#include <nmrBernsteinPolynomial.h>

Inheritance diagram for nmrBernsteinPolynomial:

Public Types
typedef nmrDynAllocPolynomialContainer	BaseType

typedef std::pair < nmrPolynomialBase::CoefficientType, nmrPolynomialTermPowerIndex::MultinomialCoefficientType >	BernsteinTermInfo

Public Types inherited from nmrDynAllocPolynomialContainer
typedef nmrPolynomialContainer < void * >	BaseType

Public Types inherited from nmrPolynomialContainer< void * >
typedef nmrPolynomialBase	BaseType

typedef void *	TermInfoType

typedef std::pair < nmrPolynomialTermPowerIndex, TermInfoType >	ContainerElementType

typedef std::list < ContainerElementType >	TermContainerType

typedef TermContainerType::value_type	TermType

typedef TermContainerType::iterator	TermIteratorType

typedef TermContainerType::const_iterator	TermConstIteratorType

Public Types inherited from nmrPolynomialBase
enum	InsertStatus { INSERT_FAIL = -1, INSERT_NEW = 0, INSERT_REPLACE = 1 }

typedef double	ValueType

typedef double	VariableType

typedef double	CoefficientType

typedef nmrPolynomialTermPowerIndex::VariableIndexType	VariableIndexType

typedef nmrPolynomialTermPowerIndex::PowerType	PowerType

typedef nmrPolynomialTermPowerIndex::MultinomialCoefficientType	TermCounterType

Public Member Functions
	nmrBernsteinPolynomial (VariableIndexType numVariables, PowerType degree)

virtual InsertStatus	SetCoefficient (const nmrPolynomialTermPowerIndex &where, CoefficientType coefficient)

virtual InsertStatus	SetCoefficient (TermIteratorType &where, CoefficientType coefficient)

virtual CoefficientType	GetCoefficient (const nmrPolynomialTermPowerIndex &where) const

virtual CoefficientType	GetCoefficient (const TermConstIteratorType &where) const

virtual CoefficientType	GetCoefficient (const TermIteratorType &where) const

virtual void	RemoveTerm (TermIteratorType &where)

virtual void	Clear ()

virtual ValueType	EvaluateBasis (const nmrPolynomialTermPowerIndex &where, const nmrMultiVariablePowerBasis &variables) const

virtual ValueType	EvaluateBasis (const TermConstIteratorType &where, const nmrMultiVariablePowerBasis &variables) const

virtual ValueType	EvaluateBasis (const TermIteratorType &where, const nmrMultiVariablePowerBasis &variables) const

virtual void	SerializeTermInfo (std::ostream &output, const TermConstIteratorType &termIterator) const

virtual void	DeserializeTermInfo (std::istream &input, TermIteratorType &termIterator)

virtual void	AddConstant (CoefficientType shiftAmount)

virtual void	AddConstantToCoefficients (CoefficientType coefficients[], CoefficientType shiftAmount) const

const nmrPolynomialTermPowerIndex::MultinomialCoefficientType &	GetMultinomialCoefficient (const TermIteratorType &where) const

const nmrPolynomialTermPowerIndex::MultinomialCoefficientType &	GetMultinomialCoefficient (const TermConstIteratorType &where) const

Public Member Functions inherited from nmrDynAllocPolynomialContainer
	nmrDynAllocPolynomialContainer (unsigned int numVariables, unsigned int minDegree, unsigned int maxDegree)

Public Member Functions inherited from nmrPolynomialContainer< void * >
	nmrPolynomialContainer (VariableIndexType numVariables, PowerType minDegree, PowerType maxDegree)

virtual	~nmrPolynomialContainer ()

virtual TermCounterType	GetNumberOfTerms () const

virtual bool	IsEmpty () const

virtual void	SetMinDegree (PowerType newMin) throw (std::runtime_error)

virtual void	SetMaxDegree (PowerType newMax) throw (std::runtime_error)

virtual void	FillAllTerms ()

virtual bool	IncludesIndex (const nmrPolynomialTermPowerIndex &target) const

virtual TermCounterType	GetIndexPosition (const nmrPolynomialTermPowerIndex &term) const

