dim-dimensional tensor-product Bezier polynomial function. More...

#include <bezier_tp.hpp>

Inheritance diagram for qugar::impl::BezierTP< dim, range >:

Collaboration diagram for qugar::impl::BezierTP< dim, range >:

Public Types
using	Parent = PolynomialTP<dim, range>
	Parent type.

using	CoefsType = typename Parent::CoefsType
	Coefs type.

template<typename T >
using	Value = typename Parent::template Value<T>
	Value type.

template<typename T >
using	Gradient = typename Parent::template Gradient<T>
	Gradient type.

template<typename T >
using	Hessian = typename Parent::template Hessian<T>
	Hessian type.

template<int N>
using	Interval = ::algoim::Interval<N>
	Algoim's interval alias.

Public Types inherited from qugar::impl::PolynomialTP< dim, range >
using	CoefsType = std::conditional_t<range == 1, real, Point<range>>
	Coefs type.

Public Types inherited from qugar::impl::DomainFunc< dim, range >
template<int N>
using	Interval = ::algoim::Interval<N>
	Algoim's interval alias.

template<typename T >
using	Value = std::conditional_t<range == 1, T, Vector<T, range>>
	Value type.

template<typename T >
using	Gradient = Vector<Value<T>, dim>
	Gradient type.

template<typename T >
using	Hessian = Vector<Value<T>, num_hessian>
	Hessian (symmetric type).

Public Member Functions
	BezierTP (const TensorSizeTP< dim > &order)
	Constructor.

	BezierTP (const TensorSizeTP< dim > &order, const CoefsType &value)
	Constructs a constant value Bezier tensor product.

	BezierTP (const TensorSizeTP< dim > &order, const std::vector< CoefsType > &coefs)
	Constructor.

	BezierTP (const BezierTP< dim, range > &bezier)
	Copy constructor.

	BezierTP (const MonomialsTP< dim, range > &monomials)
	Constructor.

virtual Value< real >	operator() (const Point< dim > &point) const final
	Evaluator operator.

virtual Value< Interval< dim > >	operator() (const Point< dim, Interval< dim > > &point) const final
	Evaluator operator.

virtual Gradient< real >	grad (const Point< dim > &point) const final
	Gradient evaluator operator.

virtual Gradient< Interval< dim > >	grad (const Point< dim, Interval< dim > > &point) const final
	Gradient evaluator operator.

virtual Hessian< real >	hessian (const Point< dim > &point) const final
	Hessian evaluator operator.

const ::algoim::xarray< CoefsType, dim > &	get_xarray () const
	Gets a constant reference to the stored xarray view of the polynomial coefficients.

template<int dim_aux = dim> requires (dim == dim_aux && dim > 1)
std::shared_ptr< BezierTP< dim - 1, range > >	extract_facet (const int local_facet_id) const

std::shared_ptr< BezierTP< dim, range > >	raise_order (const TensorSizeTP< dim > &new_order) const
	Raises the order of the Bezier tensor product.

std::shared_ptr< BezierTP< dim, range > >	negate () const
	Creates a new Bezier tensor product (TP) object that is the negation of the current object.

template<int range_aux = range> requires (range_aux == range && range == 1)
void	rescale_domain (const BoundBox< dim > &new_domain)
	Recomputes (in-place) the Bezier coefficients for a new domain (that may not be [0, 1]).

template<int range_aux = range> requires (range_aux == range && range == 1)
FuncSign	sign () const
	Returns the sign of the function represented by the Bézier tensor-product using the properties of the control points convex hull.

std::shared_ptr< BezierTP< dim, range > >	operator* (const BezierTP< dim, range > &rhs) const
	Product of two Beziers.

std::shared_ptr< BezierTP< dim, range > >	operator+ (const BezierTP< dim, range > &rhs) const
	Addition of two Beziers.

std::shared_ptr< BezierTP< dim, range > >	operator- (const BezierTP< dim, range > &rhs) const
	Subtraction of two Beziers.

template<int sub_dim>
std::shared_ptr< BezierTP< sub_dim, range > >	compose (const BezierTP< sub_dim, dim > &rhs) const
	Composes the current Bezier with the given Bezier `rhs`.

