OCC.Core.AppDef module

AppDef module, see official documentation at https://www.opencascade.com/doc/occt-7.4.0/refman/html/package_appdef.html

class AppDef_Array1OfMultiPointConstraint(*args)

Bases: object

Assign()

ChangeFirst()

ChangeLast()

ChangeValue()

First()

Init()

IsAllocated()

IsDeletable()

IsEmpty()

Last()

Length()

Lower()

Move()

Resize()

Set()

SetValue()

Size()

Upper()

Value()

begin()

cbegin()

cend()

end()

next()

property thisown

The membership flag

class AppDef_BSpGradient_BFGSOfMyBSplGradientOfBSplineCompute(*args)

Bases: OCC.Core.math.math_BFGS

Parameters

F –

type F

math_MultipleVarFunctionWithGradient

param StartingPoint

type StartingPoint

math_Vector

param Tolerance3d

type Tolerance3d

float

param Tolerance2d

type Tolerance2d

float

param Eps

type Eps

float

param NbIterations

default value is 200

type NbIterations

int

rtype

None

property thisown

The membership flag

class AppDef_BSpParFunctionOfMyBSplGradientOfBSplineCompute(*args)

Bases: OCC.Core.math.math_MultipleVarFunctionWithGradient

• initializes the fields of the function. The approximating curve has <NbPol> control points.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param NbPol

  type NbPol

  int

  rtype

  None

CurveValue()

• returns the MultiBSpCurve approximating the set after computing the value F or Grad(F).

  rtype

  AppParCurves_MultiBSpCurve

DerivativeFunctionMatrix()

• returns the derivative function matrix used to approximate the multiline.

  rtype

  math_Matrix

Error()

• returns the distance between the MultiPoint of range IPoint and the curve CurveIndex.

  param IPoint

  type IPoint

  int

  param CurveIndex

  type CurveIndex

  int

  rtype

  float

FirstConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param FirstPoint

type FirstPoint

int

rtype

AppParCurves_Constraint

FunctionMatrix()

• returns the function matrix used to approximate the multiline.

  rtype

  math_Matrix

Index()

• 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.

  rtype

  math_IntegerVector

LastConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param LastPoint

type LastPoint

int

rtype

AppParCurves_Constraint

MaxError2d()

• returns the maximum distance between the points and the MultiBSpCurve.

  rtype

  float

MaxError3d()

• returns the maximum distance between the points and the MultiBSpCurve.

  rtype

  float

NewParameters()

• returns the new parameters of the MultiLine.

  rtype

  math_Vector

SetFirstLambda()

Parameters

l1 –

type l1

float

rtype

None

SetLastLambda()

Parameters

l2 –

type l2

float

rtype

None

property thisown

The membership flag

class AppDef_BSpParLeastSquareOfMyBSplGradientOfBSplineCompute(*args)

Bases: object

• 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None* 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None

BSplineValue()

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

  rtype

  AppParCurves_MultiBSpCurve

BezierValue()

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

  rtype

  AppParCurves_MultiCurve

DerivativeFunctionMatrix()

• returns the derivative function matrix used to approximate the set.

  rtype

  math_Matrix

Distance()

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

  rtype

  math_Matrix

Error()

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

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

ErrorGradient()

• 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.

  param Grad

  type Grad

  math_Vector

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

FirstLambda()

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

  rtype

  float

FunctionMatrix()

• returns the function matrix used to approximate the set.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

KIndex()

• 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.

  rtype

  math_IntegerVector

LastLambda()

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

  rtype

  float

Perform()

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

  param Parameters

  type Parameters

  math_Vector

  rtype

  None* Is used after having initialized the fields.

  param Parameters

  type Parameters

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param V1c

  type V1c

  math_Vector

  param V2c

  type V2c

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None

Points()

• returns the matrix of points value.

  rtype

  math_Matrix

Poles()

• returns the matrix of resulting control points value.

  rtype

  math_Matrix

property thisown

The membership flag

class AppDef_BSplineCompute(*args)

Bases: object

• The MultiLine <Line> will be approximated until tolerances will be reached. The approximation will be done from degreemin to degreemax with a cutting if the corresponding boolean is True. If <Squares> is True, the computation will be done with no iteration at all. //! The multiplicities of the internal knots is set by default.

  param Line

  type Line

  AppDef_MultiLine

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-3

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-6

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param parametrization

  default value is Approx_ChordLength

  type parametrization

  Approx_ParametrizationType

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None* The MultiLine <Line> will be approximated until tolerances will be reached. The approximation will be done from degreemin to degreemax with a cutting if the corresponding boolean is True. If <Squares> is True, the computation will be done with no iteration at all.

  param Line

  type Line

  AppDef_MultiLine

  param Parameters

  type Parameters

  math_Vector

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None* Initializes the fields of the algorithm.

  param Parameters

  type Parameters

  math_Vector

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None* Initializes the fields of the algorithm.

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param parametrization

  default value is Approx_ChordLength

  type parametrization

  Approx_ParametrizationType

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None

ChangeValue()

• returns the result of the approximation.

  rtype

  AppParCurves_MultiBSpCurve

Error()

• returns the tolerances 2d and 3d of the MultiBSpCurve.

  param tol3d

  type tol3d

  float

  param tol2d

  type tol2d

  float

  rtype

  None

Init()

• Initializes the fields of the algorithm.

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param parametrization

  default value is Approx_ChordLength

  type parametrization

  Approx_ParametrizationType

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None

Interpol()

• Constructs an interpolation of the MultiLine <Line> The result will be a C2 curve of degree 3.

  param Line

  type Line

  AppDef_MultiLine

  rtype

  None

IsAllApproximated()

• returns False if at a moment of the approximation, the status NoApproximation has been sent by the user when more points were needed.

  rtype

  bool

IsToleranceReached()

• returns False if the status NoPointsAdded has been sent.

  rtype

  bool

Parameters()

• returns the new parameters of the approximation corresponding to the points of the MultiBSpCurve.

  rtype

  TColStd_Array1OfReal

Perform()

• runs the algorithm after having initialized the fields.

  param Line

  type Line

  AppDef_MultiLine

  rtype

  None

SetConstraints()

• changes the first and the last constraint points.

  param firstC

  type firstC

  AppParCurves_Constraint

  param lastC

  type lastC

  AppParCurves_Constraint

  rtype

  None

SetContinuity()

• sets the continuity of the spline. if C = 2, the spline will be C2.

  param C

  type C

  int

  rtype

  None

SetDegrees()

• changes the degrees of the approximation.

  param degreemin

  type degreemin

  int

  param degreemax

  type degreemax

  int

  rtype

  None

SetKnots()

• The approximation will be done with the set of knots <Knots>. The multiplicities will be set with the degree and the desired continuity.

  param Knots

  type Knots

  TColStd_Array1OfReal

  rtype

  None

SetKnotsAndMultiplicities()

• The approximation will be done with the set of knots <Knots> and the multiplicities <Mults>.

