Reference documentation for deal.II version Git cb0bd54b52 2019-09-21 16:31:22 -0400
\(\newcommand{\dealcoloneq}{\mathrel{\vcenter{:}}=}\)
Public Member Functions | List of all members
PolynomialsBernstein< number > Class Template Reference

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

Inheritance diagram for PolynomialsBernstein< number >:
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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 ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (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.


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