Public Member Functions inherited from qugar::impl::PolynomialTP< dim, range >
	PolynomialTP (const TensorSizeTP< dim > &order)
	Constructor.

	PolynomialTP (const TensorSizeTP< dim > &order, const CoefsType &value)
	Constructs a constant value PolynomialTP object with the specified order.

	PolynomialTP (const TensorSizeTP< dim > &order, const std::vector< CoefsType > &coefs)
	Constructor.

std::size_t	get_num_coefs () const
	Get the number of coeficients.

const std::vector< CoefsType > &	get_coefs () const
	Gets the polynomial coefficients.

const TensorSizeTP< dim > &	get_order () const
	Gets the polynomial order along the parametric directions.

int	get_order (int dir) const
	Gets the polynomial order (degree + 1) along the direction `dir`.

const CoefsType &	get_coef (int index) const
	Retrieves the coefficients at the specified index.

CoefsType &	get_coef (int index)
	Retrieves the coefficients at the specified index.

const CoefsType &	get_coef (const TensorIndexTP< dim > &index) const
	Retrieves the coefficient associated with the given tensor index.

CoefsType &	get_coef (const TensorIndexTP< dim > &index)
	Retrieves the coefficient associated with the given tensor index.

int	get_degree (int dir) const
	Gets the polynomial degree (order - 1) along the direction `dir`.

void	transform_image (const BoundBox< range > &old_domain, const BoundBox< range > &new_domain)
	Transforms (in place) the coefficients of the polynomial from `old_domain` to `new_domain`.

void	coefs_linear_transform (const real scale, const CoefsType &shift)
	Applies a linear transformation to every coefficient.

Public Member Functions inherited from qugar::impl::DomainFunc< dim, range >
	DomainFunc ()=default
	Default constructor.

	DomainFunc (const DomainFunc &)=default
	Default copy constructor.

	DomainFunc (DomainFunc &&)=default
	Default move constructor.

DomainFunc &	operator= (const DomainFunc &)=default
	Default copy assignment operator.

DomainFunc &	operator= (DomainFunc &&)=default
	Default move assignment operator.

virtual	~DomainFunc ()=default
	Default virtual destructor.

Static Public Member Functions
template<typename T >
static Value< T >	casteljau (const Point< dim, T > &point, typename std::vector< CoefsType >::const_iterator &coefs, const Vector< int, dim > &order)
	Evaluates a Bezier polynomial using the Casteljau's algorithm.

template<typename T >
static Vector< Value< T >, dim+1 >	casteljau_der (const Point< dim, T > &point, typename std::vector< CoefsType >::const_iterator &coefs, const Vector< int, dim > &order)
	Evaluates the gradient Bezier polynomial using the Casteljau's algorithm.

Private Member Functions
template<typename T >
Value< T >	eval_ (const Point< dim, T > &point) const
	Evaluator operator.

template<typename T >
Gradient< T >	grad_ (const Point< dim, T > &point) const
	Gradient evaluator operator.

template<typename T >
Hessian< T >	hessian_ (const Point< dim, T > &point) const
	Hessian evaluator operator.

Private Attributes
::algoim::xarray< CoefsType, dim >	coefs_xarray_
	dim-dimensional array view of the coefficients.

Additional Inherited Members
Static Public Attributes inherited from qugar::impl::DomainFunc< dim, range >
static const int	num_hessian = dim * (dim + 1) / 2
	Number of Hessian (symmetric) components.

Protected Attributes inherited from qugar::impl::PolynomialTP< dim, range >
TensorSizeTP< dim >	order_
	Order of the polynomial along each parametric direction.

std::vector< CoefsType >	coefs_

Detailed Description

template<int dim, int range>
class qugar::impl::BezierTP< dim, range >

dim-dimensional tensor-product Bezier polynomial function.

Template Parameters

dim	Dimension of the parametric domain.
range	Dimension of the image.

