pbat::math::polynomial::MonomialBasis< Dims, Order > Struct Template Reference

Polynomial basis \( \left\{ \Pi_{i=1}^{d} \mathbf{X}_i^{p_i} \; \text{s.t.} \; 0 \leq \sum_{i=1}^d p_i \leq p \right\} \) in dimensions \( d \) and order \( p \). More...

#include <Basis.h>

Inheritance diagram for pbat::math::polynomial::MonomialBasis< Dims, Order >:

Public Types
using	BaseType = detail::MonomialBasis<Dims, Order>
	Base type.

Public Member Functions
Vector< kSize >	eval (Vector< kDims > const &X) const
Matrix< kDims, kSize >	derivatives (Vector< kDims > const &X) const
Matrix< kSize, kDims >	antiderivatives (Vector< kDims > const &X) const

Static Public Attributes
static constexpr int	kDims = BaseType::kDims
	Spatial dimensions.
static constexpr int	kOrder = BaseType::kOrder
	Polynomial order.
static constexpr int	kSize = BaseType::kSize
	Number of basis functions.

Detailed Description

template<int Dims, int Order>
struct pbat::math::polynomial::MonomialBasis< Dims, Order >

Polynomial basis \( \left\{ \Pi_{i=1}^{d} \mathbf{X}_i^{p_i} \; \text{s.t.} \; 0 \leq \sum_{i=1}^d p_i \leq p \right\} \) in dimensions \( d \) and order \( p \).

See Monomial basis.

Template Parameters

Dims	Spatial dimensions
Order	Polynomial order

Member Function Documentation

antiderivatives()

template<int Dims, int Order>

Matrix< kSize, kDims > pbat::math::polynomial::MonomialBasis< Dims, Order >::antiderivatives ( Vector< kDims > const & X ) const

inline

Parameters

X

Returns

derivatives()

template<int Dims, int Order>

Matrix< kDims, kSize > pbat::math::polynomial::MonomialBasis< Dims, Order >::derivatives ( Vector< kDims > const & X ) const

inline

Parameters

X

Returns

eval()

template<int Dims, int Order>

Vector< kSize > pbat::math::polynomial::MonomialBasis< Dims, Order >::eval ( Vector< kDims > const & X ) const

inline

Parameters

X

Returns

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

• C:/git/PhysicsBasedAnimationToolkit/source/pbat/math/polynomial/Basis.h