Open CASCADE Technology
6.9.0

Describes a rational or nonrational Bezier curve. More...
#include <Geom_BezierCurve.hxx>
Public Member Functions  
Geom_BezierCurve (const TColgp_Array1OfPnt &CurvePoles)  
Creates a non rational Bezier curve with a set of poles CurvePoles. The weights are defaulted to all being 1. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2. More...  
Geom_BezierCurve (const TColgp_Array1OfPnt &CurvePoles, const TColStd_Array1OfReal &PoleWeights)  
Creates a rational Bezier curve with the set of poles CurvePoles and the set of weights PoleWeights . If all the weights are identical the curve is considered as non rational. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2 or CurvePoles and CurveWeights have not the same length or one weight value is lower or equal to Resolution from package gp. More...  
void  Increase (const Standard_Integer Degree) 
Increases the degree of a bezier curve. Degree is the new degree of <me>. Raises ConstructionError if Degree is greater than MaxDegree or lower than 2 or lower than the initial degree of <me>. More...  
void  InsertPoleAfter (const Standard_Integer Index, const gp_Pnt &P) 
Inserts a pole P after the pole of range Index. If the curve <me> is rational the weight value for the new pole of range Index is 1.0. raised if Index is not in the range [1, NbPoles]. More...  
void  InsertPoleAfter (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight) 
Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. Raised if Index is not in the range [1, NbPoles]. More...  
void  InsertPoleBefore (const Standard_Integer Index, const gp_Pnt &P) 
Inserts a pole P before the pole of range Index. If the curve <me> is rational the weight value for the new pole of range Index is 1.0. Raised if Index is not in the range [1, NbPoles]. More...  
void  InsertPoleBefore (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight) 
Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. Raised if Index is not in the range [1, NbPoles]. More...  
void  RemovePole (const Standard_Integer Index) 
Removes the pole of range Index. If the curve was rational it can become non rational. Raised if Index is not in the range [1, NbPoles] Raised if Degree is lower than 2. More...  
void  Reverse () 
Reverses the direction of parametrization of <me> Value (NewU) = Value (1  OldU) More...  
Standard_Real  ReversedParameter (const Standard_Real U) const 
Returns the parameter on the reversed curve for the point of parameter U on <me>. More...  
void  Segment (const Standard_Real U1, const Standard_Real U2) 
Segments the curve between U1 and U2 which can be out of the bounds of the curve. The curve is oriented from U1 to U2. The control points are modified, the first and the last point are not the same but the parametrization range is [0, 1] else it could not be a Bezier curve. Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the curve <me> or if the curve makes loop. After the segmentation the length of a curve can be null. More...  
void  SetPole (const Standard_Integer Index, const gp_Pnt &P) 
Substitutes the pole of range index with P. If the curve <me> is rational the weight of range Index is not modified. raiseD if Index is not in the range [1, NbPoles]. More...  
void  SetPole (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight) 
Substitutes the pole and the weights of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. Raised if Index is not in the range [1, NbPoles] Raised if Weight <= Resolution from package gp. More...  
void  SetWeight (const Standard_Integer Index, const Standard_Real Weight) 
Changes the weight of the pole of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. Raised if Index is not in the range [1, NbPoles] Raised if Weight <= Resolution from package gp. More...  
Standard_Boolean  IsClosed () const 
Returns True if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp. More...  
Standard_Boolean  IsCN (const Standard_Integer N) const 
Continuity of the curve, returns True. More...  
Standard_Boolean  IsPeriodic () const 
Returns True if the parametrization of a curve is periodic. (P(u) = P(u + T) T = constante) More...  
Standard_Boolean  IsRational () const 
Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp. More...  
GeomAbs_Shape  Continuity () const 
a Bezier curve is CN More...  
Standard_Integer  Degree () const 
Returns the polynomial degree of the curve. it is the number of poles  1 point P and derivatives (V1, V2, V3) computation The Bezier Curve has a Polynomial representation so the parameter U can be out of the bounds of the curve. More...  
void  D0 (const Standard_Real U, gp_Pnt &P) const 
Returns in P the point of parameter U. If the curve is periodic then the returned point is P(U) with U = Ustart + (U  Uend) where Ustart and Uend are the parametric bounds of the curve. More...  
void  D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const 
Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1. More...  
void  D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const 
Returns the point P of parameter U, the first and second derivatives V1 and V2. Raised if the continuity of the curve is not C2. More...  
void  D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const 
For this Bezier curve, computes. More...  
gp_Vec  DN (const Standard_Real U, const Standard_Integer N) const 
For the point of parameter U of this Bezier curve, computes the vector corresponding to the Nth derivative. Note: the parameter U can be outside the bounds of the curve. Exceptions Standard_RangeError if N is less than 1. More...  
gp_Pnt  StartPoint () const 
Returns Value (U=0.), it is the first control point of the curve. More...  
gp_Pnt  EndPoint () const 
Returns Value (U=1.), it is the last control point of the Bezier curve. More...  
Standard_Real  FirstParameter () const 