Member Typedef Documentation

◆ CoefsType

template<int dim, int range>

using qugar::impl::BezierTP< dim, range >::CoefsType = typename Parent::CoefsType

Coefs type.

◆ Gradient

template<int dim, int range>

template<typename T >

using qugar::impl::BezierTP< dim, range >::Gradient = typename Parent::template Gradient<T>

Gradient type.

◆ Hessian

template<int dim, int range>

template<typename T >

using qugar::impl::BezierTP< dim, range >::Hessian = typename Parent::template Hessian<T>

Hessian type.

◆ Interval

template<int dim, int range>

template<int N>

using qugar::impl::BezierTP< dim, range >::Interval = ::algoim::Interval<N>

Algoim's interval alias.

◆ Parent

template<int dim, int range>

using qugar::impl::BezierTP< dim, range >::Parent = PolynomialTP<dim, range>

Parent type.

◆ Value

template<int dim, int range>

template<typename T >

using qugar::impl::BezierTP< dim, range >::Value = typename Parent::template Value<T>

Value type.

Constructor & Destructor Documentation

◆ BezierTP() [1/5]

template<int dim, int range>

qugar::impl::BezierTP< dim, range >::BezierTP ( const TensorSizeTP< dim > & order )

explicit

Constructor.

The coefficients vector is allocated by the constructor.

Parameters

order Order of the polynomial along each parametric direction.

◆ BezierTP() [2/5]

template<int dim, int range>

qugar::impl::BezierTP< dim, range >::BezierTP	(	const TensorSizeTP< dim > &	order,
		const CoefsType &	value )

Constructs a constant value Bezier tensor product.

Parameters

order	Order of the polynomial along each parametric direction.
value	The value to set for all the coefficients.

◆ BezierTP() [3/5]

template<int dim, int range>

qugar::impl::BezierTP< dim, range >::BezierTP	(	const TensorSizeTP< dim > &	order,
		const std::vector< CoefsType > &	coefs )

Constructor.

Parameters

coefs	Coefficients of the polynomial. The ordering is such that dimension 0 is inner-most, i.e., iterates the fastest, while dimension dim-1 is outer-most and iterates the slowest.
order	Order of the polynomial along each parametric direction.

◆ BezierTP() [4/5]

template<int dim, int range>

qugar::impl::BezierTP< dim, range >::BezierTP ( const BezierTP< dim, range > & bezier )

Copy constructor.

Parameters

bezier Bezier to copy.

◆ BezierTP() [5/5]

template<int dim, int range>

qugar::impl::BezierTP< dim, range >::BezierTP ( const MonomialsTP< dim, range > & monomials )

explicit

Constructor.

Constructs from monomials.

Parameters

monomials Monomials from which the Bezier is created.

Member Function Documentation

◆ casteljau()

template<int dim, int range>

template<typename T >

static Value< T > qugar::impl::BezierTP< dim, range >::casteljau	(	const Point< dim, T > &	point,
		typename std::vector< CoefsType >::const_iterator &	coefs,
		const Vector< int, dim > &	order )

static

Evaluates a Bezier polynomial using the Casteljau's algorithm.

For the algorithm details check: https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm

The evaluation along the dimensions is performed by recursively calling this function.

Template Parameters

T	Type of the input and output variables.

Parameters

point	Evaluation point.
coefs	Iterator to the coefficients of the polynomial. Their ordering is the same as the coefficients members of the class.
order	Order of the polynomial along the dim dimensions.

Returns: Value of the polynomial at point.

◆ casteljau_der()

template<int dim, int range>

template<typename T >

static Vector< Value< T >, dim+1 > qugar::impl::BezierTP< dim, range >::casteljau_der	(	const Point< dim, T > &	point,
		typename std::vector< CoefsType >::const_iterator &	coefs,
		const Vector< int, dim > &	order )

static

Evaluates the gradient Bezier polynomial using the Casteljau's algorithm.

For the algorithm details check: https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm

The evaluation along the dimensions is performed by recursively calling this function.

Template Parameters

T	Type of the input and output variables.

Parameters

point	Evaluation point.
coefs	Iterator to the coefficients of the polynomial. Their ordering is the same as the coefficients members of the class.
order	Order of the polynomial along the dim dimensions.

