`#include <GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox.hxx>`

## Public Member Functions

GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox (const GeomInt_TheMultiLineOfWLApprox &SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector &Parameters, const Standard_Integer 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). More...

GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox (const GeomInt_TheMultiLineOfWLApprox &SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const Standard_Integer NbPol)
Initializes the fields of the object. More...

GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox (const GeomInt_TheMultiLineOfWLApprox &SSP, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector &Parameters, const Standard_Integer 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). More...

GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox (const GeomInt_TheMultiLineOfWLApprox &SSP, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const Standard_Integer NbPol)
Initializes the fields of the object. More...

void Perform (const math_Vector &Parameters)
Is used after having initialized the fields. The case "CurvaturePoint" is not treated in this method. More...

void Perform (const math_Vector &Parameters, const Standard_Real l1, const Standard_Real l2)
Is used after having initialized the fields. More...

void Perform (const math_Vector &Parameters, const math_Vector &V1t, const math_Vector &V2t, const Standard_Real l1, const Standard_Real 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. More...

void Perform (const math_Vector &Parameters, const math_Vector &V1t, const math_Vector &V2t, const math_Vector &V1c, const math_Vector &V2c, const Standard_Real l1, const Standard_Real 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. More...

Standard_Boolean IsDone () const
returns True if all has been correctly done. More...

AppParCurves_MultiCurve BezierValue ()
returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone. More...

const AppParCurves_MultiBSpCurveBSplineValue ()
returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone. More...

const math_MatrixFunctionMatrix () const
returns the function matrix used to approximate the set. More...

const math_MatrixDerivativeFunctionMatrix () const
returns the derivative function matrix used to approximate the set. More...

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. More...

const math_MatrixDistance ()
returns the distances between the points of the multiline and the approximation curves. More...

void Error (Standard_Real &F, Standard_Real &MaxE3d, Standard_Real &MaxE2d)
returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances. More...

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

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

const math_MatrixPoints () const
returns the matrix of points value. More...

const math_MatrixPoles () const
returns the matrix of resulting control points value. More...

const math_IntegerVectorKIndex () 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. More...

## Protected Member Functions

void Init (const GeomInt_TheMultiLineOfWLApprox &SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint)
is used by the constructors above. More...

Standard_Integer NbBColumns (const GeomInt_TheMultiLineOfWLApprox &SSP) const
returns the number of second member columns. Is used internally to initialize the fields. More...

Standard_Integer TheFirstPoint (const AppParCurves_Constraint FirstCons, const Standard_Integer FirstPoint) const
returns the first point being fitted. More...

Standard_Integer TheLastPoint (const AppParCurves_Constraint LastCons, const Standard_Integer LastPoint) const
returns the last point being fitted. More...

void Affect (const GeomInt_TheMultiLineOfWLApprox &SSP, const Standard_Integer Index, AppParCurves_Constraint &Cons, math_Vector &Vt, math_Vector &Vc)
Affects the fields in the case of a constraint point. More...

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 More...

void MakeTAA (math_Vector &TheA)
computes internal matrixes for the resolution More...

void MakeTAA (math_Vector &TheA, math_Matrix &TheB)
computes internal matrixes for the resolution More...

## Constructor & Destructor Documentation

 GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox ( const GeomInt_TheMultiLineOfWLApprox & SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector & Parameters, const Standard_Integer 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).

 GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox ( const GeomInt_TheMultiLineOfWLApprox & SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const Standard_Integer NbPol )

Initializes the fields of the object.

 GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox ( const GeomInt_TheMultiLineOfWLApprox & SSP, const TColStd_Array1OfReal & Knots, const TColStd_Array1OfInteger & Mults, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector & Parameters, const Standard_Integer 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).

 GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox ( const GeomInt_TheMultiLineOfWLApprox & SSP, const TColStd_Array1OfReal & Knots, const TColStd_Array1OfInteger & Mults, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const Standard_Integer NbPol )

Initializes the fields of the object.

## ◆ Affect()

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Affect ( const GeomInt_TheMultiLineOfWLApprox & SSP, const Standard_Integer Index, AppParCurves_Constraint & Cons, math_Vector & Vt, math_Vector & Vc )
protected

Affects the fields in the case of a constraint point.

## ◆ BezierValue()

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

## ◆ BSplineValue()

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

## ◆ ComputeFunction()

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::ComputeFunction ( const math_Vector & Parameters )
protected

## ◆ DerivativeFunctionMatrix()

 const math_Matrix& GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::DerivativeFunctionMatrix ( ) const

returns the derivative function matrix used to approximate the set.

## ◆ Distance()

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

## ◆ Error()

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Error ( Standard_Real & F, Standard_Real & MaxE3d, Standard_Real & MaxE2d )

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

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()

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

## ◆ FunctionMatrix()

 const math_Matrix& GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::FunctionMatrix ( ) const

returns the function matrix used to approximate the set.

## ◆ Init()

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Init ( const GeomInt_TheMultiLineOfWLApprox & SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint )
protected

is used by the constructors above.

## ◆ IsDone()

returns True if all has been correctly done.

## ◆ KIndex()

 const math_IntegerVector& GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::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()

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

## ◆ MakeTAA() [1/3]

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::MakeTAA ( math_Vector & TheA )
protected

computes internal matrixes for the resolution

## ◆ MakeTAA() [2/3]

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::MakeTAA ( math_Vector & TheA, math_Matrix & TheB )
protected

computes internal matrixes for the resolution

## ◆ MakeTAA() [3/3]

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::MakeTAA ( math_Vector & TheA, math_Vector & TheB )
protected

computes internal matrixes for the resolution

## ◆ NbBColumns()

 Standard_Integer GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::NbBColumns ( const GeomInt_TheMultiLineOfWLApprox & SSP ) const
protected

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

## ◆ Perform() [1/4]

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::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 GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Perform ( const math_Vector & Parameters, const math_Vector & V1t, const math_Vector & V2t, const math_Vector & V1c, const math_Vector & V2c, const Standard_Real l1, const Standard_Real 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.

## ◆ Perform() [3/4]

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Perform ( const math_Vector & Parameters, const math_Vector & V1t, const math_Vector & V2t, const Standard_Real l1, const Standard_Real 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 GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Perform ( const math_Vector & Parameters, const Standard_Real l1, const Standard_Real l2 )

Is used after having initialized the fields.

## ◆ Points()

 const math_Matrix& GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Points ( ) const

returns the matrix of points value.

## ◆ Poles()

 const math_Matrix& GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::Poles ( ) const

returns the matrix of resulting control points value.

## ◆ SearchIndex()

 void GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::SearchIndex ( math_IntegerVector & Index )
protected

## ◆ TheFirstPoint()

 Standard_Integer GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::TheFirstPoint ( const AppParCurves_Constraint FirstCons, const Standard_Integer FirstPoint ) const
protected

returns the first point being fitted.

## ◆ TheLastPoint()

 Standard_Integer GeomInt_ParLeastSquareOfMyGradientbisOfTheComputeLineOfWLApprox::TheLastPoint ( const AppParCurves_Constraint LastCons, const Standard_Integer LastPoint ) const
protected

returns the last point being fitted.

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