Returns the value of the first parameter of this Bezier curve. This is 0.0, which gives the start point of this Bezier curve. More...  
Standard_Real  LastParameter () const 
Returns the value of the last parameter of this Bezier curve. This is 1.0, which gives the end point of this Bezier curve. More...  
Standard_Integer  NbPoles () const 
Returns the number of poles of this Bezier curve. More...  
gp_Pnt  Pole (const Standard_Integer Index) const 
Returns the pole of range Index. Raised if Index is not in the range [1, NbPoles]. More...  
void  Poles (TColgp_Array1OfPnt &P) const 
Returns all the poles of the curve. More...  
Standard_Real  Weight (const Standard_Integer Index) const 
Returns the weight of range Index. Raised if Index is not in the range [1, NbPoles]. More...  
void  Weights (TColStd_Array1OfReal &W) const 
Returns all the weights of the curve. More...  
void  Transform (const gp_Trsf &T) 
Applies the transformation T to this Bezier curve. More...  
void  Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance) 
Computes for this Bezier curve the parametric tolerance UTolerance for a given 3D tolerance Tolerance3D. If f(t) is the equation of this Bezier curve, UTolerance ensures that: t1t0 < UTolerance ===> f(t1)f(t0) < Tolerance3D. More...  
Handle< Geom_Geometry >  Copy () const 
Creates a new object which is a copy of this Bezier curve. More...  
Public Member Functions inherited from Geom_Curve  
virtual Standard_Real  TransformedParameter (const Standard_Real U, const gp_Trsf &T) const 
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>. More...  
virtual Standard_Real  ParametricTransformation (const gp_Trsf &T) const 
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>. More...  
Handle< Geom_Curve >  Reversed () const 
Returns a copy of <me> reversed. More...  
virtual Standard_Real  Period () const 
Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic. More...  
gp_Pnt  Value (const Standard_Real U) const 
Computes the point of parameter U on <me>. If the curve is periodic then the returned point is P(U) with U = Ustart + (U  Uend) where Ustart and Uend are the parametric bounds of the curve. it is implemented with D0. More...  
Public Member Functions inherited from Geom_Geometry  
void  Mirror (const gp_Pnt &P) 
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry. More...  
void  Mirror (const gp_Ax1 &A1) 
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...  
void  Mirror (const gp_Ax2 &A2) 
Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection). More...  
void  Rotate (const gp_Ax1 &A1, const Standard_Real Ang) 
Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...  
void  Scale (const gp_Pnt &P, const Standard_Real S) 
Scales a Geometry. S is the scaling value. More...  
void  Translate (const gp_Vec &V) 
Translates a Geometry. V is the vector of the tanslation. More...  
void  Translate (const gp_Pnt &P1, const gp_Pnt &P2) 
Translates a Geometry from the point P1 to the point P2. More...  
Handle< Geom_Geometry >  Mirrored (const gp_Pnt &P) const 
Handle< Geom_Geometry >  Mirrored (const gp_Ax1 &A1) const 
Handle< Geom_Geometry >  Mirrored (const gp_Ax2 &A2) const 
Handle< Geom_Geometry >  Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const 
Handle< Geom_Geometry >  Scaled (const gp_Pnt &P, const Standard_Real S) const 
Handle< Geom_Geometry >  Transformed (const gp_Trsf &T) const 
Handle< Geom_Geometry >  Translated (const gp_Vec &V) const 
Handle< Geom_Geometry >  Translated (const gp_Pnt &P1, const gp_Pnt &P2) const 
Public Member Functions inherited from MMgt_TShared  
virtual void  Delete () const 
Memory deallocator for transient classes. More...  
Public Member Functions inherited from Standard_Transient  
Standard_Transient ()  
Empty constructor. More...  
Standard_Transient (const Standard_Transient &)  
Copy constructor – does nothing. More...  
Standard_Transient &  operator= (const Standard_Transient &) 
Assignment operator, needed to avoid copying reference counter. More...  
virtual  ~Standard_Transient () 
Destructor must be virtual. More...  
virtual const Handle_Standard_Type &  DynamicType () const 
Returns a type information object about this object. More...  
Standard_Boolean  IsInstance (const Handle_Standard_Type &theType) const 
Returns a true value if this is an instance of Type. More...  
Standard_Boolean  IsInstance (const Standard_CString theTypeName) const 
Returns a true value if this is an instance of TypeName. More...  
Standard_Boolean  IsKind (const Handle_Standard_Type &theType) const 
Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...  
Standard_Boolean  IsKind (const Standard_CString theTypeName) const 
Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...  
virtual Handle_Standard_Transient  This () const 
Returns a Handle which references this object. Must never be called to objects created in stack. More...  
Standard_Integer  GetRefCount () const 
Get the reference counter of this object. More...  
Static Public Member Functions  
static Standard_Integer  MaxDegree () 
Returns the value of the maximum polynomial degree of any Geom_BezierCurve curve. This value is 25. More...  
Describes a rational or nonrational Bezier curve.
Geom_BezierCurve::Geom_BezierCurve  (  const TColgp_Array1OfPnt &  CurvePoles  ) 
Creates a non rational Bezier curve with a set of poles CurvePoles. The weights are defaulted to all being 1. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2.
Geom_BezierCurve::Geom_BezierCurve  (  const TColgp_Array1OfPnt &  CurvePoles, 
const TColStd_Array1OfReal &  PoleWeights  
) 
Creates a rational Bezier curve with the set of poles CurvePoles and the set of weights PoleWeights . If all the weights are identical the curve is considered as non rational. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2 or CurvePoles and CurveWeights have not the same length or one weight value is lower or equal to Resolution from package gp.

