ERC CISST - cisst software

nmrPolynomialBase Class Reference

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List of all members.

Detailed Description

Definition at line 52 of file nmrPolynomialBase.h.

Public Types

Public Member Functions

Protected Attributes

Member Function Documentation

virtual ValueType nmrPolynomialBase::EvaluateBasis ( const nmrPolynomialTermPowerIndex &  where,
const nmrMultiVariablePowerBasis &  variables 
) const [pure virtual]

Evaluate the basis function for a term. The term is regarded as a list of powers, without any user defined coefficient. However, for different families of polynomial the set of basis functions are different. For example, Bezier polynomials have the multinomial coefficient in addition to each user defined coefficient. Implemented for each concrete polynomial class.

Referenced by nmrPolynomialContainer< void * >::EvaluateBasisVector(), and nmrPolynomialContainer< void * >::EvaluateTerm().

ValueType nmrPolynomialBase::EvaluateTerm ( const nmrPolynomialTermPowerIndex &  where,
const nmrMultiVariablePowerBasis &  variables 
) const [inline]

Evaluate a single term at the point specified by the `variables' argument, including the basis function and the term's coefficient. This function uses the internally stored coefficient.

Definition at line 305 of file nmrPolynomialBase.h.

Referenced by nmrPolynomialContainer< void * >::Evaluate().

ValueType nmrPolynomialBase::EvaluateTerm ( const nmrPolynomialTermPowerIndex &  where,
const nmrMultiVariablePowerBasis &  variables,
CoefficientType  coefficient 
) const [inline]

Evaluate a single term at the point specified by the `variables' argument, including the basis function and the term's coefficient. This function takes the coefficient as a parameter.

Definition at line 316 of file nmrPolynomialBase.h.

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

Evaluate the basis vector for extrnally given variables. Evaluate the basis function for each terms in the polynomial, and store the results into an array of termBaseValues.

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

Evaluate the polynomial at the currently specified point, using externally defined coefficients. This lets the user create many polynomials over the same set of basis functions without having to duplicate the terms. The input coefficients must be ordered the same way as the terms in this object. It is best to order them using CollectCoefficients()

virtual ValueType nmrPolynomialBase::Evaluate ( const nmrMultiVariablePowerBasis &  variables  )  const [pure virtual]

Evaluate the polynomial for externally given variables

virtual void nmrPolynomialBase::Scale ( CoefficientType  scaleFactor  )  [pure virtual]

Scale the polynomial by a given scalar value. Basically, it means multiplying all the term coefficient by the scale factor.

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

Scale a given set of external coefficients which correspond to the terms of this polynomial. Basically, it means multiplying them all by the scale factor.

Parameters:
coefficients [i/o] the external coefficients to be scales (in place).
scaleFactor the scaling factor.
Note:
this function is not declared virtual, as it seems to behave uniformly for all types of polynomial representations we use. But it may have to be declared virtual eventually. Technically, it could be declared static, but I find it too far fetched.

The same rules that apply to evaluating the polynomial for external coefficients apply here as well.

the function is declared as deprecated. Generally, using the Multiply operation on cisstVector containers of coefficients should be prefered.

virtual void nmrPolynomialBase::AddConstant ( CoefficientType  shiftAmount  )  [pure virtual]

Add a constant value to this polynomial. That is, if p is a polynomial and s is a constant then the following returns true: ValueType v0 = p.Evaluate(); p.AddConstant(s); ValueType v1 = p.Evaluate(); v1 - v0 == s // up to floating point precision error

Note:
the implementation varies between different representations of the polynomial. Specifically, terms may be added to this polynomial to support the addition of the constant.

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

Modify external coefficients so that they evaluate a new polynomial shifted by a constant amount. That is, if p is a polynomial, c is an array of external coefficients, and s is a constant, the following returns true: ValueType v0 = p.EvaluateForCoefficients(c); p.AddConstantToCoefficients(c, s); ValueType v1 = p.EvaluateForCoefficients(c); v1 - v0 == s; // up to floating point precision error

Note:
The implementation of this function may vary based on the representation of the polynomial. In particular, for a Bernstein polynomial it requires that all possible terms be present in the polynomial and in the coefficients correspondingly. For a standard polynomial, it requires that this polynomial actually contains a term of power zero.

The current implementations assert that this polynomial and the external coefficients meet the preconditions for the operation. That is, we do not throw an exception but rather issue an assertion error.

virtual void nmrPolynomialBase::SerializeRaw ( std::ostream &  output  )  const [virtual]

Serialize NumVariables, MinDegree, MaxDegree

Reimplemented in nmrPolynomialContainer< _TermInfo >, and nmrPolynomialContainer< void * >.

virtual void nmrPolynomialBase::DeserializeRaw ( std::istream &  input  )  [virtual]

Deserialize NumVariables, MinDegree, MaxDegree

The documentation for this class was generated from the following file:
erc-cisst-devel<at>lists.johnshopkins.edu