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Reference documentation for deal.II version 9.0.0
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Reference documentation for deal.II version 9.0.0
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#include <deal.II/base/polynomials_bernstein.h>
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 (const char *identifier=nullptr) const |
| void | unsubscribe (const char *identifier=nullptr) const |
| unsigned int | n_subscriptions () 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 |
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.
Definition at line 40 of file polynomials_bernstein.h.
| 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*}
| index | |
| degree |
Definition at line 45 of file polynomials_bernstein.cc.
1.8.14