GCPnts_QuasiUniformDeflection Class Reference

This class computes a distribution of points on a curve. The points may respect the deflection. The algorithm is not based on the classical prediction (with second derivative of curve), but either on the evaluation of the distance between the mid point and the point of mid parameter of the two points, or the distance between the mid point and the point at parameter 0.5 on the cubic interpolation of the two points and their tangents. More...

#include <GCPnts_QuasiUniformDeflection.hxx>

Public Member Functions
	GCPnts_QuasiUniformDeflection ()
	Constructs an empty algorithm. To define the problem to be solved, use the function Initialize(). More...
	GCPnts_QuasiUniformDeflection (const Adaptor3d_Curve &theC, const Standard_Real theDeflection, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution of points on the Curve. More...
	GCPnts_QuasiUniformDeflection (const Adaptor2d_Curve2d &theC, const Standard_Real theDeflection, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution of points on the Curve. More...
	GCPnts_QuasiUniformDeflection (const Adaptor3d_Curve &theC, const Standard_Real theDeflection, const Standard_Real theU1, const Standard_Real theU2, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution of points on a part of the Curve. More...
	GCPnts_QuasiUniformDeflection (const Adaptor2d_Curve2d &theC, const Standard_Real theDeflection, const Standard_Real theU1, const Standard_Real theU2, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution of points on a part of the Curve. This and the above algorithms compute a distribution of points: More...
void	Initialize (const Adaptor3d_Curve &theC, const Standard_Real theDeflection, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Initialize the algorithms with 3D curve and deflection. More...
void	Initialize (const Adaptor2d_Curve2d &theC, const Standard_Real theDeflection, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Initialize the algorithms with 2D curve and deflection. More...
void	Initialize (const Adaptor3d_Curve &theC, const Standard_Real theDeflection, const Standard_Real theU1, const Standard_Real theU2, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Initialize the algorithms with 3D curve, deflection and parameter range. More...
void	Initialize (const Adaptor2d_Curve2d &theC, const Standard_Real theDeflection, const Standard_Real theU1, const Standard_Real theU2, const GeomAbs_Shape theContinuity=GeomAbs_C1)
	Initialize the algorithms with theC, theDeflection, theU1, theU2. This and the above algorithms initialize (or reinitialize) this algorithm and compute a distribution of points: More...
Standard_Boolean	IsDone () const
	Returns true if the computation was successful. IsDone is a protection against: More...
Standard_Integer	NbPoints () const
	Returns the number of points of the distribution computed by this algorithm. Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful. More...
Standard_Real	Parameter (const Standard_Integer Index) const
	Returns the parameter of the point of index Index in the distribution computed by this algorithm. Warning Index must be greater than or equal to 1, and less than or equal to the number of points of the distribution. However, pay particular attention as this condition is not checked by this function. Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful. More...
gp_Pnt	Value (const Standard_Integer Index) const
	Returns the point of index Index in the distribution computed by this algorithm. Warning Index must be greater than or equal to 1, and less than or equal to the number of points of the distribution. However, pay particular attention as this condition is not checked by this function. Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful. More...
Standard_Real	Deflection () const
	Returns the deflection between the curve and the polygon resulting from the points of the distribution computed by this algorithm. This is the value given to the algorithm at the time of construction (or initialization). Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful. More...

Detailed Description

This class computes a distribution of points on a curve. The points may respect the deflection. The algorithm is not based on the classical prediction (with second derivative of curve), but either on the evaluation of the distance between the mid point and the point of mid parameter of the two points, or the distance between the mid point and the point at parameter 0.5 on the cubic interpolation of the two points and their tangents.

Note: this algorithm is faster than a GCPnts_UniformDeflection algorithm, and is able to work with non-"C2" continuous curves. However, it generates more points in the distribution.

Constructor & Destructor Documentation

GCPnts_QuasiUniformDeflection() [1/5]

GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection

(

)

Constructs an empty algorithm. To define the problem to be solved, use the function Initialize().

GCPnts_QuasiUniformDeflection() [2/5]

GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	const Adaptor3d_Curve &	theC,
		const Standard_Real	theDeflection,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Computes a QuasiUniform Deflection distribution of points on the Curve.

GCPnts_QuasiUniformDeflection() [3/5]

GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	const Adaptor2d_Curve2d &	theC,
		const Standard_Real	theDeflection,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Computes a QuasiUniform Deflection distribution of points on the Curve.

GCPnts_QuasiUniformDeflection() [4/5]

GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	const Adaptor3d_Curve &	theC,
		const Standard_Real	theDeflection,
		const Standard_Real	theU1,
		const Standard_Real	theU2,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Computes a QuasiUniform Deflection distribution of points on a part of the Curve.

GCPnts_QuasiUniformDeflection() [5/5]

GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	const Adaptor2d_Curve2d &	theC,
		const Standard_Real	theDeflection,
		const Standard_Real	theU1,
		const Standard_Real	theU2,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Computes a QuasiUniform Deflection distribution of points on a part of the Curve. This and the above algorithms compute a distribution of points:

• on the curve theC, or
• on the part of curve theC limited by the two parameter values theU1 and theU2, where the deflection resulting from the distributed points is not greater than theDeflection.

The first point of the distribution is either the origin of curve theC or the point of parameter theU1. The last point of the distribution is either the end point of curve theC or the point of parameter theU2.