TermIteratorType	GetTermIteratorForPosition (TermCounterType position)

TermIteratorType	FirstTermIterator ()

TermConstIteratorType	FirstTermIterator () const

TermIteratorType	EndTermIterator ()

TermConstIteratorType	EndTermIterator () const

TermIteratorType	FindTerm (const nmrPolynomialTermPowerIndex &target)

TermConstIteratorType	FindTerm (const nmrPolynomialTermPowerIndex &target) const

virtual void	RemoveTerm (const nmrPolynomialTermPowerIndex &where)

virtual void	CollectCoefficients (CoefficientType target[]) const

virtual void	RestoreCoefficients (const CoefficientType source[])

const nmrPolynomialTermPowerIndex &	GetTermPowerIndex (const TermConstIteratorType &where) const

const nmrPolynomialTermPowerIndex &	GetTermPowerIndex (const TermIteratorType &where) const

ValueType	EvaluateTerm (const TermConstIteratorType &where) const

ValueType	EvaluateTerm (const TermIteratorType &where) const

ValueType	EvaluateTerm (const TermConstIteratorType &where, const nmrMultiVariablePowerBasis &variables) const

ValueType	EvaluateTerm (const TermIteratorType &where, const nmrMultiVariablePowerBasis &variables) const

virtual ValueType	Evaluate (const nmrMultiVariablePowerBasis &variables) const

virtual void	EvaluateBasisVector (const nmrMultiVariablePowerBasis &variables, ValueType termBaseValues[]) const

virtual ValueType	EvaluateForCoefficients (const nmrMultiVariablePowerBasis &variables, const CoefficientType coefficients[]) const

virtual void	Scale (CoefficientType scaleFactor)

virtual void	SerializeRaw (std::ostream &output) const

virtual void	DeserializeRaw (std::istream &input)

Public Member Functions inherited from nmrPolynomialBase
	nmrPolynomialBase (VariableIndexType numVariables, PowerType minDegree, PowerType maxDegree)

virtual	~nmrPolynomialBase ()

VariableIndexType	GetNumVariables () const

PowerType	GetMinDegree () const

PowerType	GetMaxDegree () const

TermCounterType	GetMaxNumberOfTerms () const

bool	CanIncludeIndex (const nmrPolynomialTermPowerIndex &term) const

virtual CoefficientType	GetCoefficient (const nmrPolynomialTermPowerIndex &CMN_UNUSED(where)) const

ValueType	EvaluateTerm (const nmrPolynomialTermPowerIndex &where, const nmrMultiVariablePowerBasis &variables) const

ValueType	EvaluateTerm (const nmrPolynomialTermPowerIndex &where, const nmrMultiVariablePowerBasis &variables, CoefficientType coefficient) const

void CISST_DEPRECATED	ScaleCoefficients (CoefficientType coefficients[], CoefficientType scaleFactor) const

Protected Member Functions
nmrPolynomialTermPowerIndex::MultinomialCoefficientType &	RefMultinomialCoefficient (const TermIteratorType &where)

const CoefficientType &	GetTermCoefficient (const TermConstIteratorType &where) const

const CoefficientType &	GetTermCoefficient (const TermIteratorType &where) const

CoefficientType &	RefTermCoefficient (const TermIteratorType &where)

Protected Member Functions inherited from nmrPolynomialContainer< void * >
const TermInfoType &	GetTermInfo (const TermConstIteratorType &termIterator) const

TermInfoType &	GetTermInfo (const TermConstIteratorType &termIterator)

Additional Inherited Members
Protected Attributes inherited from nmrPolynomialContainer< void * >
TermContainerType	Terms

Protected Attributes inherited from nmrPolynomialBase
VariableIndexType	NumVariables

