Open CASCADE Technology
7.5.0

The abstract class Curve describes the common behavior of curves in 3D space. The Geom package provides numerous concrete classes of derived curves, including lines, circles, conics, Bezier or BSpline curves, etc. The main characteristic of these curves is that they are parameterized. The Geom_Curve class shows: More...
#include <Geom_Curve.hxx>
Public Member Functions  
virtual void  Reverse ()=0 
Changes the direction of parametrization of <me>. The "FirstParameter" and the "LastParameter" are not changed but the orientation of the curve is modified. If the curve is bounded the StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve. More...  
virtual Standard_Real  ReversedParameter (const Standard_Real U) const =0 
Returns the parameter on the reversed curve for the point of parameter U on <me>. More...  
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  FirstParameter () const =0 
Returns the value of the first parameter. Warnings : It can be RealFirst from package Standard if the curve is infinite. More...  
virtual Standard_Real  LastParameter () const =0 
Returns the value of the last parameter. Warnings : It can be RealLast from package Standard if the curve is infinite. More...  
virtual Standard_Boolean  IsClosed () const =0 
Returns true if the curve is closed. Some curves such as circle are always closed, others such as line are never closed (by definition). Some Curves such as OffsetCurve can be closed or not. These curves are considered as closed if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp wich is a fixed criterion independant of the application. More...  
virtual Standard_Boolean  IsPeriodic () const =0 
Is the parametrization of the curve periodic ? It is possible only if the curve is closed and if the following relation is satisfied : for each parametric value U the distance between the point P(u) and the point P (u + T) is lower or equal to Resolution from package gp, T is the period and must be a constant. There are three possibilities : . the curve is never periodic by definition (SegmentLine) . the curve is always periodic by definition (Circle) . the curve can be defined as periodic (BSpline). In this case a function SetPeriodic allows you to give the shape of the curve. The general rule for this case is : if a curve can be periodic or not the default periodicity set is non periodic and you have to turn (explicitly) the curve into a periodic curve if you want the curve to be periodic. More...  
virtual Standard_Real  Period () const 
Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic. More...  
virtual GeomAbs_Shape  Continuity () const =0 
It is the global continuity of the curve C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, G1 : tangency continuity all along the Curve, G2 : curvature continuity all along the Curve, CN : the order of continuity is infinite. More...  
virtual Standard_Boolean  IsCN (const Standard_Integer N) const =0 
Returns true if the degree of continuity of this curve is at least N. Exceptions  Standard_RangeError if N is less than 0. More...  
virtual void  D0 (const Standard_Real U, gp_Pnt &P) const =0 
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...  
virtual void  D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const =0 
Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1. More...  
virtual void  D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const =0 
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...  
virtual void  D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const =0 
Returns the point P of parameter U, the first, the second and the third derivative. Raised if the continuity of the curve is not C3. More...  
virtual gp_Vec  DN (const Standard_Real U, const Standard_Integer N) const =0 
The returned vector gives the value of the derivative for the order of derivation N. Raised if the continuity of the curve is not CN. 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...  
virtual void  DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=1) const override 
Dumps the content of me into the stream. 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...  
virtual void  Transform (const gp_Trsf &T)=0 
Transformation of a geometric object. This tansformation can be a translation, a rotation, a symmetry, a scaling or a complex transformation obtained by combination of the previous elementaries transformations. (see class Transformation of the package Geom). 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 
virtual Handle< Geom_Geometry >  Copy () const =0 
Creates a new object which is a copy of this geometric object. 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 void  Delete () const 
Memory deallocator for transient classes. More...  
virtual const opencascade::handle< Standard_Type > &  DynamicType () const 
Returns a type descriptor about this object. More...  
Standard_Boolean  IsInstance (const opencascade::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 opencascade::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...  
Standard_Transient *  This () const 
Returns nonconst pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero. More...  
Standard_Integer  GetRefCount () const 
Get the reference counter of this object. More...  
void  IncrementRefCounter () const 
Increments the reference counter of this object. More...  
Standard_Integer  DecrementRefCounter () const 
Decrements the reference counter of this object; returns the decremented value. More...  
Additional Inherited Members  
Public Types inherited from Standard_Transient  
typedef void  base_type 
Returns a type descriptor about this object. More...  
Static Public Member Functions inherited from Standard_Transient  
static const char *  get_type_name () 
Returns a type descriptor about this object. More...  
static const opencascade::handle< Standard_Type > &  get_type_descriptor () 
Returns type descriptor of Standard_Transient class. More...  
The abstract class Curve describes the common behavior of curves in 3D space. The Geom package provides numerous concrete classes of derived curves, including lines, circles, conics, Bezier or BSpline curves, etc. The main characteristic of these curves is that they are parameterized. The Geom_Curve class shows:

pure virtual 
It is the global continuity of the curve C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, G1 : tangency continuity all along the Curve, G2 : curvature continuity all along the Curve, CN : the order of continuity is infinite.
Implemented in Geom_BSplineCurve, Geom_BezierCurve, Geom_OffsetCurve, Geom_TrimmedCurve, Geom_Line, Geom_Conic, and ShapeExtend_ComplexCurve.