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  rtype

  None

SetParameters()

• The approximation will begin with the set of parameters <ThePar>.

  param ThePar

  type ThePar

  math_Vector

  rtype

  None

SetPeriodic()

• Sets periodic flag. If thePeriodic = Standard_True, algorith tries to build periodic multicurve using corresponding C1 boundary condition for first and last multipoints. Multiline must be closed.

  param thePeriodic

  type thePeriodic

  bool

  rtype

  None

SetTolerances()

• Changes the tolerances of the approximation.

  param Tolerance3d

  type Tolerance3d

  float

  param Tolerance2d

  type Tolerance2d

  float

  rtype

  None

Value()

• returns the result of the approximation.

  rtype

  AppParCurves_MultiBSpCurve

property thisown

The membership flag

class AppDef_Compute(*args)

Bases: object

• The MultiLine <Line> will be approximated until tolerances will be reached. The approximation will be done from degreemin to degreemax with a cutting if the corresponding boolean is True. If <Squares> is True, the computation will be done with no iteration at all.

  param Line

  type Line

  AppDef_MultiLine

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-3

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-6

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param parametrization

  default value is Approx_ChordLength

  type parametrization

  Approx_ParametrizationType

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None* The MultiLine <Line> will be approximated until tolerances will be reached. The approximation will be done from degreemin to degreemax with a cutting if the corresponding boolean is True. If <Squares> is True, the computation will be done with no iteration at all.

  param Line

  type Line

  AppDef_MultiLine

  param Parameters

  type Parameters

  math_Vector

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None* Initializes the fields of the algorithm.

  param Parameters

  type Parameters

  math_Vector

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None* Initializes the fields of the algorithm.

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param parametrization

  default value is Approx_ChordLength

  type parametrization

  Approx_ParametrizationType

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None

ChangeValue()

• returns the result of the approximation.

  param Index

  default value is 1

  type Index

  int

  rtype

  AppParCurves_MultiCurve

Error()

• returns the tolerances 2d and 3d of the <Index> MultiCurve.

  param Index

  type Index

  int

  param tol3d

  type tol3d

  float

  param tol2d

  type tol2d

  float

  rtype

  None

Init()

• Initializes the fields of the algorithm.

  param degreemin

  default value is 4

  type degreemin

  int

  param degreemax

  default value is 8

  type degreemax

  int

  param Tolerance3d

  default value is 1.0e-03

  type Tolerance3d

  float

  param Tolerance2d

  default value is 1.0e-06

  type Tolerance2d

  float

  param NbIterations

  default value is 5

  type NbIterations

  int

  param cutting

  default value is Standard_True

  type cutting

  bool

  param parametrization

  default value is Approx_ChordLength

  type parametrization

  Approx_ParametrizationType

  param Squares

  default value is Standard_False

  type Squares

  bool

  rtype

  None

IsAllApproximated()

• returns False if at a moment of the approximation, the status NoApproximation has been sent by the user when more points were needed.

  rtype

  bool

IsToleranceReached()

• returns False if the status NoPointsAdded has been sent.

  rtype

  bool

NbMultiCurves()

• Returns the number of MultiCurve doing the approximation of the MultiLine.

  rtype

  int

Parameters()

• returns the new parameters of the approximation corresponding to the points of the multicurve <Index>.

  param Index

  default value is 1

  type Index

  int

  rtype

  TColStd_Array1OfReal

Parametrization()

• returns the type of parametrization

  rtype

  Approx_ParametrizationType

Perform()

• runs the algorithm after having initialized the fields.

  param Line

  type Line

  AppDef_MultiLine

  rtype

  None

SetConstraints()

• changes the first and the last constraint points.

  param firstC

  type firstC

  AppParCurves_Constraint

  param lastC

  type lastC

  AppParCurves_Constraint

  rtype

  None

SetDegrees()

• changes the degrees of the approximation.

  param degreemin

  type degreemin

  int

  param degreemax

  type degreemax

  int

  rtype

  None

SetTolerances()

• Changes the tolerances of the approximation.

  param Tolerance3d

  type Tolerance3d

  float

  param Tolerance2d

  type Tolerance2d

  float

  rtype

  None

SplineValue()

• returns the result of the approximation.

  rtype

  AppParCurves_MultiBSpCurve

Value()

• returns the result of the approximation.

  param Index

  default value is 1

  type Index

  int

  rtype

  AppParCurves_MultiCurve

property thisown

The membership flag

class AppDef_Gradient_BFGSOfMyGradientOfCompute(*args)

Bases: OCC.Core.math.math_BFGS

Parameters

F –

type F

math_MultipleVarFunctionWithGradient

param StartingPoint

type StartingPoint

math_Vector

param Tolerance3d

type Tolerance3d

float

param Tolerance2d

type Tolerance2d

float

param Eps

type Eps

float

param NbIterations

default value is 200

type NbIterations

int

rtype

None

property thisown

The membership flag

class AppDef_Gradient_BFGSOfMyGradientbisOfBSplineCompute(*args)

Bases: OCC.Core.math.math_BFGS

Parameters

F –

type F

math_MultipleVarFunctionWithGradient

param StartingPoint

type StartingPoint

math_Vector

param Tolerance3d

type Tolerance3d

float

param Tolerance2d

type Tolerance2d

float

param Eps

type Eps

float

param NbIterations

default value is 200

type NbIterations

int

rtype

None

property thisown

The membership flag

class AppDef_Gradient_BFGSOfTheGradient(*args)

Bases: OCC.Core.math.math_BFGS

Parameters

F –

type F

math_MultipleVarFunctionWithGradient

param StartingPoint

type StartingPoint

math_Vector

param Tolerance3d

type Tolerance3d

float

param Tolerance2d

type Tolerance2d

float

param Eps

type Eps

float

param NbIterations

default value is 200

type NbIterations

int

rtype

None

property thisown

The membership flag

class AppDef_HArray1OfMultiPointConstraint(*args)

Bases: OCC.Core.AppDef.AppDef_Array1OfMultiPointConstraint, OCC.Core.Standard.Standard_Transient

• Empty constructor

Return type

None* Copy constructor – does nothing

Parameters

& (Standard_Transient) –

Return type

None

Array1()

ChangeArray1()

static DownCast(t)

property thisown

The membership flag

class AppDef_LinearCriteria(*args)

Bases: OCC.Core.AppDef.AppDef_SmoothCriterion

Parameters

SSP –

type SSP

AppDef_MultiLine

param FirstPoint

type FirstPoint

int

param LastPoint

type LastPoint

int

rtype

None

static DownCast(t)

