The abstract class Conic describes the common
behavior of conic curves in 3D space and, in
particular, their general characteristics. The Geom
package provides four concrete classes of conics:
Geom_Circle, Geom_Ellipse, Geom_Hyperbola and Geom_Parabola.
A conic is positioned in space with a right-handed
coordinate system (gp_Ax2 object), where:
More...

#include <Geom_Conic.hxx>

Inheritance diagram for Geom_Conic:

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Public Member Functions
void	SetAxis (const gp_Ax1 &A1)
	Changes the orientation of the conic's plane. The normal <br> axis to the plane is A1. The XAxis and the YAxis are recomputed. raised if the A1 is parallel to the XAxis of the conic. More...

void	SetLocation (const gp_Pnt &P)
	changes the location point of the conic. More...

void	SetPosition (const gp_Ax2 &A2)
	changes the local coordinate system of the conic. More...

gp_Ax1	Axis () const
	Returns the "main Axis" of this conic. This axis is <br> normal to the plane of the conic. More...

virtual Standard_Real	Eccentricity () const =0
	Returns the eccentricity value of the conic e. <br> e = 0 for a circle 0 < e < 1 for an ellipse (e = 0 if MajorRadius = MinorRadius) e > 1 for a hyperbola e = 1 for a parabola Exceptions Standard_DomainError in the case of a hyperbola if its major radius is null. More...

gp_Pnt	Location () const
	Returns the location point of the conic. For the circle, the ellipse and the hyperbola it is the center of the conic. For the parabola it is the Apex of the parabola. More...

const gp_Ax2 &	Position () const
	Returns the local coordinates system of the conic. The main direction of the Axis2Placement is normal to the plane of the conic. The X direction of the Axis2placement is in the plane of the conic and corresponds to the origin for the conic's parametric value u. More...

gp_Ax1	XAxis () const
	Returns the XAxis of the conic. This axis defines the origin of parametrization of the conic. This axis is perpendicular to the Axis of the conic. This axis and the Yaxis define the plane of the conic. More...

gp_Ax1	YAxis () const
	Returns the YAxis of the conic. The YAxis is perpendicular to the Xaxis. This axis and the Xaxis define the plane of the conic. More...

void	Reverse ()
	Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. More...

virtual Standard_Real	ReversedParameter (const Standard_Real U) const =0
	Returns the parameter on the reversed curve for <br> the point of parameter U on <me>. <br> More...

GeomAbs_Shape	Continuity () const
	The continuity of the conic is Cn. More...

Standard_Boolean	IsCN (const Standard_Integer N) const
	Returns True. //! Raised if N < 0. 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 <br> the transform of the point of parameter U on <me>. <br> 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. More...

virtual Standard_Real	ParametricTransformation (const gp_Trsf &T) const
	Returns a coefficient to compute the parameter on <br> the transformed curve for the transform of the <br> point on <me>. <br> 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. 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. <br> 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. <br> 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. <br> 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 ? <br> 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. <br> Exceptions Standard_NoSuchObject if this curve is not periodic. More...

virtual void	D0 (const Standard_Real U, gp_Pnt &P) const =0
	Returns in P the point of parameter U. <br> 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. 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. //! Raised if the derivative cannot be computed easily. e.g. rational bspline and n > 3. //! Raised if N < 1. More...

gp_Pnt	Value (const Standard_Real U) const
	Computes the point of parameter U on <me>. <br> 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. 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 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 void	ShallowDump (Standard_OStream &) const

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...

Protected Attributes
gp_Ax2	pos

Detailed Description

The abstract class Conic describes the common
behavior of conic curves in 3D space and, in
particular, their general characteristics. The Geom
package provides four concrete classes of conics:
Geom_Circle, Geom_Ellipse, Geom_Hyperbola and Geom_Parabola.
A conic is positioned in space with a right-handed
coordinate system (gp_Ax2 object), where:

the origin is the center of the conic (or the apex in
the case of a parabola),
the origin, "X Direction" and "Y Direction" define the
plane of the conic.
This coordinate system is the local coordinate
system of the conic.
The "main Direction" of this coordinate system is the
vector normal to the plane of the conic. The axis, of
which the origin and unit vector are respectively the
origin and "main Direction" of the local coordinate
system, is termed the "Axis" or "main Axis" of the conic.
The "main Direction" of the local coordinate system
gives an explicit orientation to the conic, determining
the direction in which the parameter increases along
the conic. The "X Axis" of the local coordinate system
also defines the origin of the parameter of the conic.

Member Function Documentation

gp_Ax1 Geom_Conic::Axis ( ) const

 Returns the "main Axis" of this conic. This axis is <br>

normal to the plane of the conic.

GeomAbs_Shape Geom_Conic::Continuity ( ) const

virtual

The continuity of the conic is Cn.

Implements Geom_Curve.

virtual Standard_Real Geom_Conic::Eccentricity ( ) const

pure virtual

Returns the eccentricity value of the conic e. <br>

e = 0 for a circle
0 < e < 1 for an ellipse (e = 0 if MajorRadius = MinorRadius)
e > 1 for a hyperbola
e = 1 for a parabola
Exceptions
Standard_DomainError in the case of a hyperbola if
its major radius is null.

Implemented in Geom_Hyperbola, Geom_Ellipse, Geom_Parabola, and Geom_Circle.

Standard_Boolean Geom_Conic::IsCN ( const Standard_Integer N ) const

virtual

Returns True.
//! