Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC > Class Template Reference

Template class for computing extremal distance function between a point and a curve. Searches for a parameter value u such that dist(P, C(u)) passes through an extremum. Inherits from math_FunctionWithDerivative and is used by math_FunctionRoot and math_FunctionRoots algorithms. More...

#include <Extrema_GFuncExtPC.hxx>

Inheritance diagram for Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >:

Public Member Functions
	Extrema_GFuncExtPC ()
	Default constructor.
	Extrema_GFuncExtPC (const ThePoint &theP, const TheCurve &theC)
	Constructor with point and curve initialization.
void	Initialize (const TheCurve &theC)
	Sets the curve field.
void	SetPoint (const ThePoint &theP)
	Sets the point field.
bool	Value (const double theU, double &theF) override
	Calculation of F(u).
bool	Derivative (const double theU, double &theDF) override
	Calculation of F'(u).
bool	Values (const double theU, double &theF, double &theDF) override
	Calculation of F(u) and F'(u).
int	GetStateNumber () override
	Save the found extremum.
int	NbExt () const
	Return the number of found extrema.
double	SquareDistance (const int theN) const
	Returns the Nth square distance.
bool	IsMin (const int theN) const
	Shows if the Nth distance is a minimum.
const ThePOnC &	Point (const int theN) const
	Returns the Nth extremum point.
void	SubIntervalInitialize (const double theUfirst, const double theUlast)
	Determines boundaries of subinterval for root finding.
double	SearchOfTolerance ()
	Computes a tolerance value. If 1st derivative of curve |D1| < Tol, it is considered D1=0.
Public Member Functions inherited from math_FunctionWithDerivative
	~math_FunctionWithDerivative () override
Public Member Functions inherited from math_Function
virtual	~math_Function ()=default
	Virtual destructor, for safe inheritance.

Detailed Description

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>
class Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >

Template class for computing extremal distance function between a point and a curve. Searches for a parameter value u such that dist(P, C(u)) passes through an extremum. Inherits from math_FunctionWithDerivative and is used by math_FunctionRoot and math_FunctionRoots algorithms.

If D1c and D2c are the first and second derivatives: F(u) = (C(u)-P).D1c(u) / ||D1c|| DF(u) = ||D1c|| + (C(u)-P).D2c(u)/||D1c|| - F(u)*D2c.D1c/||D1c||^2

Template Parameters

TheCurve	Curve type (e.g., Adaptor3d_Curve, Adaptor2d_Curve2d)
TheCurveTool	Tool for curve operations
ThePOnC	Point on curve type
ThePoint	Point type (e.g., gp_Pnt, gp_Pnt2d)
TheVector	Vector type (e.g., gp_Vec, gp_Vec2d)
TheSeqPOnC	Sequence of points on curve type

Constructor & Destructor Documentation

Extrema_GFuncExtPC() [1/2]

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::Extrema_GFuncExtPC ( )

inline

Default constructor.

Extrema_GFuncExtPC() [2/2]

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::Extrema_GFuncExtPC ( const ThePoint & theP, const TheCurve & theC )

inline

Constructor with point and curve initialization.

Parameters

theP	Point to compute distance from
theC	Curve to compute distance to

Member Function Documentation

Derivative()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

bool Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::Derivative ( const double theU, double & theDF )

inlineoverridevirtual

Calculation of F'(u).

Parameters

theU	Parameter value
theDF	Output derivative value

Returns

True if computation succeeded

Implements math_FunctionWithDerivative.

GetStateNumber()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

int Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::GetStateNumber ( )

inlineoverridevirtual

Save the found extremum.

Returns

State number

Reimplemented from math_Function.

Initialize()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

void Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::Initialize ( const TheCurve & theC )

inline

Sets the curve field.

Parameters

theC	Curve to set

IsMin()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

bool Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::IsMin ( const int theN ) const

inline

Shows if the Nth distance is a minimum.

Parameters

theN	Index of extremum

NbExt()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

int Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::NbExt ( ) const

inline

Return the number of found extrema.

Point()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

const ThePOnC & Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::Point ( const int theN ) const

inline

Returns the Nth extremum point.

Parameters

theN	Index of extremum

SearchOfTolerance()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

double Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::SearchOfTolerance ( )

inline

Computes a tolerance value. If 1st derivative of curve |D1| < Tol, it is considered D1=0.

SetPoint()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

void Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::SetPoint ( const ThePoint & theP )

inline

Sets the point field.

Parameters

theP	Point to set

SquareDistance()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

double Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::SquareDistance ( const int theN ) const

inline

Returns the Nth square distance.

Parameters

theN	Index of extremum

SubIntervalInitialize()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

void Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::SubIntervalInitialize ( const double theUfirst, const double theUlast )

inline

Determines boundaries of subinterval for root finding.

Parameters

theUfirst	First parameter bound
theUlast	Last parameter bound

Value()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

bool Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::Value ( const double theU, double & theF )

inlineoverridevirtual

Calculation of F(u).

Parameters

theU	Parameter value
theF	Output function value

Returns

True if computation succeeded

Implements math_FunctionWithDerivative.

Values()

template<typename TheCurve, typename TheCurveTool, typename ThePOnC, typename ThePoint, typename TheVector, typename TheSeqPOnC>

bool Extrema_GFuncExtPC< TheCurve, TheCurveTool, ThePOnC, ThePoint, TheVector, TheSeqPOnC >::Values ( const double theU, double & theF, double & theDF )

inlineoverridevirtual

Calculation of F(u) and F'(u).

Parameters

theU	Parameter value
theF	Output function value
theDF	Output derivative value

Returns

True if computation succeeded

Implements math_FunctionWithDerivative.

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

• Extrema_GFuncExtPC.hxx