GetEstLength(AppDef_LinearCriteria self) → Standard_Real

SetEstLength(AppDef_LinearCriteria self, Standard_Real value)

SetWeight()

Parameters

QuadraticWeight –

type QuadraticWeight

float

param QualityWeight

type QualityWeight

float

param percentJ1

type percentJ1

float

param percentJ2

type percentJ2

float

param percentJ3

type percentJ3

float

rtype

None:param Weight:

type Weight

TColStd_Array1OfReal

rtype

None

property thisown

The membership flag

class AppDef_MultiLine(*args)

Bases: object

• creates an undefined MultiLine.

  rtype

  None* given the number NbMult of MultiPointConstraints of this MultiLine , it initializes all the fields.SetValue must be called in order for the values of the multipoint constraint to be taken into account. An exception is raised if NbMult < 0.

  param NbMult

  type NbMult

  int

  rtype

  None* Constructs a MultiLine with an array of MultiPointConstraints.

  param tabMultiP

  type tabMultiP

  AppDef_Array1OfMultiPointConstraint

  rtype

  None* The MultiLine constructed will have one line of 3d points without their tangencies.

  param tabP3d

  type tabP3d

  TColgp_Array1OfPnt

  rtype

  None* The MultiLine constructed will have one line of 2d points without their tangencies.

  param tabP2d

  type tabP2d

  TColgp_Array1OfPnt2d

  rtype

  None

DumpToString(AppDef_MultiLine self) → std::string

NbMultiPoints()

• returns the number of MultiPointConstraints of the MultiLine.

  rtype

  int

NbPoints()

• returns the number of Points from MultiPoints composing the MultiLine.

  rtype

  int

SetValue()

• It sets the MultiPointConstraint of range Index to the value MPoint. An exception is raised if Index < 0 or Index> MPoint. An exception is raised if the dimensions of the MultiPoints are different.

  param Index

  type Index

  int

  param MPoint

  type MPoint

  AppDef_MultiPointConstraint

  rtype

  None

Value()

• returns the MultiPointConstraint of range Index An exception is raised if Index<0 or Index>MPoint.

  param Index

  type Index

  int

  rtype

  AppDef_MultiPointConstraint

property thisown

The membership flag

class AppDef_MultiPointConstraint(*args)

Bases: OCC.Core.AppParCurves.AppParCurves_MultiPoint

• creates an undefined MultiPointConstraint.

  rtype

  None* constructs a set of Points used to approximate a Multiline. These Points can be of 2 or 3 dimensions. Points will be initialized with SetPoint and SetPoint2d.

  param NbPoints

  type NbPoints

  int

  param NbPoints2d

  type NbPoints2d

  int

  rtype

  None* creates a MultiPoint only composed of 3D points.

  param tabP

  type tabP

  TColgp_Array1OfPnt

  rtype

  None* creates a MultiPoint only composed of 2D points.

  param tabP

  type tabP

  TColgp_Array1OfPnt2d

  rtype

  None* constructs a set of Points used to approximate a Multiline. These Points can be of 2 or 3 dimensions. Points will be initialized with SetPoint and SetPoint2d.

  param tabP

  type tabP

  TColgp_Array1OfPnt

  param tabP2d

  type tabP2d

  TColgp_Array1OfPnt2d

  rtype

  None* creates a MultiPointConstraint with a constraint of Curvature. An exception is raised if (length of <tabP> + length of <tabP2d> ) is different from (length of <tabVec> + length of <tabVec2d> ) or from (length of <tabCur> + length of <tabCur2d> )

  param tabP

  type tabP

  TColgp_Array1OfPnt

  param tabP2d

  type tabP2d

  TColgp_Array1OfPnt2d

  param tabVec

  type tabVec

  TColgp_Array1OfVec

  param tabVec2d

  type tabVec2d

  TColgp_Array1OfVec2d

  param tabCur

  type tabCur

  TColgp_Array1OfVec

  param tabCur2d

  type tabCur2d

  TColgp_Array1OfVec2d

  rtype

  None* creates a MultiPointConstraint with a constraint of Tangency. An exception is raised if (length of <tabP> + length of <tabP2d> ) is different from (length of <tabVec> + length of <tabVec2d> )

  param tabP

  type tabP

  TColgp_Array1OfPnt

  param tabP2d

  type tabP2d

  TColgp_Array1OfPnt2d

  param tabVec

  type tabVec

  TColgp_Array1OfVec

  param tabVec2d

  type tabVec2d

  TColgp_Array1OfVec2d

  rtype

  None* creates a MultiPointConstraint only composed of 3d points with constraints of curvature. An exception is raised if the length of tabP is different from the length of tabVec or from tabCur.

  param tabP

  type tabP

  TColgp_Array1OfPnt

  param tabVec

  type tabVec

  TColgp_Array1OfVec

  param tabCur

  type tabCur

  TColgp_Array1OfVec

  rtype

  None* creates a MultiPointConstraint only composed of 3d points with constraints of tangency. An exception is raised if the length of tabP is different from the length of tabVec.

  param tabP

  type tabP

  TColgp_Array1OfPnt

  param tabVec

  type tabVec

  TColgp_Array1OfVec

  rtype

  None* creates a MultiPointConstraint only composed of 2d points with constraints of tangency. An exception is raised if the length of tabP is different from the length of tabVec2d.

  param tabP2d

  type tabP2d

  TColgp_Array1OfPnt2d

  param tabVec2d

  type tabVec2d

  TColgp_Array1OfVec2d

  rtype

  None* creates a MultiPointConstraint only composed of 2d points with constraints of curvature. An exception is raised if the length of tabP is different from the length of tabVec2d or from tabCur2d.

  param tabP2d

  type tabP2d

  TColgp_Array1OfPnt2d

  param tabVec2d

  type tabVec2d

  TColgp_Array1OfVec2d

  param tabCur2d

  type tabCur2d

  TColgp_Array1OfVec2d

  rtype

  None

Curv()

• returns the normal vector at the point of range Index. An exception is raised if Index < 0 or if Index > number of 3d points.

  param Index

  type Index

  int

  rtype

  gp_Vec

Curv2d()

• returns the normal vector at the point of range Index. An exception is raised if Index < 0 or if Index > number of 3d points.

  param Index

  type Index

  int

  rtype

  gp_Vec2d

DumpToString(AppDef_MultiPointConstraint self) → std::string

IsCurvaturePoint()

• returns True if the MultiPoint has a curvature value.

  rtype

  bool

IsTangencyPoint()

• returns True if the MultiPoint has a tangency value.

  rtype

  bool

SetCurv()