Returns: The first component of the return vector corresponds to the value of the polynomial itself, while the gradient is stored in the following dim components.

◆ compose()

template<int dim, int range>

template<int sub_dim>

std::shared_ptr< BezierTP< sub_dim, range > > qugar::impl::BezierTP< dim, range >::compose ( const BezierTP< sub_dim, dim > & rhs ) const

nodiscard

Composes the current Bezier with the given Bezier rhs.

Template Parameters

sub_dim Subdimension of the right-hand-size Bezier.

Parameters

rhs	Right-hand-side Bezier for the composition.

Returns: Generated Bezier composition.

◆ eval_()

template<int dim, int range>

template<typename T >

Value< T > qugar::impl::BezierTP< dim, range >::eval_ ( const Point< dim, T > & point ) const

nodiscardprivate

Evaluator operator.

Template Parameters

T	Input and output's type.

Parameters

point Point at which the function is evaluated.

Returns: Function value at point.

◆ extract_facet()

template<int dim, int range>

template<int dim_aux = dim>
requires (dim == dim_aux && dim > 1)

std::shared_ptr< BezierTP< dim - 1, range > > qugar::impl::BezierTP< dim, range >::extract_facet ( const int local_facet_id ) const

nodiscard

◆ get_xarray()

template<int dim, int range>

const ::algoim::xarray< CoefsType, dim > & qugar::impl::BezierTP< dim, range >::get_xarray ( ) const

nodiscard

Gets a constant reference to the stored xarray view of the polynomial coefficients.

Returns: Constant view of the polynomial coefficients.

◆ grad() [1/2]

template<int dim, int range>

virtual Gradient< real > qugar::impl::BezierTP< dim, range >::grad ( const Point< dim > & point ) const

nodiscardfinalvirtual

Gradient evaluator operator.

Parameters

point Point at which the function's gradient is evaluated.

Returns: Function gradient at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ grad() [2/2]

template<int dim, int range>

virtual Gradient< Interval< dim > > qugar::impl::BezierTP< dim, range >::grad ( const Point< dim, Interval< dim > > & point ) const

nodiscardfinalvirtual

Gradient evaluator operator.

Parameters

point Point at which the function's gradient is evaluated.

Returns: Function gradient at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ grad_()

template<int dim, int range>

template<typename T >

Gradient< T > qugar::impl::BezierTP< dim, range >::grad_ ( const Point< dim, T > & point ) const

nodiscardprivate

Gradient evaluator operator.

Template Parameters

T	Input and output's type.

Parameters

point Point at which the function's gradient is evaluated.

Returns: Function gradient at point.

◆ hessian()

template<int dim, int range>

virtual Hessian< real > qugar::impl::BezierTP< dim, range >::hessian ( const Point< dim > & point ) const

nodiscardfinalvirtual

Hessian evaluator operator.

Parameters

point Point at which the function's hessian is evaluated.

Returns: Function hessian at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ hessian_()

template<int dim, int range>

template<typename T >

Hessian< T > qugar::impl::BezierTP< dim, range >::hessian_ ( const Point< dim, T > & point ) const

nodiscardprivate

Hessian evaluator operator.

Template Parameters

T	Input and output's type.

Parameters

point Point at which the function's hessian is evaluated.

Returns: Function hessian at point.

◆ negate()

template<int dim, int range>

std::shared_ptr< BezierTP< dim, range > > qugar::impl::BezierTP< dim, range >::negate ( ) const

nodiscard

Creates a new Bezier tensor product (TP) object that is the negation of the current object.

This function returns a shared pointer to a new BezierTP object where each control point has the same value but with negative sign.

Returns: A shared pointer to the negated BezierTP object.

◆ operator()() [1/2]

template<int dim, int range>

virtual Value< real > qugar::impl::BezierTP< dim, range >::operator() ( const Point< dim > & point ) const

nodiscardfinalvirtual

Evaluator operator.

Parameters

point Point at which the function is evaluated.