PowerType	MinDegree

PowerType	MaxDegree

Detailed Description

class nmrBernsteinPolynomial defines a polynomial in Bernstein basis. In a Bernstein polynomial, all the terms are of equal degree (that is, the sum of powers is a constant), and the variables sum up to a unity. Each term is associated with a scalar coefficient and with a multinomial factor, which reflects the relative weight of the term in the expression:

$1 = (x_0 + ... + x_{n-1}) ^ d = \sum_{(p_0 + ... + p_{n-1}) = d} \choose{d}{p_0 p_1 ... p_{n-1}} x_0^{p_0} ... x_{n-1}^{p_{n-1}}$

To make repeated evaluations quicker, we cache the multinomial factor along with the coefficient of the term in a BernsteinTermInfo object. Appropriate accessors are defined.

Since the sum of the variables is 1, one of the variables depends on the others. Typically, it is either the last or the first, but the user can choose any variable to be the ``implicit'' variable. Once the implicit variable has been determined, its value cannot be updated directly, and instead it is reassigned every time one of the other variables is set. However, the user of the class still has the flexibility to replace the choice of the implicit variable at any time. The only thing that matters is that the variables sum to 1.

Note: We use dynamic allocation for the term information (BernsteinTermInfo), which is separate from the STL provided dynamic allocation for the container elements. We store the pointer to the dynamically allocated term info in the container. Therefore:

We had to override the base-class's RemoveTerm() and Clear() methods.
Do not even try to make a copy of a nmrBernsteinPolynomial using copy-ctor or operator= (yeah, like you would). Just for safety, we declare these operations protected, and do not provide implementation.
A better solution may be to define a common base type for TermInfo, and have it declare a virtual dtor. Go for it, if you have time.

Member Typedef Documentation

typedef nmrDynAllocPolynomialContainer nmrBernsteinPolynomial::BaseType

typedef std::pair<nmrPolynomialBase::CoefficientType, nmrPolynomialTermPowerIndex::MultinomialCoefficientType> nmrBernsteinPolynomial::BernsteinTermInfo

Constructor & Destructor Documentation

nmrBernsteinPolynomial::nmrBernsteinPolynomial	(	VariableIndexType	numVariables,
		PowerType	degree
	)

inline

Constructor determines the number of variables and the degree of the polynomial. Note that Bernstein polynomial contains an additional implicit variable. The argument numVariables must include the implicit variable, since we want to be consistent with the GetNumVariables() method. The degree defines both maximum and minimum degrees for the terms, as all terms are of equal degree. The constructor initializes the free variables to zero, and the implicit variable to 1, so that they all sum up to

The constructor sets the implicit variable to be the last one (the numVariable - 1) by default. The user can change this setting by calling SetImplicitVarIndex().

Member Function Documentation

virtual void nmrBernsteinPolynomial::AddConstant ( CoefficientType shiftAmount )

virtual

Overloaded from nmrPolynomialBase. This implementation goes over all the possible for this polynomial, reads their current coefficient (which may be zero if the term is not included so far) then adds the given shift amount. It may not be the most efficient method, but it should not be called too many times.

Implements nmrPolynomialContainer< void * >.

virtual void nmrBernsteinPolynomial::AddConstantToCoefficients	(	CoefficientType	coefficients[],
		CoefficientType	shiftAmount
	)		const

virtual

Overloaded from nmrPolynomialBase. This implementation asserts that this polynomial contains all the possible terms, and then iterates on all the terms and adds the shift amount to the corresponding external coefficient.

Implements nmrPolynomialContainer< void * >.

virtual void nmrBernsteinPolynomial::Clear ( )

virtual

Remove all the terms to make an empty (zero) polynomial We cannot use nmrPolynomialContainer::Clear(), since it does not reclaim the space allocated for the term. This implementation does.

Reimplemented from nmrPolynomialContainer< void * >.

virtual void nmrBernsteinPolynomial::DeserializeTermInfo	(	std::istream &	input,
		TermIteratorType &	termIterator
	)

virtual

This function is overridden to allocate memory for the multinomial factor and the term coefficient, read the latter from the stream and calculate the former from the term power index. It is called from nmrPolynomialContainer::DeserializeRaw().