• Vec sets the value of the normal vector at the point of index Index. The norm of the normal vector at the point of position Index is set to the normal curvature. An exception is raised if Index <0 or if Index > number of 3d points. An exception is raised if Curv has an incorrect number of dimensions.

  param Index

  type Index

  int

  param Curv

  type Curv

  gp_Vec

  rtype

  None

SetCurv2d()

• Vec sets the value of the normal vector at the point of index Index. The norm of the normal vector at the point of position Index is set to the normal curvature. An exception is raised if Index <0 or if Index > number of 3d points. An exception is raised if Curv has an incorrect number of dimensions.

  param Index

  type Index

  int

  param Curv2d

  type Curv2d

  gp_Vec2d

  rtype

  None

SetTang()

• sets the value of the tangency of the point of range Index. An exception is raised if Index <0 or if Index > number of 3d points. An exception is raised if Tang has an incorrect number of dimensions.

  param Index

  type Index

  int

  param Tang

  type Tang

  gp_Vec

  rtype

  None

SetTang2d()

• sets the value of the tangency of the point of range Index. An exception is raised if Index <number of 3d points or if Index > total number of Points An exception is raised if Tang has an incorrect number of dimensions.

  param Index

  type Index

  int

  param Tang2d

  type Tang2d

  gp_Vec2d

  rtype

  None

Tang()

• returns the tangency value of the point of range Index. An exception is raised if Index < 0 or if Index > number of 3d points.

  param Index

  type Index

  int

  rtype

  gp_Vec

Tang2d()

• returns the tangency value of the point of range Index. An exception is raised if Index < number of 3d points or if Index > total number of points.

  param Index

  type Index

  int

  rtype

  gp_Vec2d

property thisown

The membership flag

class AppDef_MyBSplGradientOfBSplineCompute(*args)

Bases: object

• Tries to minimize the sum (square(||Qui - Bi*Pi||)) where Pui describe the approximating BSpline curves’Poles and Qi the MultiLine points with a parameter ui. In this algorithm, the parameters ui are the unknowns. The tolerance required on this sum is given by Tol. The desired degree of the resulting curve is Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param Deg

  type Deg

  int

  param Tol3d

  type Tol3d

  float

  param Tol2d

  type Tol2d

  float

  param NbIterations

  default value is 1

  type NbIterations

  int

  rtype

  None* Tries to minimize the sum (square(||Qui - Bi*Pi||)) where Pui describe the approximating BSpline curves’Poles and Qi the MultiLine points with a parameter ui. In this algorithm, the parameters ui are the unknowns. The tolerance required on this sum is given by Tol. The desired degree of the resulting curve is Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param Deg

  type Deg

  int

  param Tol3d

  type Tol3d

  float

  param Tol2d

  type Tol2d

  float

  param NbIterations

  type NbIterations

  int

  param lambda1

  type lambda1

  float

  param lambda2

  type lambda2

  float

  rtype

  None

AverageError()

• returns the average error between the old and the new approximation.

  rtype

  float

Error()

• returns the difference between the old and the new approximation. An exception is raised if NotDone. An exception is raised if Index<1 or Index>NbParameters.

  param Index

  type Index

  int

  rtype

  float

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

MaxError2d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

MaxError3d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

Value()

• returns all the BSpline curves approximating the MultiLine SSP after minimization of the parameter.

  rtype

  AppParCurves_MultiBSpCurve

property thisown

The membership flag

class AppDef_MyGradientOfCompute(*args)

Bases: object

• Tries to minimize the sum (square(||Qui - Bi*Pi||)) where Pui describe the approximating Bezier curves’Poles and Qi the MultiLine points with a parameter ui. In this algorithm, the parameters ui are the unknowns. The tolerance required on this sum is given by Tol. The desired degree of the resulting curve is Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  param Tol3d

  type Tol3d

  float

  param Tol2d

  type Tol2d

  float

  param NbIterations

  default value is 200

  type NbIterations

  int

  rtype

  None

AverageError()

• returns the average error between the old and the new approximation.

  rtype

  float

Error()

• returns the difference between the old and the new approximation. An exception is raised if NotDone. An exception is raised if Index<1 or Index>NbParameters.

  param Index

  type Index

  int

  rtype

  float

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

MaxError2d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

MaxError3d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

Value()

• returns all the Bezier curves approximating the MultiLine SSP after minimization of the parameter.

  rtype

  AppParCurves_MultiCurve

property thisown

The membership flag

class AppDef_MyGradientbisOfBSplineCompute(*args)

Bases: object

• Tries to minimize the sum (square(||Qui - Bi*Pi||)) where Pui describe the approximating Bezier curves’Poles and Qi the MultiLine points with a parameter ui. In this algorithm, the parameters ui are the unknowns. The tolerance required on this sum is given by Tol. The desired degree of the resulting curve is Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  param Tol3d

  type Tol3d

  float

  param Tol2d

  type Tol2d

  float

  param NbIterations

  default value is 200

  type NbIterations

  int

  rtype

  None

AverageError()

• returns the average error between the old and the new approximation.

  rtype

  float

Error()

• returns the difference between the old and the new approximation. An exception is raised if NotDone. An exception is raised if Index<1 or Index>NbParameters.

  param Index

  type Index

  int

  rtype

  float

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

MaxError2d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

MaxError3d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

Value()

• returns all the Bezier curves approximating the MultiLine SSP after minimization of the parameter.

  rtype

  AppParCurves_MultiCurve

property thisown

The membership flag

class AppDef_MyLineTool

Bases: object

static Curvature()

• returns the 3d curvatures of the multipoint <MPointIndex> when only 3d points exist.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabV

  type tabV

  TColgp_Array1OfVec

  rtype

  bool* returns the 2d curvatures of the multipoint <MPointIndex> only when 2d points exist.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabV2d

  type tabV2d

  TColgp_Array1OfVec2d

  rtype

  bool* returns the 3d and 2d curvatures of the multipoint <MPointIndex>.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabV

  type tabV

  TColgp_Array1OfVec

  param tabV2d

  type tabV2d

  TColgp_Array1OfVec2d

  rtype

  bool

static FirstPoint()

• Returns the first index of multipoints of the MultiLine.

  param ML

  type ML

  AppDef_MultiLine

  rtype

  int

static LastPoint()

• Returns the last index of multipoints of the MultiLine.

  param ML

  type ML

  AppDef_MultiLine

  rtype

  int

static MakeMLBetween()

• Is never called in the algorithms. Nothing is done.

  param ML

  type ML

  AppDef_MultiLine

  param I1

  type I1

  int

  param I2

  type I2

  int

  param NbPMin

  type NbPMin

  int

  rtype

  AppDef_MultiLine

static MakeMLOneMorePoint()

• Is never called in the algorithms. Nothing is done.