virtual 
a Bezier curve is CN
Implements Geom_Curve.

virtual 
Creates a new object which is a copy of this Bezier curve.
Implements Geom_Geometry.

virtual 
Returns in P the point of parameter U. If the curve is periodic then the returned point is P(U) with U = Ustart + (U  Uend) where Ustart and Uend are the parametric bounds of the curve.
Raised only for the "OffsetCurve" if it is not possible to compute the current point. For example when the first derivative on the basis curve and the offset direction are parallel.
Implements Geom_Curve.

virtual 
Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1.
Implements Geom_Curve.

virtual 
Returns the point P of parameter U, the first and second derivatives V1 and V2. Raised if the continuity of the curve is not C2.
Implements Geom_Curve.

virtual 
For this Bezier curve, computes.
Implements Geom_Curve.
Standard_Integer Geom_BezierCurve::Degree  (  )  const 
Returns the polynomial degree of the curve. it is the number of poles  1 point P and derivatives (V1, V2, V3) computation The Bezier Curve has a Polynomial representation so the parameter U can be out of the bounds of the curve.

virtual 
For the point of parameter U of this Bezier curve, computes the vector corresponding to the Nth derivative. Note: the parameter U can be outside the bounds of the curve. Exceptions Standard_RangeError if N is less than 1.
Implements Geom_Curve.

virtual 
Returns Value (U=1.), it is the last control point of the Bezier curve.
Implements Geom_BoundedCurve.

virtual 
Returns the value of the first parameter of this Bezier curve. This is 0.0, which gives the start point of this Bezier curve.
Implements Geom_Curve.
void Geom_BezierCurve::Increase  (  const Standard_Integer  Degree  ) 
Increases the degree of a bezier curve. Degree is the new degree of <me>. Raises ConstructionError if Degree is greater than MaxDegree or lower than 2 or lower than the initial degree of <me>.
void Geom_BezierCurve::InsertPoleAfter  (  const Standard_Integer  Index, 
const gp_Pnt &  P  
) 
Inserts a pole P after the pole of range Index. If the curve <me> is rational the weight value for the new pole of range Index is 1.0. raised if Index is not in the range [1, NbPoles].
raised if the resulting number of poles is greater than MaxDegree + 1.
void Geom_BezierCurve::InsertPoleAfter  (  const Standard_Integer  Index, 
const gp_Pnt &  P,  
const Standard_Real  Weight  
) 
Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. Raised if Index is not in the range [1, NbPoles].
Raised if the resulting number of poles is greater than MaxDegree + 1. Raised if Weight is lower or equal to Resolution from package gp.
void Geom_BezierCurve::InsertPoleBefore  (  const Standard_Integer  Index, 
const gp_Pnt &  P  
) 
Inserts a pole P before the pole of range Index. If the curve <me> is rational the weight value for the new pole of range Index is 1.0. Raised if Index is not in the range [1, NbPoles].
Raised if the resulting number of poles is greater than MaxDegree + 1.
void Geom_BezierCurve::InsertPoleBefore  (  const Standard_Integer  Index, 
const gp_Pnt &  P,  
const Standard_Real  Weight  
) 
Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. Raised if Index is not in the range [1, NbPoles].
Raised if the resulting number of poles is greater than MaxDegree + 1. Raised if Weight is lower or equal to Resolution from package gp.

