PolynomialsBernstein< number > Class Template Reference

#include <deal.II/base/polynomials_bernstein.h>

Inheritance diagram for PolynomialsBernstein< number >:

Public Member Functions
	PolynomialsBernstein (const unsigned int index, const unsigned int degree)
Public Member Functions inherited from Polynomials::Polynomial< number >
	Polynomial (const std::vector< number > &coefficients)
	Polynomial (const unsigned int n)
	Polynomial (const std::vector< Point< 1 >> &lagrange_support_points, const unsigned int evaluation_point)
	Polynomial ()
number	value (const number x) const
void	value (const number x, std::vector< number > &values) const
void	value (const number x, const unsigned int n_derivatives, number *values) const
unsigned int	degree () const
void	scale (const number factor)
template<typename number2 >
void	shift (const number2 offset)
Polynomial< number >	derivative () const
Polynomial< number >	primitive () const
Polynomial< number > &	operator*= (const double s)
Polynomial< number > &	operator*= (const Polynomial< number > &p)
Polynomial< number > &	operator+= (const Polynomial< number > &p)
Polynomial< number > &	operator-= (const Polynomial< number > &p)
bool	operator== (const Polynomial< number > &p) const
void	print (std::ostream &out) const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
Public Member Functions inherited from Subscriptor
	Subscriptor ()
	Subscriptor (const Subscriptor &)
	Subscriptor (Subscriptor &&) noexcept
virtual	~Subscriptor ()
Subscriptor &	operator= (const Subscriptor &)
Subscriptor &	operator= (Subscriptor &&) noexcept
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Additional Inherited Members
Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)
Protected Member Functions inherited from Polynomials::Polynomial< number >
void	transform_into_standard_form ()
Static Protected Member Functions inherited from Polynomials::Polynomial< number >
static void	scale (std::vector< number > &coefficients, const number factor)
template<typename number2 >
static void	shift (std::vector< number > &coefficients, const number2 shift)
static void	multiply (std::vector< number > &coefficients, const number factor)
Protected Attributes inherited from Polynomials::Polynomial< number >
std::vector< number >	coefficients
bool	in_lagrange_product_form
std::vector< number >	lagrange_support_points
number	lagrange_weight

Detailed Description

template<typename number>
class PolynomialsBernstein< number >

This class implements Bernstein basis polynomials of desire degree as described in http://www.idav.ucdavis.edu/education/CAGDNotes/Bernstein-Polynomials.pdf in the paragraph "Converting from the Bernstein Basis to the Power Basis".

They are used to create the Bernstein finite element FE_Bernstein.

Author

Luca Heltai, Marco Tezzele

Date

2013, 2015

Definition at line 41 of file polynomials_bernstein.h.

Constructor & Destructor Documentation

PolynomialsBernstein()

template<typename number >

PolynomialsBernstein< number >::PolynomialsBernstein	(	const unsigned int	index,
		const unsigned int	degree
	)

Construct the index -th Bernstein Polynomial of degree degree.

\begin{align*} B_{\text{index}, \text{degree}} (t) &= \text{binom}(\text{degree}, \text{index}) \cdot t^{\text{index}} \cdot (1 - t)^{\text{degree} - \text{index}} \\ &= \sum_{i = \text{index}}^\text{degree} \cdot (-1)^{i - \text{index}} \cdot \text{binom}(\text{degree}, i) \cdot \text{binom}(i, \text{index}) \cdot t^i \end{align*}

Parameters

index
degree

Definition at line 45 of file polynomials_bernstein.cc.

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

• deal.II/base/polynomials_bernstein.h
• source/base/polynomials_bernstein.cc