Returns: Function value at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ operator()() [2/2]

template<int dim, int range>

virtual Value< Interval< dim > > qugar::impl::BezierTP< dim, range >::operator() ( const Point< dim, Interval< dim > > & point ) const

nodiscardfinalvirtual

Evaluator operator.

Parameters

point Point at which the function is evaluated.

Returns: Function value at point.

Implements qugar::impl::DomainFunc< dim, range >.

◆ operator*()

template<int dim, int range>

std::shared_ptr< BezierTP< dim, range > > qugar::impl::BezierTP< dim, range >::operator* ( const BezierTP< dim, range > & rhs ) const

nodiscard

Product of two Beziers.

Parameters

rhs	Second Bezier to multiply.

Returns: Product of Beziers.

◆ operator+()

template<int dim, int range>

std::shared_ptr< BezierTP< dim, range > > qugar::impl::BezierTP< dim, range >::operator+ ( const BezierTP< dim, range > & rhs ) const

nodiscard

Addition of two Beziers.

Parameters

rhs	Second Bezier to sum.

Returns: Sum of Beziers. The resulting Bezier has the maximum order of the two Beziers along each dimension.

◆ operator-()

template<int dim, int range>

std::shared_ptr< BezierTP< dim, range > > qugar::impl::BezierTP< dim, range >::operator- ( const BezierTP< dim, range > & rhs ) const

nodiscard

Subtraction of two Beziers.

Parameters

rhs	Bezier to subtract.

Returns: Subtraction of Beziers. The resulting Bezier has the maximum order of the two Beziers along each dimension.

◆ raise_order()

template<int dim, int range>

std::shared_ptr< BezierTP< dim, range > > qugar::impl::BezierTP< dim, range >::raise_order ( const TensorSizeTP< dim > & new_order ) const

nodiscard

Raises the order of the Bezier tensor product.

This function creates a new Bezier tensor product with an increased order as specified by the new_order parameter. The new Bezier will represent the same polynomial function as the original, but with a higher order.

Parameters

new_order The new order for each dimension of the tensor product. Along each dimension, the new order must be greater or equal than the current order.

Returns: A shared pointer to the new Bezier tensor product with the raised order.

◆ rescale_domain()

template<int dim, int range>

template<int range_aux = range>
requires (range_aux == range && range == 1)

void qugar::impl::BezierTP< dim, range >::rescale_domain ( const BoundBox< dim > & new_domain )

Recomputes (in-place) the Bezier coefficients for a new domain (that may not be [0, 1]).

Parameters

new_domain New domain for which the coefficientes are computed.

◆ sign()

template<int dim, int range>

template<int range_aux = range>
requires (range_aux == range && range == 1)

FuncSign qugar::impl::BezierTP< dim, range >::sign ( ) const

nodiscard

Returns the sign of the function represented by the Bézier tensor-product using the properties of the control points convex hull.

Returns: FuncSign The sign of the function.

Member Data Documentation

◆ coefs_xarray_

template<int dim, int range>

::algoim::xarray<CoefsType, dim> qugar::impl::BezierTP< dim, range >::coefs_xarray_

private

dim-dimensional array view of the coefficients.

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

/__w/qugar/qugar/cpp/include/qugar/bezier_tp.hpp
/__w/qugar/qugar/cpp/include/qugar/monomials_tp.hpp

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ CoefsType

◆ Gradient

◆ Hessian

◆ Interval

◆ Parent

◆ Value

Constructor & Destructor Documentation

◆ BezierTP() [1/5]

◆ BezierTP() [2/5]

◆ BezierTP() [3/5]

◆ BezierTP() [4/5]

◆ BezierTP() [5/5]

Member Function Documentation

◆ casteljau()

◆ casteljau_der()

◆ compose()

◆ eval_()

◆ extract_facet()

◆ get_xarray()

◆ grad() [1/2]

◆ grad() [2/2]

◆ grad_()

◆ hessian()

◆ hessian_()

◆ negate()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ operator+()

◆ operator-()

◆ raise_order()

◆ rescale_domain()

◆ sign()

Member Data Documentation

◆ coefs_xarray_