knots are only inserted in the specified dimension.

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

include/bspline.hpp

Public Types

Public Member Functions

Static Public Member Functions

Private Types

Private Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

◆ derived_self_type

◆ derived_type

◆ real_derived_self_type

◆ self_type

◆ value_type

Constructor & Destructor Documentation

◆ NonUniformBSplineCore() [1/2]

◆ NonUniformBSplineCore() [2/2]

Member Function Documentation

◆ eval() [1/4]

◆ eval() [2/4]

◆ eval() [3/4]

◆ eval() [4/4]

◆ find_knot_indices() [1/2]

◆ find_knot_indices() [2/2]

◆ from_gismo()

◆ init_knots()

◆ insert_knots()

◆ is_nonuniform()

◆ is_uniform()

◆ reduce_continuity()

◆ uniform_refine()