BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox Class Reference

#include <BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox.hxx>

Public Member Functions
	BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox (const BRepApprox_TheMultiLineOfApprox &SSP, const int FirstPoint, const int LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector &Parameters, const int NbPol)
	given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. NbPol is the number of control points wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the Bernstein matrix computed with the parameters, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).
	BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox (const BRepApprox_TheMultiLineOfApprox &SSP, const int FirstPoint, const int LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const int NbPol)
	Initializes the fields of the object.
	BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox (const BRepApprox_TheMultiLineOfApprox &SSP, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const int FirstPoint, const int LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector &Parameters, const int NbPol)
	given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. Deg is the degree wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the BSpline functions matrix computed with <parameters>, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).
	BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox (const BRepApprox_TheMultiLineOfApprox &SSP, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const int FirstPoint, const int LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const int NbPol)
	Initializes the fields of the object.
void	Perform (const math_Vector &Parameters)
	Is used after having initialized the fields. The case "CurvaturePoint" is not treated in this method.
void	Perform (const math_Vector &Parameters, const double l1, const double l2)
	Is used after having initialized the fields.
void	Perform (const math_Vector &Parameters, const math_Vector &V1t, const math_Vector &V2t, const double l1, const double l2)
	Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point.
void	Perform (const math_Vector &Parameters, const math_Vector &V1t, const math_Vector &V2t, const math_Vector &V1c, const math_Vector &V2c, const double l1, const double l2)
	Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point. <V1c> is the tangent vector at the first point. <V2c> is the tangent vector at the last point.
bool	IsDone () const
	returns True if all has been correctly done.
AppParCurves_MultiCurve	BezierValue ()
	returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.
const AppParCurves_MultiBSpCurve &	BSplineValue ()
	returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.
const math_Matrix &	FunctionMatrix () const
	returns the function matrix used to approximate the set.
const math_Matrix &	DerivativeFunctionMatrix () const
	returns the derivative function matrix used to approximate the set.
void	ErrorGradient (math_Vector &Grad, double &F, double &MaxE3d, double &MaxE2d)
	returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances. Grad is the derivative vector of the function F.
const math_Matrix &	Distance ()
	returns the distances between the points of the multiline and the approximation curves.
void	Error (double &F, double &MaxE3d, double &MaxE2d)
	returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances.
double	FirstLambda () const
	returns the value (P2 - P1)/ V1 if the first point was a tangency point.
double	LastLambda () const
	returns the value (PN - PN-1)/ VN if the last point was a tangency point.
const math_Matrix &	Points () const
	returns the matrix of points value.
const math_Matrix &	Poles () const
	returns the matrix of resulting control points value.
const math_IntegerVector &	KIndex () const
	Returns the indexes of the first non null values of A and DA. The values are non null from Index(ieme point) +1 to Index(ieme point) + degree +1.

Protected Member Functions
void	Init (const BRepApprox_TheMultiLineOfApprox &SSP, const int FirstPoint, const int LastPoint)
	is used by the constructors above.
int	NbBColumns (const BRepApprox_TheMultiLineOfApprox &SSP) const
	returns the number of second member columns. Is used internally to initialize the fields.
int	TheFirstPoint (const AppParCurves_Constraint FirstCons, const int FirstPoint) const
	returns the first point being fitted.
int	TheLastPoint (const AppParCurves_Constraint LastCons, const int LastPoint) const
	returns the last point being fitted.
void	Affect (const BRepApprox_TheMultiLineOfApprox &SSP, const int Index, AppParCurves_Constraint &Cons, math_Vector &Vt, math_Vector &Vc)
	Affects the fields in the case of a constraint point.
void	ComputeFunction (const math_Vector &Parameters)
void	SearchIndex (math_IntegerVector &Index)
void	MakeTAA (math_Vector &TheA, math_Vector &TheB)
	computes internal matrixes for the resolution
void	MakeTAA (math_Vector &TheA)
	computes internal matrixes for the resolution
void	MakeTAA (math_Vector &TheA, math_Matrix &TheB)
	computes internal matrixes for the resolution

Constructor & Destructor Documentation

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox() [1/4]

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox	(	const BRepApprox_TheMultiLineOfApprox &	SSP,
		const int	FirstPoint,
		const int	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const math_Vector &	Parameters,
		const int	NbPol )

given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. NbPol is the number of control points wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the Bernstein matrix computed with the parameters, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox() [2/4]

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox	(	const BRepApprox_TheMultiLineOfApprox &	SSP,
		const int	FirstPoint,
		const int	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const int	NbPol )

Initializes the fields of the object.