pure 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.
Implemented in Geom_BSplineCurve, Geom_BezierCurve, Geom_Hyperbola, Geom_TrimmedCurve, Geom_Ellipse, Geom_OffsetCurve, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

pure virtual 
Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1.
Implemented in Geom_BSplineCurve, Geom_Hyperbola, Geom_BezierCurve, Geom_TrimmedCurve, Geom_Ellipse, Geom_OffsetCurve, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

pure 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.
Implemented in Geom_BSplineCurve, Geom_Hyperbola, Geom_BezierCurve, Geom_TrimmedCurve, Geom_Ellipse, Geom_OffsetCurve, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

pure virtual 
Returns the point P of parameter U, the first, the second and the third derivative. Raised if the continuity of the curve is not C3.
Implemented in Geom_BSplineCurve, Geom_Hyperbola, Geom_BezierCurve, Geom_TrimmedCurve, Geom_Ellipse, Geom_OffsetCurve, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

pure virtual 
The returned vector gives the value of the derivative for the order of derivation N. Raised if the continuity of the curve is not CN.
Raised if the derivative cannot be computed easily. e.g. rational bspline and n > 3. Raised if N < 1.
Implemented in Geom_BSplineCurve, Geom_Hyperbola, Geom_BezierCurve, Geom_TrimmedCurve, Geom_Ellipse, Geom_OffsetCurve, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

overridevirtual 
Dumps the content of me into the stream.
Reimplemented from Geom_Geometry.
Reimplemented in Geom_BSplineCurve, Geom_BezierCurve, Geom_OffsetCurve, Geom_Hyperbola, Geom_TrimmedCurve, Geom_Parabola, Geom_Ellipse, Geom_Line, Geom_Circle, Geom_Conic, and Geom_BoundedCurve.

pure virtual 
Returns the value of the first parameter. Warnings : It can be RealFirst from package Standard if the curve is infinite.
Implemented in Geom_BSplineCurve, Geom_BezierCurve, Geom_OffsetCurve, Geom_Ellipse, Geom_TrimmedCurve, Geom_Hyperbola, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

pure virtual 
Returns true if the curve is closed. Some curves such as circle are always closed, others such as line are never closed (by definition). Some Curves such as OffsetCurve can be closed or not. These curves are considered as closed if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp wich is a fixed criterion independant of the application.
Implemented in Geom_BSplineCurve, Geom_OffsetCurve, Geom_BezierCurve, Geom_Ellipse, Geom_TrimmedCurve, Geom_Hyperbola, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

pure virtual 
Returns true if the degree of continuity of this curve is at least N. Exceptions  Standard_RangeError if N is less than 0.
Implemented in Geom_BSplineCurve, Geom_OffsetCurve, Geom_BezierCurve, Geom_TrimmedCurve, Geom_Line, Geom_Conic, and ShapeExtend_ComplexCurve.

pure virtual 
Is the parametrization of the curve periodic ? It is possible only if the curve is closed and if the following relation is satisfied : for each parametric value U the distance between the point P(u) and the point P (u + T) is lower or equal to Resolution from package gp, T is the period and must be a constant. There are three possibilities : . the curve is never periodic by definition (SegmentLine) . the curve is always periodic by definition (Circle) . the curve can be defined as periodic (BSpline). In this case a function SetPeriodic allows you to give the shape of the curve. The general rule for this case is : if a curve can be periodic or not the default periodicity set is non periodic and you have to turn (explicitly) the curve into a periodic curve if you want the curve to be periodic.
Implemented in Geom_BSplineCurve, Geom_OffsetCurve, Geom_BezierCurve, Geom_Ellipse, Geom_TrimmedCurve, Geom_Hyperbola, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

pure virtual 
Returns the value of the last parameter. Warnings : It can be RealLast from package Standard if the curve is infinite.
Implemented in Geom_BSplineCurve, Geom_BezierCurve, Geom_OffsetCurve, Geom_TrimmedCurve, Geom_Ellipse, Geom_Hyperbola, Geom_Parabola, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

virtual 
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
Transformed(T)>Value(U * ParametricTransformation(T))
is the same point as
Value(U).Transformed(T)
This methods returns 1.
It can be redefined. For example on the Line.
Reimplemented in Geom_OffsetCurve, Geom_TrimmedCurve, Geom_Parabola, and Geom_Line.

virtual 
Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic.
Reimplemented in Geom_OffsetCurve, and Geom_TrimmedCurve.

pure virtual 
Changes the direction of parametrization of <me>. The "FirstParameter" and the "LastParameter" are not changed but the orientation of the curve is modified. If the curve is bounded the StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve.
Implemented in Geom_BSplineCurve, Geom_BezierCurve, Geom_OffsetCurve, Geom_TrimmedCurve, Geom_Conic, and Geom_Line.
Handle< Geom_Curve > Geom_Curve::Reversed  (  )  const 
Returns a copy of <me> reversed.

pure virtual 
Returns the parameter on the reversed curve for the point of parameter U on <me>.
me>Reversed()>Value(me>ReversedParameter(U))
is the same point as
me>Value(U)
Implemented in Geom_BSplineCurve, Geom_BezierCurve, Geom_Hyperbola, Geom_OffsetCurve, Geom_Ellipse, Geom_Parabola, Geom_TrimmedCurve, Geom_Conic, Geom_Circle, Geom_Line, and ShapeExtend_ComplexCurve.

virtual 
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.
me>Transformed(T)>Value(me>TransformedParameter(U,T))
is the same point as
me>Value(U).Transformed(T)
This methods returns <U>
It can be redefined. For example on the Line.
Reimplemented in Geom_OffsetCurve, Geom_TrimmedCurve, Geom_Parabola, and Geom_Line.
gp_Pnt Geom_Curve::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.
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.