  param ML

  type ML

  AppDef_MultiLine

  param I1

  type I1

  int

  param I2

  type I2

  int

  param indbad

  type indbad

  int

  param OtherLine

  type OtherLine

  AppDef_MultiLine

  rtype

  bool

static NbP2d()

• Returns the number of 2d points of a MultiLine.

  param ML

  type ML

  AppDef_MultiLine

  rtype

  int

static NbP3d()

• Returns the number of 3d points of a MultiLine.

  param ML

  type ML

  AppDef_MultiLine

  rtype

  int

static Tangency()

• returns the 3d points of the multipoint <MPointIndex> when only 3d points exist.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabV

  type tabV

  TColgp_Array1OfVec

  rtype

  bool* returns the 2d tangency points of the multipoint <MPointIndex> only when 2d points exist.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabV2d

  type tabV2d

  TColgp_Array1OfVec2d

  rtype

  bool* returns the 3d and 2d points of the multipoint <MPointIndex>.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabV

  type tabV

  TColgp_Array1OfVec

  param tabV2d

  type tabV2d

  TColgp_Array1OfVec2d

  rtype

  bool

static Value()

• returns the 3d points of the multipoint <MPointIndex> when only 3d points exist.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabPt

  type tabPt

  TColgp_Array1OfPnt

  rtype

  void* returns the 2d points of the multipoint <MPointIndex> when only 2d points exist.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabPt2d

  type tabPt2d

  TColgp_Array1OfPnt2d

  rtype

  void* returns the 3d and 2d points of the multipoint <MPointIndex>.

  param ML

  type ML

  AppDef_MultiLine

  param MPointIndex

  type MPointIndex

  int

  param tabPt

  type tabPt

  TColgp_Array1OfPnt

  param tabPt2d

  type tabPt2d

  TColgp_Array1OfPnt2d

  rtype

  void

static WhatStatus()

• returns NoPointsAdded

  param ML

  type ML

  AppDef_MultiLine

  param I1

  type I1

  int

  param I2

  type I2

  int

  rtype

  Approx_Status

property thisown

The membership flag

class AppDef_ParFunctionOfMyGradientOfCompute(*args)

Bases: OCC.Core.math.math_MultipleVarFunctionWithGradient

• initializes the fields of the function. The approximating curve has the desired degree Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  rtype

  None

CurveValue()

• returns the MultiCurve approximating the set after computing the value F or Grad(F).

  rtype

  AppParCurves_MultiCurve

Error()

• returns the distance between the MultiPoint of range IPoint and the curve CurveIndex.

  param IPoint

  type IPoint

  int

  param CurveIndex

  type CurveIndex

  int

  rtype

  float

FirstConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param FirstPoint

type FirstPoint

int

rtype

AppParCurves_Constraint

LastConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param LastPoint

type LastPoint

int

rtype

AppParCurves_Constraint

MaxError2d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

MaxError3d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

NewParameters()

• returns the new parameters of the MultiLine.

  rtype

  math_Vector

property thisown

The membership flag

class AppDef_ParFunctionOfMyGradientbisOfBSplineCompute(*args)

Bases: OCC.Core.math.math_MultipleVarFunctionWithGradient

• initializes the fields of the function. The approximating curve has the desired degree Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  rtype

  None

CurveValue()

• returns the MultiCurve approximating the set after computing the value F or Grad(F).

  rtype

  AppParCurves_MultiCurve

Error()

• returns the distance between the MultiPoint of range IPoint and the curve CurveIndex.

  param IPoint

  type IPoint

  int

  param CurveIndex

  type CurveIndex

  int

  rtype

  float

FirstConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param FirstPoint

type FirstPoint

int

rtype

AppParCurves_Constraint

LastConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param LastPoint

type LastPoint

int

rtype

AppParCurves_Constraint

MaxError2d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

MaxError3d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

NewParameters()

• returns the new parameters of the MultiLine.

  rtype

  math_Vector

property thisown

The membership flag

class AppDef_ParFunctionOfTheGradient(*args)

Bases: OCC.Core.math.math_MultipleVarFunctionWithGradient

• initializes the fields of the function. The approximating curve has the desired degree Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  rtype

  None

CurveValue()

• returns the MultiCurve approximating the set after computing the value F or Grad(F).

  rtype

  AppParCurves_MultiCurve

Error()

• returns the distance between the MultiPoint of range IPoint and the curve CurveIndex.

  param IPoint

  type IPoint

  int

  param CurveIndex

  type CurveIndex

  int

  rtype

  float

FirstConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param FirstPoint

type FirstPoint

int

rtype

AppParCurves_Constraint

LastConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param LastPoint

type LastPoint

int

rtype

AppParCurves_Constraint

MaxError2d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

MaxError3d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

NewParameters()

• returns the new parameters of the MultiLine.

  rtype

  math_Vector

property thisown

The membership flag

class AppDef_ParLeastSquareOfMyGradientOfCompute(*args)

Bases: object

• 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None* 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None

BSplineValue()

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

  rtype

  AppParCurves_MultiBSpCurve

BezierValue()

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

  rtype

  AppParCurves_MultiCurve

DerivativeFunctionMatrix()

• returns the derivative function matrix used to approximate the set.

  rtype

  math_Matrix

Distance()

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

  rtype

  math_Matrix

Error()

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

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

ErrorGradient()

• 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.

  param Grad

  type Grad

  math_Vector

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

FirstLambda()

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

  rtype

  float

FunctionMatrix()

• returns the function matrix used to approximate the set.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

KIndex()

• 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.

  rtype

  math_IntegerVector

LastLambda()

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

  rtype

  float

Perform()

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

  param Parameters

  type Parameters

  math_Vector

  rtype

  None* Is used after having initialized the fields.

  param Parameters

  type Parameters

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param V1c

  type V1c

  math_Vector

  param V2c

  type V2c

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None

Points()

• returns the matrix of points value.

  rtype

  math_Matrix

Poles()

• returns the matrix of resulting control points value.

  rtype

  math_Matrix

property thisown

The membership flag

class AppDef_ParLeastSquareOfMyGradientbisOfBSplineCompute(*args)

Bases: object

• 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None* 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None

BSplineValue()

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

  rtype

  AppParCurves_MultiBSpCurve

BezierValue()

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

  rtype

  AppParCurves_MultiCurve

DerivativeFunctionMatrix()

• returns the derivative function matrix used to approximate the set.

  rtype

  math_Matrix

Distance()

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

  rtype

  math_Matrix

Error()

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

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

ErrorGradient()

• 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.

  param Grad

  type Grad

  math_Vector

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

FirstLambda()

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

  rtype

  float

FunctionMatrix()

• returns the function matrix used to approximate the set.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

KIndex()

• 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.

  rtype

  math_IntegerVector

LastLambda()

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

  rtype

  float

Perform()

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

  param Parameters

  type Parameters

  math_Vector

  rtype

  None* Is used after having initialized the fields.

  param Parameters

  type Parameters

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param V1c

  type V1c

  math_Vector

  param V2c

  type V2c

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None

Points()

• returns the matrix of points value.

  rtype

  math_Matrix

Poles()

• returns the matrix of resulting control points value.

  rtype

  math_Matrix

property thisown

The membership flag

class AppDef_ParLeastSquareOfTheGradient(*args)

Bases: object

• 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None* 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None

BSplineValue()

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

  rtype

  AppParCurves_MultiBSpCurve

BezierValue()

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

  rtype

  AppParCurves_MultiCurve

DerivativeFunctionMatrix()

• returns the derivative function matrix used to approximate the set.

  rtype

  math_Matrix

Distance()

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

  rtype

  math_Matrix

Error()

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

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

ErrorGradient()

• 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.

  param Grad

  type Grad

  math_Vector

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

FirstLambda()

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

  rtype

  float

FunctionMatrix()

• returns the function matrix used to approximate the set.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

KIndex()

• 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.

  rtype

  math_IntegerVector

LastLambda()

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

  rtype

  float

Perform()

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

  param Parameters

  type Parameters

  math_Vector

  rtype

  None* Is used after having initialized the fields.

  param Parameters

  type Parameters

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param V1c

  type V1c

  math_Vector

  param V2c

  type V2c

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None

Points()

• returns the matrix of points value.

  rtype

  math_Matrix

Poles()

• returns the matrix of resulting control points value.

  rtype

  math_Matrix

property thisown

The membership flag

class AppDef_ResConstraintOfMyGradientOfCompute(*args)

Bases: object

• Given a MultiLine SSP with constraints points, this algorithm finds the best curve solution to approximate it. The poles from SCurv issued for example from the least squares are used as a guess solution for the uzawa algorithm. The tolerance used in the Uzawa algorithms is Tolerance. A is the Bernstein matrix associated to the MultiLine and DA is the derivative bernstein matrix.(They can come from an approximation with ParLeastSquare.) The MultiCurve is modified. New MultiPoles are given.

  param SSP

  type SSP

  AppDef_MultiLine

  param SCurv

  type SCurv

  AppParCurves_MultiCurve

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param Constraints

  type Constraints

  AppParCurves_HArray1OfConstraintCouple

  param Bern

  type Bern

  math_Matrix

  param DerivativeBern

  type DerivativeBern

  math_Matrix

  param Tolerance

  default value is 1.0e-10

  type Tolerance

  float

  rtype

  None

ConstraintDerivative()

• Returns the derivative of the constraint matrix.

  param SSP

  type SSP

  AppDef_MultiLine

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  param DA

  type DA

  math_Matrix

  rtype

  math_Matrix

ConstraintMatrix()

Return type

math_Matrix

Duale()

• returns the duale variables of the system.

  rtype

  math_Vector

InverseMatrix()

• returns the Inverse of Cont*Transposed(Cont), where Cont is the constraint matrix for the algorithm.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

property thisown

The membership flag

class AppDef_ResConstraintOfMyGradientbisOfBSplineCompute(*args)

Bases: object

• Given a MultiLine SSP with constraints points, this algorithm finds the best curve solution to approximate it. The poles from SCurv issued for example from the least squares are used as a guess solution for the uzawa algorithm. The tolerance used in the Uzawa algorithms is Tolerance. A is the Bernstein matrix associated to the MultiLine and DA is the derivative bernstein matrix.(They can come from an approximation with ParLeastSquare.) The MultiCurve is modified. New MultiPoles are given.

  param SSP

  type SSP

  AppDef_MultiLine

  param SCurv

  type SCurv

  AppParCurves_MultiCurve

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param Constraints

  type Constraints

  AppParCurves_HArray1OfConstraintCouple

  param Bern

  type Bern

  math_Matrix

  param DerivativeBern

  type DerivativeBern

  math_Matrix

  param Tolerance

  default value is 1.0e-10

  type Tolerance

  float

  rtype

  None

ConstraintDerivative()

• Returns the derivative of the constraint matrix.

  param SSP

  type SSP

  AppDef_MultiLine

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  param DA

  type DA

  math_Matrix

  rtype

  math_Matrix

ConstraintMatrix()

Return type

math_Matrix

Duale()

• returns the duale variables of the system.

  rtype

  math_Vector

InverseMatrix()

• returns the Inverse of Cont*Transposed(Cont), where Cont is the constraint matrix for the algorithm.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

property thisown

The membership flag

class AppDef_ResConstraintOfTheGradient(*args)

Bases: object

• Given a MultiLine SSP with constraints points, this algorithm finds the best curve solution to approximate it. The poles from SCurv issued for example from the least squares are used as a guess solution for the uzawa algorithm. The tolerance used in the Uzawa algorithms is Tolerance. A is the Bernstein matrix associated to the MultiLine and DA is the derivative bernstein matrix.(They can come from an approximation with ParLeastSquare.) The MultiCurve is modified. New MultiPoles are given.

  param SSP

  type SSP

  AppDef_MultiLine

  param SCurv

  type SCurv

  AppParCurves_MultiCurve

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param Constraints

  type Constraints

  AppParCurves_HArray1OfConstraintCouple

  param Bern

  type Bern

  math_Matrix

  param DerivativeBern

  type DerivativeBern

  math_Matrix

  param Tolerance

  default value is 1.0e-10

  type Tolerance

  float

  rtype

  None

ConstraintDerivative()

• Returns the derivative of the constraint matrix.

  param SSP

  type SSP

  AppDef_MultiLine

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  param DA

  type DA

  math_Matrix

  rtype

  math_Matrix

ConstraintMatrix()

Return type

math_Matrix

Duale()

• returns the duale variables of the system.

  rtype

  math_Vector

InverseMatrix()

• returns the Inverse of Cont*Transposed(Cont), where Cont is the constraint matrix for the algorithm.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

property thisown

The membership flag

class AppDef_SmoothCriterion(*args, **kwargs)

Bases: OCC.Core.Standard.Standard_Transient

• Empty constructor

Return type

None* Copy constructor – does nothing

Parameters

& (Standard_Transient) –

Return type

None

AssemblyTable()

Return type

opencascade::handle<FEmTool_HAssemblyTable>

DependenceTable()

Return type

opencascade::handle<TColStd_HArray2OfInteger>

static DownCast(t)

ErrorValues()

Parameters

MaxError –

type MaxError

float

param QuadraticError

type QuadraticError

float

param AverageError

type AverageError

float

rtype

void

EstLength()

Return type

float

GetCurve()

Parameters

C –

type C

FEmTool_Curve

rtype

void

GetEstimation()