Intermediate points of the distribution are built such that the deflection is not greater than theDeflection. Using the following evaluation of the deflection: if Pi and Pj are two consecutive points of the distribution, respectively of parameter ui and uj on the curve, the deflection is the distance between:

• the mid-point of Pi and Pj (the center of the chord joining these two points)
• and the point of mid-parameter of these two points (the point of parameter [(ui+uj) / 2] on curve theC). theContinuity, defaulted to GeomAbs_C1, gives the degree of continuity of the curve theC. (Note that C is an Adaptor3d_Curve or an Adaptor2d_Curve2d object, and does not know the degree of continuity of the underlying curve). Use the function IsDone() to verify that the computation was successful, the function NbPoints() to obtain the number of points of the computed distribution, and the function Parameter() to read the parameter of each point.

Warning

• The roles of theU1 and theU2 are inverted if theU1 > theU2.
• Derivative functions on the curve are called according to theContinuity. An error may occur if theContinuity is greater than the real degree of continuity of the curve.

Warning theC is an adapted curve, i.e. an object which is an interface between:

• the services provided by either a 2D curve from the package Geom2d (in the case of an Adaptor2d_Curve2d curve) or a 3D curve from the package Geom (in the case of an Adaptor3d_Curve curve),
• and those required on the curve by the computation algorithm.

Member Function Documentation

Deflection()

Standard_Real GCPnts_QuasiUniformDeflection::Deflection ( ) const

inline

Returns the deflection between the curve and the polygon resulting from the points of the distribution computed by this algorithm. This is the value given to the algorithm at the time of construction (or initialization). Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful.

Initialize() [1/4]

void GCPnts_QuasiUniformDeflection::Initialize	(	const Adaptor2d_Curve2d &	theC,
		const Standard_Real	theDeflection,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Initialize the algorithms with 2D curve and deflection.

Initialize() [2/4]

void GCPnts_QuasiUniformDeflection::Initialize	(	const Adaptor2d_Curve2d &	theC,
		const Standard_Real	theDeflection,
		const Standard_Real	theU1,
		const Standard_Real	theU2,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Initialize the algorithms with theC, theDeflection, theU1, theU2. This and the above algorithms initialize (or reinitialize) this algorithm and compute a distribution of points:

• on the curve theC, or
• on the part of curve theC limited by the two parameter values theU1 and theU2, where the deflection resulting from the distributed points is not greater than theDeflection.

The first point of the distribution is either the origin of curve theC or the point of parameter theU1. The last point of the distribution is either the end point of curve theC or the point of parameter theU2.

Intermediate points of the distribution are built in such a way that the deflection is not greater than theDeflection. Using the following evaluation of the deflection: if Pi and Pj are two consecutive points of the distribution, respectively of parameter ui and uj on the curve, the deflection is the distance between:

• the mid-point of Pi and Pj (the center of the chord joining these two points)
• and the point of mid-parameter of these two points (the point of parameter [(ui+uj) / 2] on curve theC). theContinuity, defaulted to GeomAbs_C1, gives the degree of continuity of the curve theC. (Note that C is an Adaptor3d_Curve or an Adaptor2d_Curve2d object, and does not know the degree of continuity of the underlying curve). Use the function IsDone to verify that the computation was successful, the function NbPoints() to obtain the number of points of the computed distribution, and the function Parameter() to read the parameter of each point.

Warning

• The roles of theU1 and theU2 are inverted if theU1 > theU2.
• Derivative functions on the curve are called according to theContinuity. An error may occur if theContinuity is greater than the real degree of continuity of the curve.

Warning theC is an adapted curve, i.e. an object which is an interface between:

• the services provided by either a 2D curve from the package Geom2d (in the case of an Adaptor2d_Curve2d curve) or a 3D curve from the package Geom (in the case of an Adaptor3d_Curve curve), and those required on the curve by the computation algorithm.

Initialize() [3/4]

void GCPnts_QuasiUniformDeflection::Initialize	(	const Adaptor3d_Curve &	theC,
		const Standard_Real	theDeflection,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Initialize the algorithms with 3D curve and deflection.

Initialize() [4/4]

void GCPnts_QuasiUniformDeflection::Initialize	(	const Adaptor3d_Curve &	theC,
		const Standard_Real	theDeflection,
		const Standard_Real	theU1,
		const Standard_Real	theU2,
		const GeomAbs_Shape	theContinuity = GeomAbs_C1
	)

Initialize the algorithms with 3D curve, deflection and parameter range.

IsDone()

Standard_Boolean GCPnts_QuasiUniformDeflection::IsDone ( ) const

inline

Returns true if the computation was successful. IsDone is a protection against:

• non-convergence of the algorithm
• querying the results before computation.

NbPoints()

Standard_Integer GCPnts_QuasiUniformDeflection::NbPoints ( ) const

inline

Returns the number of points of the distribution computed by this algorithm. Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful.

Parameter()

Standard_Real GCPnts_QuasiUniformDeflection::Parameter ( const Standard_Integer  Index ) const

inline

Returns the parameter of the point of index Index in the distribution computed by this algorithm. Warning Index must be greater than or equal to 1, and less than or equal to the number of points of the distribution. However, pay particular attention as this condition is not checked by this function. Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful.

Value()

gp_Pnt GCPnts_QuasiUniformDeflection::Value

(

const Standard_Integer

Index

)

const

Returns the point of index Index in the distribution computed by this algorithm. Warning Index must be greater than or equal to 1, and less than or equal to the number of points of the distribution. However, pay particular attention as this condition is not checked by this function. Exceptions StdFail_NotDone if this algorithm has not been initialized, or if the computation was not successful.

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

• GCPnts_QuasiUniformDeflection.hxx