virtual 
Returns True if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp.
Implements Geom_Curve.

virtual 
Continuity of the curve, returns True.
Implements Geom_Curve.

virtual 
Returns True if the parametrization of a curve is periodic. (P(u) = P(u + T) T = constante)
Implements Geom_Curve.
Standard_Boolean Geom_BezierCurve::IsRational  (  )  const 
Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp.

virtual 
Returns the value of the last parameter of this Bezier curve. This is 1.0, which gives the end point of this Bezier curve.
Implements Geom_Curve.

static 
Returns the value of the maximum polynomial degree of any Geom_BezierCurve curve. This value is 25.
Standard_Integer Geom_BezierCurve::NbPoles  (  )  const 
Returns the number of poles of this Bezier curve.
gp_Pnt Geom_BezierCurve::Pole  (  const Standard_Integer  Index  )  const 
Returns the pole of range Index. Raised if Index is not in the range [1, NbPoles].
void Geom_BezierCurve::Poles  (  TColgp_Array1OfPnt &  P  )  const 
Returns all the poles of the curve.
Raised if the length of P is not equal to the number of poles.
void Geom_BezierCurve::RemovePole  (  const Standard_Integer  Index  ) 
Removes the pole of range Index. If the curve was rational it can become non rational. Raised if Index is not in the range [1, NbPoles] Raised if Degree is lower than 2.
void Geom_BezierCurve::Resolution  (  const Standard_Real  Tolerance3D, 
Standard_Real &  UTolerance  
) 
Computes for this Bezier curve the parametric tolerance UTolerance for a given 3D tolerance Tolerance3D. If f(t) is the equation of this Bezier curve, UTolerance ensures that: t1t0 < UTolerance ===> f(t1)f(t0) < Tolerance3D.

virtual 
Reverses the direction of parametrization of <me> Value (NewU) = Value (1  OldU)
Implements Geom_Curve.

virtual 
Returns the parameter on the reversed curve for the point of parameter U on <me>.
returns 1U
Implements Geom_Curve.
void Geom_BezierCurve::Segment  (  const Standard_Real  U1, 
const Standard_Real  U2  
) 
Segments the curve between U1 and U2 which can be out of the bounds of the curve. The curve is oriented from U1 to U2. The control points are modified, the first and the last point are not the same but the parametrization range is [0, 1] else it could not be a Bezier curve. Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the curve <me> or if the curve makes loop. After the segmentation the length of a curve can be null.
void Geom_BezierCurve::SetPole  (  const Standard_Integer  Index, 
const gp_Pnt &  P  
) 
Substitutes the pole of range index with P. If the curve <me> is rational the weight of range Index is not modified. raiseD if Index is not in the range [1, NbPoles].
void Geom_BezierCurve::SetPole  (  const Standard_Integer  Index, 
const gp_Pnt &  P,  
const Standard_Real  Weight  
) 
Substitutes the pole and the weights of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. Raised if Index is not in the range [1, NbPoles] Raised if Weight <= Resolution from package gp.
void Geom_BezierCurve::SetWeight  (  const Standard_Integer  Index, 
const Standard_Real  Weight  
) 
Changes the weight of the pole of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. Raised if Index is not in the range [1, NbPoles] Raised if Weight <= Resolution from package gp.

virtual 
Returns Value (U=0.), it is the first control point of the curve.
Implements Geom_BoundedCurve.

virtual 
Applies the transformation T to this Bezier curve.
Implements Geom_Geometry.
Standard_Real Geom_BezierCurve::Weight  (  const Standard_Integer  Index  )  const 
Returns the weight of range Index. Raised if Index is not in the range [1, NbPoles].
void Geom_BezierCurve::Weights  (  TColStd_Array1OfReal &  W  )  const 
Returns all the weights of the curve.
Raised if the length of W is not equal to the number of poles.