Parameters

E1 –

type E1

float

param E2

type E2

float

param E3

type E3

float

rtype

void

GetWeight()

Parameters

QuadraticWeight –

type QuadraticWeight

float

param QualityWeight

type QualityWeight

float

rtype

void

Gradient()

Parameters

Element –

type Element

int

param Dimension

type Dimension

int

param G

type G

math_Vector

rtype

void

Hessian()

Parameters

Element –

type Element

int

param Dimension1

type Dimension1

int

param Dimension2

type Dimension2

int

param H

type H

math_Matrix

rtype

void

InputVector()

• Convert the assembly Vector in an Curve;

  param X

  type X

  math_Vector

  param AssTable

  type AssTable

  FEmTool_HAssemblyTable

  rtype

  void

QualityValues()

Parameters

J1min –

type J1min

float

param J2min

type J2min

float

param J3min

type J3min

float

param J1

type J1

float

param J2

type J2

float

param J3

type J3

float

rtype

int

SetCurve()

Parameters

C –

type C

FEmTool_Curve

rtype

void

SetEstimation()

Parameters

E1 –

type E1

float

param E2

type E2

float

param E3

type E3

float

rtype

void

SetParameters()

Parameters

Parameters –

type Parameters

TColStd_HArray1OfReal

rtype

void

SetWeight()

Parameters

QuadraticWeight –

type QuadraticWeight

float

param QualityWeight

type QualityWeight

float

param percentJ1

type percentJ1

float

param percentJ2

type percentJ2

float

param percentJ3

type percentJ3

float

rtype

void:param Weight:

type Weight

TColStd_Array1OfReal

rtype

void

property thisown

The membership flag

class AppDef_TheFunction(*args)

Bases: OCC.Core.math.math_MultipleVarFunctionWithGradient

• initializes the fields of the function. The approximating curve has the desired degree Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  rtype

  None

CurveValue()

• returns the MultiCurve approximating the set after computing the value F or Grad(F).

  rtype

  AppParCurves_MultiCurve

Error()

• returns the distance between the MultiPoint of range IPoint and the curve CurveIndex.

  param IPoint

  type IPoint

  int

  param CurveIndex

  type CurveIndex

  int

  rtype

  float

FirstConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param FirstPoint

type FirstPoint

int

rtype

AppParCurves_Constraint

LastConstraint()

Parameters

TheConstraints –

type TheConstraints

AppParCurves_HArray1OfConstraintCouple

param LastPoint

type LastPoint

int

rtype

AppParCurves_Constraint

MaxError2d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

MaxError3d()

• returns the maximum distance between the points and the MultiCurve.

  rtype

  float

NewParameters()

• returns the new parameters of the MultiLine.

  rtype

  math_Vector

property thisown

The membership flag

class AppDef_TheGradient(*args)

Bases: object

• Tries to minimize the sum (square(||Qui - Bi*Pi||)) where Pui describe the approximating Bezier curves’Poles and Qi the MultiLine points with a parameter ui. In this algorithm, the parameters ui are the unknowns. The tolerance required on this sum is given by Tol. The desired degree of the resulting curve is Deg.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  param Tol3d

  type Tol3d

  float

  param Tol2d

  type Tol2d

  float

  param NbIterations

  default value is 200

  type NbIterations

  int

  rtype

  None

AverageError()

• returns the average error between the old and the new approximation.

  rtype

  float

Error()

• returns the difference between the old and the new approximation. An exception is raised if NotDone. An exception is raised if Index<1 or Index>NbParameters.

  param Index

  type Index

  int

  rtype

  float

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

MaxError2d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

MaxError3d()

• returns the maximum difference between the old and the new approximation.

  rtype

  float

Value()

• returns all the Bezier curves approximating the MultiLine SSP after minimization of the parameter.

  rtype

  AppParCurves_MultiCurve

property thisown

The membership flag

class AppDef_TheLeastSquares(*args)

Bases: object

• 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None* 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).

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param Parameters

  type Parameters

  math_Vector

  param NbPol

  type NbPol

  int

  rtype

  None* Initializes the fields of the object.

  param SSP

  type SSP

  AppDef_MultiLine

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param FirstCons

  type FirstCons

  AppParCurves_Constraint

  param LastCons

  type LastCons

  AppParCurves_Constraint

  param NbPol

  type NbPol

  int

  rtype

  None

BSplineValue()

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

  rtype

  AppParCurves_MultiBSpCurve

BezierValue()

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

  rtype

  AppParCurves_MultiCurve

DerivativeFunctionMatrix()

• returns the derivative function matrix used to approximate the set.

  rtype

  math_Matrix

Distance()

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

  rtype

  math_Matrix

Error()

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

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

ErrorGradient()

• 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.

  param Grad

  type Grad

  math_Vector

  param F

  type F

  float

  param MaxE3d

  type MaxE3d

  float

  param MaxE2d

  type MaxE2d

  float

  rtype

  None

FirstLambda()

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

  rtype

  float

FunctionMatrix()

• returns the function matrix used to approximate the set.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

KIndex()

• 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.

  rtype

  math_IntegerVector

LastLambda()

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

  rtype

  float

Perform()

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

  param Parameters

  type Parameters

  math_Vector

  rtype

  None* Is used after having initialized the fields.

  param Parameters

  type Parameters

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None* 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.

  param Parameters

  type Parameters

  math_Vector

  param V1t

  type V1t

  math_Vector

  param V2t

  type V2t

  math_Vector

  param V1c

  type V1c

  math_Vector

  param V2c

  type V2c

  math_Vector

  param l1

  type l1

  float

  param l2

  type l2

  float

  rtype

  None

Points()

• returns the matrix of points value.

  rtype

  math_Matrix

Poles()

• returns the matrix of resulting control points value.

  rtype

  math_Matrix

property thisown

The membership flag

class AppDef_TheResol(*args)

Bases: object

• Given a MultiLine SSP with constraints points, this algorithm finds the best curve solution to approximate it. The poles from SCurv issued for example from the least squares are used as a guess solution for the uzawa algorithm. The tolerance used in the Uzawa algorithms is Tolerance. A is the Bernstein matrix associated to the MultiLine and DA is the derivative bernstein matrix.(They can come from an approximation with ParLeastSquare.) The MultiCurve is modified. New MultiPoles are given.

  param SSP

  type SSP

  AppDef_MultiLine

  param SCurv

  type SCurv

  AppParCurves_MultiCurve

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param Constraints

  type Constraints

  AppParCurves_HArray1OfConstraintCouple

  param Bern

  type Bern

  math_Matrix

  param DerivativeBern

  type DerivativeBern

  math_Matrix

  param Tolerance

  default value is 1.0e-10

  type Tolerance

  float

  rtype

  None

ConstraintDerivative()