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox() [3/4]

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox	(	const BRepApprox_TheMultiLineOfApprox &	SSP,
		const NCollection_Array1< double > &	Knots,
		const NCollection_Array1< int > &	Mults,
		const int	FirstPoint,
		const int	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const math_Vector &	Parameters,
		const int	NbPol )

given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. Deg is the degree wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the BSpline functions matrix computed with <parameters>, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox() [4/4]

BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox	(	const BRepApprox_TheMultiLineOfApprox &	SSP,
		const NCollection_Array1< double > &	Knots,
		const NCollection_Array1< int > &	Mults,
		const int	FirstPoint,
		const int	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const int	NbPol )

Initializes the fields of the object.

Member Function Documentation

Affect()

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Affect ( const BRepApprox_TheMultiLineOfApprox & SSP, const int Index, AppParCurves_Constraint & Cons, math_Vector & Vt, math_Vector & Vc )

protected

Affects the fields in the case of a constraint point.

BezierValue()

AppParCurves_MultiCurve BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::BezierValue

(

)

returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.

BSplineValue()

const AppParCurves_MultiBSpCurve & BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::BSplineValue

(

)

returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.

ComputeFunction()

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::ComputeFunction ( const math_Vector & Parameters )

protected

DerivativeFunctionMatrix()

const math_Matrix & BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::DerivativeFunctionMatrix

(

)

const

returns the derivative function matrix used to approximate the set.

Distance()

const math_Matrix & BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Distance

(

)

returns the distances between the points of the multiline and the approximation curves.

Error()

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Error	(	double &	F,
		double &	MaxE3d,
		double &	MaxE2d )

returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances.

ErrorGradient()

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::ErrorGradient	(	math_Vector &	Grad,
		double &	F,
		double &	MaxE3d,
		double &	MaxE2d )

returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances. Grad is the derivative vector of the function F.

FirstLambda()

double BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::FirstLambda

(

)

const

returns the value (P2 - P1)/ V1 if the first point was a tangency point.

FunctionMatrix()

const math_Matrix & BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::FunctionMatrix

(

)

const

returns the function matrix used to approximate the set.

Init()

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Init ( const BRepApprox_TheMultiLineOfApprox & SSP, const int FirstPoint, const int LastPoint )

protected

is used by the constructors above.

IsDone()

bool BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::IsDone

(

)

const

returns True if all has been correctly done.

KIndex()

const math_IntegerVector & BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::KIndex

(

)

const

Returns the indexes of the first non null values of A and DA. The values are non null from Index(ieme point) +1 to Index(ieme point) + degree +1.

LastLambda()

double BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::LastLambda

(

)

const

returns the value (PN - PN-1)/ VN if the last point was a tangency point.

MakeTAA() [1/3]

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::MakeTAA ( math_Vector & TheA )

protected

computes internal matrixes for the resolution

MakeTAA() [2/3]

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::MakeTAA ( math_Vector & TheA, math_Matrix & TheB )

protected

computes internal matrixes for the resolution

MakeTAA() [3/3]

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::MakeTAA ( math_Vector & TheA, math_Vector & TheB )

protected

computes internal matrixes for the resolution

NbBColumns()

int BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::NbBColumns ( const BRepApprox_TheMultiLineOfApprox & SSP ) const

protected

returns the number of second member columns. Is used internally to initialize the fields.

Perform() [1/4]

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Perform

(

const math_Vector &

Parameters

)

Is used after having initialized the fields. The case "CurvaturePoint" is not treated in this method.

Perform() [2/4]

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Perform	(	const math_Vector &	Parameters,
		const double	l1,
		const double	l2 )

Is used after having initialized the fields.

Perform() [3/4]

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Perform	(	const math_Vector &	Parameters,
		const math_Vector &	V1t,
		const math_Vector &	V2t,
		const double	l1,
		const double	l2 )

Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point.

Perform() [4/4]

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Perform	(	const math_Vector &	Parameters,
		const math_Vector &	V1t,
		const math_Vector &	V2t,
		const math_Vector &	V1c,
		const math_Vector &	V2c,
		const double	l1,
		const double	l2 )

Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point. <V1c> is the tangent vector at the first point. <V2c> is the tangent vector at the last point.

Points()

const math_Matrix & BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Points

(

)

const

returns the matrix of points value.

Poles()

const math_Matrix & BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::Poles

(

)

const

returns the matrix of resulting control points value.

SearchIndex()

void BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::SearchIndex ( math_IntegerVector & Index )

protected

TheFirstPoint()

int BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::TheFirstPoint ( const AppParCurves_Constraint FirstCons, const int FirstPoint ) const

protected

returns the first point being fitted.

TheLastPoint()

int BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox::TheLastPoint ( const AppParCurves_Constraint LastCons, const int LastPoint ) const

protected

returns the last point being fitted.

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

• BRepApprox_ParLeastSquareOfMyGradientOfTheComputeLineBezierOfApprox.hxx