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.
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.
More...

#include <GCPnts_QuasiUniformDeflection.hxx>

Public Member Functions
	GCPnts_QuasiUniformDeflection ()
	Constructs an empty algorithm. To define the problem <br> to be solved, use the function Initialize. More...
	GCPnts_QuasiUniformDeflection (Adaptor3d_Curve &C, const Standard_Real Deflection, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution <br> of points on the Curve . More...
	GCPnts_QuasiUniformDeflection (Adaptor2d_Curve2d &C, const Standard_Real Deflection, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution <br> of points on the Curve . More...
	GCPnts_QuasiUniformDeflection (Adaptor3d_Curve &C, const Standard_Real Deflection, const Standard_Real U1, const Standard_Real U2, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution <br> of points on a part of the Curve . More...
	GCPnts_QuasiUniformDeflection (Adaptor2d_Curve2d &C, const Standard_Real Deflection, const Standard_Real U1, const Standard_Real U2, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Computes a QuasiUniform Deflection distribution <br> of points on a part of the Curve . This and the above algorithms compute a distribution of points: More...
void	Initialize (Adaptor3d_Curve &C, const Standard_Real Deflection, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Initialize the algoritms with , <Deflection> More...
void	Initialize (Adaptor2d_Curve2d &C, const Standard_Real Deflection, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Initialize the algoritms with , <Deflection> More...
void	Initialize (Adaptor3d_Curve &C, const Standard_Real Deflection, const Standard_Real U1, const Standard_Real U2, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Initialize the algoritms with , <Deflection>, <U1>,<U2> More...
void	Initialize (Adaptor2d_Curve2d &C, const Standard_Real Deflection, const Standard_Real U1, const Standard_Real U2, const GeomAbs_Shape Continuity=GeomAbs_C1)
	Initialize the algoritms with , <Deflection>, – <U1>,<U2> 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 <br> 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 <br> 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 <br> 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::GCPnts_QuasiUniformDeflection

(

)

 Constructs an empty algorithm. To define the problem <br>

to be solved, use the function Initialize.

GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	Adaptor3d_Curve &	C,
		const Standard_Real	Deflection,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

Computes  a QuasiUniform Deflection distribution <br>

of points on the Curve .


GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	Adaptor2d_Curve2d &	C,
		const Standard_Real	Deflection,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

Computes  a QuasiUniform Deflection distribution <br>

of points on the Curve .


GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	Adaptor3d_Curve &	C,
		const Standard_Real	Deflection,
		const Standard_Real	U1,
		const Standard_Real	U2,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

Computes a QuasiUniform Deflection distribution <br>

of points on a part of the Curve .


GCPnts_QuasiUniformDeflection::GCPnts_QuasiUniformDeflection	(	Adaptor2d_Curve2d &	C,
		const Standard_Real	Deflection,
		const Standard_Real	U1,
		const Standard_Real	U2,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

  Computes  a QuasiUniform Deflection distribution <br>

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


• on the curve C, or
  
• on the part of curve C limited by the two
  parameter values U1 and U2,
  where the deflection resulting from the distributed
  points is not greater than Deflection.
  The first point of the distribution is either the origin of
  curve C or the point of parameter U1. The last point
  of the distribution is either the end point of curve C or
  the point of parameter U2.
  Intermediate points of the distribution are built such
  that the deflection is not greater than Deflection.
  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 C).
  Continuity, defaulted to GeomAbs_C1, gives the
  degree of continuity of the curve C. (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 U1 and U2 are inverted if U1 > U2.
  
• Derivative functions on the curve are called
  according to Continuity. An error may occur if
  Continuity is greater than the real degree of
  continuity of the curve.
  Warning
  C 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

Standard_Real GCPnts_QuasiUniformDeflection::Deflection

(

)

const

 Returns the deflection between the curve and the <br>

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.

void GCPnts_QuasiUniformDeflection::Initialize	(	Adaptor3d_Curve &	C,
		const Standard_Real	Deflection,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

Initialize the algoritms with , <Deflection>


void GCPnts_QuasiUniformDeflection::Initialize	(	Adaptor2d_Curve2d &	C,
		const Standard_Real	Deflection,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

Initialize the algoritms with , <Deflection>


void GCPnts_QuasiUniformDeflection::Initialize	(	Adaptor3d_Curve &	C,
		const Standard_Real	Deflection,
		const Standard_Real	U1,
		const Standard_Real	U2,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

Initialize the algoritms with , <Deflection>,
<U1>,<U2>


void GCPnts_QuasiUniformDeflection::Initialize	(	Adaptor2d_Curve2d &	C,
		const Standard_Real	Deflection,
		const Standard_Real	U1,
		const Standard_Real	U2,
		const GeomAbs_Shape	Continuity = GeomAbs_C1
	)

Initialize the algoritms with , <Deflection>,
– <U1>,<U2>
This and the above algorithms initialize (or reinitialize)
this algorithm and compute a distribution of points:


• on the curve C, or
  
• on the part of curve C limited by the two
  parameter values U1 and U2,
  where the deflection resulting from the distributed
  points is not greater than Deflection.
  The first point of the distribution is either the origin
  of curve C or the point of parameter U1. The last
  point of the distribution is either the end point of
  curve C or the point of parameter U2.
  Intermediate points of the distribution are built in
  such a way that the deflection is not greater than
  Deflection. 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 C).
  Continuity, defaulted to GeomAbs_C1, gives the
  degree of continuity of the curve C. (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 U1 and U2 are inverted if U1 > U2.
  
• Derivative functions on the curve are called
  according to Continuity. An error may occur if
  Continuity is greater than the real degree of
  continuity of the curve.
  Warning
  C 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.
  

Standard_Boolean GCPnts_QuasiUniformDeflection::IsDone

(

)

const

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

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

Standard_Integer GCPnts_QuasiUniformDeflection::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.

Standard_Real GCPnts_QuasiUniformDeflection::Parameter

(

const Standard_Integer

Index

)

const

 Returns the parameter of the point of index Index in <br>

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.

gp_Pnt GCPnts_QuasiUniformDeflection::Value

(

const Standard_Integer

Index

)

const

 Returns the point of index Index in the distribution <br>

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.

---

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

• GCPnts_QuasiUniformDeflection.hxx