• Returns the derivative of the constraint matrix.

  param SSP

  type SSP

  AppDef_MultiLine

  param Parameters

  type Parameters

  math_Vector

  param Deg

  type Deg

  int

  param DA

  type DA

  math_Matrix

  rtype

  math_Matrix

ConstraintMatrix()

Return type

math_Matrix

Duale()

• returns the duale variables of the system.

  rtype

  math_Vector

InverseMatrix()

• returns the Inverse of Cont*Transposed(Cont), where Cont is the constraint matrix for the algorithm.

  rtype

  math_Matrix

IsDone()

• returns True if all has been correctly done.

  rtype

  bool

property thisown

The membership flag

class AppDef_Variational(*args)

Bases: object

• Constructor. Initialization of the fields. warningNc0number of PassagePoint consraints Nc2number of TangencyPoint constraints Nc3number of CurvaturePoint constraints if ((MaxDegree-Continuity)*MaxSegment -Nc0 - 2*Nc1 -3*Nc2) is negative The problem is over-constrained. //! LimitationThe MultiLine from AppDef has to be composed by only one Line ( Dimension 2 or 3).

  param SSP

  type SSP

  AppDef_MultiLine

  param FirstPoint

  type FirstPoint

  int

  param LastPoint

  type LastPoint

  int

  param TheConstraints

  type TheConstraints

  AppParCurves_HArray1OfConstraintCouple

  param MaxDegree

  default value is 14

  type MaxDegree

  int

  param MaxSegment

  default value is 100

  type MaxSegment

  int

  param Continuity

  default value is GeomAbs_C2

  type Continuity

  GeomAbs_Shape

  param WithMinMax

  default value is Standard_False

  type WithMinMax

  bool

  param WithCutting

  default value is Standard_True

  type WithCutting

  bool

  param Tolerance

  default value is 1.0

  type Tolerance

  float

  param NbIterations

  default value is 2

  type NbIterations

  int

  rtype

  None

Approximate()

• Makes the approximation with the current fields.

  rtype

  None

AverageError()

• returns the average error between the MultiLine from AppDef and the approximation.

  rtype

  float

Continuity()

• returns the Continuity used in the approximation

  rtype

  GeomAbs_Shape

Criterium()

• returns the values of the quality criterium.

  param VFirstOrder

  type VFirstOrder

  float

  param VSecondOrder

  type VSecondOrder

  float

  param VThirdOrder

  type VThirdOrder

  float

  rtype

  None

CriteriumWeight()

• returns the Weights (as percent) associed to the criterium used in the optimization.

  param Percent1

  type Percent1

  float

  param Percent2

  type Percent2

  float

  param Percent3

  type Percent3

  float

  rtype

  None

Distance()

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

  param mat

  type mat

  math_Matrix

  rtype

  None

DumpToString(AppDef_Variational self) → std::string

IsCreated()

• returns True if the creation is done and correspond to the current fields.

  rtype

  bool

IsDone()

• returns True if the approximation is ok and correspond to the current fields.

  rtype

  bool

IsOverConstrained()

• returns True if the problem is overconstrained in this case, approximation cannot be done.

  rtype

  bool

Knots()

• returns the knots uses to the approximations

  rtype

  opencascade::handle<TColStd_HArray1OfReal>

MaxDegree()

• returns the Maximum Degree used in the approximation

  rtype

  int

MaxError()

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

  rtype

  float

MaxErrorIndex()

• returns the index of the MultiPoint of ErrorMax

  rtype

  int

MaxSegment()

• returns the Maximum of segment used in the approximation

  rtype

  int

NbIterations()

• returns the number of iterations used in the approximation.

  rtype

  int

Parameters()

• returns the parameters uses to the approximations

  rtype

  opencascade::handle<TColStd_HArray1OfReal>

QuadraticError()

• returns the quadratic average of the distances between the points of the multiline and the approximation curves.

  rtype

  float

SetConstraints()

• Define the constraints to approximate If this value is incompatible with the others fields this method modify nothing and returns false

  param aConstrainst

  type aConstrainst

  AppParCurves_HArray1OfConstraintCouple

  rtype

  bool

SetContinuity()

• Define the Continuity used in the approximation If this value is incompatible with the others fields this method modify nothing and returns false

  param C

  type C

  GeomAbs_Shape

  rtype

  bool

SetCriteriumWeight()

• define the Weights (as percent) associed to the criterium used in the optimization. //! if Percent <= 0

  param Percent1

  type Percent1

  float

  param Percent2

  type Percent2

  float

  param Percent3

  type Percent3

  float

  rtype

  None* define the Weight (as percent) associed to the criterium Order used in the optimization : Others weights are updated. if Percent < 0 if Order < 1 or Order > 3

  param Order

  type Order

  int

  param Percent

  type Percent

  float

  rtype

  None

SetKnots()

• Defines the knots used by the approximations If this value is incompatible with the others fields this method modify nothing and returns false

  param knots

  type knots

  TColStd_HArray1OfReal

  rtype

  bool

SetMaxDegree()

• Define the Maximum Degree used in the approximation If this value is incompatible with the others fields this method modify nothing and returns false

  param Degree

  type Degree

  int

  rtype

  bool

SetMaxSegment()

• Define the maximum number of segments used in the approximation If this value is incompatible with the others fields this method modify nothing and returns false

  param NbSegment

  type NbSegment

  int

  rtype

  bool

SetNbIterations()

• define the number of iterations used in the approximation. if Iter < 1

  param Iter

  type Iter

  int

  rtype

  None

SetParameters()

• Defines the parameters used by the approximations.

  param param

  type param

  TColStd_HArray1OfReal

  rtype

  None

SetTolerance()

• define the tolerance used in the approximation.

  param Tol

  type Tol

  float

  rtype

  None

SetWithCutting()

• Define if the approximation can insert new Knots or not. If this value is incompatible with the others fields this method modify nothing and returns false

  param Cutting

  type Cutting

  bool

  rtype

  bool

SetWithMinMax()

• Define if the approximation search to minimize the maximum Error or not.

  param MinMax

  type MinMax

  bool

  rtype

  None

Tolerance()

• returns the tolerance used in the approximation.

  rtype

  float

Value()

• returns all the BSpline curves approximating the MultiLine from AppDef SSP after minimization of the parameter.

  rtype

  AppParCurves_MultiBSpCurve

WithCutting()

• returns if the approximation can insert new Knots or not.

  rtype

  bool

WithMinMax()

• returns if the approximation search to minimize the maximum Error or not.

  rtype

  bool

property thisown

The membership flag

class SwigPyIterator(*args, **kwargs)

Bases: object

advance()

copy()

decr()

distance()

equal()

incr()

next()

previous()

property thisown

The membership flag

value()