Implements nmrDynAllocPolynomialContainer.

virtual ValueType nmrBernsteinPolynomial::EvaluateBasis	(	const nmrPolynomialTermPowerIndex &	where,
		const nmrMultiVariablePowerBasis &	variables
	)		const

virtual

Evaluate the basis function for a term. This DOES NOT include the term's coefficient, but DOES include the multinomial factor.

Implements nmrPolynomialBase.

virtual ValueType nmrBernsteinPolynomial::EvaluateBasis	(	const TermConstIteratorType &	where,
		const nmrMultiVariablePowerBasis &	variables
	)		const

virtual

Implements nmrPolynomialContainer< void * >.

virtual ValueType nmrBernsteinPolynomial::EvaluateBasis	(	const TermIteratorType &	where,
		const nmrMultiVariablePowerBasis &	variables
	)		const

virtual

Implements nmrPolynomialContainer< void * >.

virtual CoefficientType nmrBernsteinPolynomial::GetCoefficient ( const nmrPolynomialTermPowerIndex & where ) const

virtual

Retrieve the value of the user defined coefficient for a given term.

virtual CoefficientType nmrBernsteinPolynomial::GetCoefficient ( const TermConstIteratorType & where ) const

inlinevirtual

Retrieve the value of the user defined coefficient for a term given by iterator.

Implements nmrPolynomialContainer< void * >.

virtual CoefficientType nmrBernsteinPolynomial::GetCoefficient ( const TermIteratorType & where ) const

inlinevirtual

Implements nmrPolynomialContainer< void * >.

const nmrPolynomialTermPowerIndex::MultinomialCoefficientType& nmrBernsteinPolynomial::GetMultinomialCoefficient ( const TermIteratorType & where ) const

inline

const nmrPolynomialTermPowerIndex::MultinomialCoefficientType& nmrBernsteinPolynomial::GetMultinomialCoefficient ( const TermConstIteratorType & where ) const

inline

const CoefficientType& nmrBernsteinPolynomial::GetTermCoefficient ( const TermConstIteratorType & where ) const

inlineprotected

const CoefficientType& nmrBernsteinPolynomial::GetTermCoefficient ( const TermIteratorType & where ) const

inlineprotected

nmrPolynomialTermPowerIndex::MultinomialCoefficientType& nmrBernsteinPolynomial::RefMultinomialCoefficient ( const TermIteratorType & where )

inlineprotected

CoefficientType& nmrBernsteinPolynomial::RefTermCoefficient ( const TermIteratorType & where )

inlineprotected

virtual void nmrBernsteinPolynomial::RemoveTerm ( TermIteratorType & where )

virtual

Remove a term from the polynomial. The term is given by iterator. The function also reclaims the space allocated for the term.

Reimplemented from nmrPolynomialContainer< void * >.

virtual void nmrBernsteinPolynomial::SerializeTermInfo	(	std::ostream &	output,
		const TermConstIteratorType &	termIterator
	)		const

virtual

This function is overridden to store the term coefficient to the stream. It is called from nmrPolynomialContainer::SerializeRaw().

Implements nmrDynAllocPolynomialContainer.

virtual InsertStatus nmrBernsteinPolynomial::SetCoefficient	(	const nmrPolynomialTermPowerIndex &	where,
		CoefficientType	coefficient
	)

virtual

Overriding nmrPolynomial::SetCoefficient(). This implementation computes the multinomial factor for the term.

Implements nmrPolynomialContainer< void * >.

virtual InsertStatus nmrBernsteinPolynomial::SetCoefficient	(	TermIteratorType &	where,
		CoefficientType	coefficient
	)

virtual

Set a coefficient for the given term iterator. Implemented from nmrPolynomialContainer.

Implements nmrPolynomialContainer< void * >.

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

/home/adeguet1/catkin_ws/src/cisst-saw/cisst/cisstNumerical/nmrBernsteinPolynomial.h

Public Types

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation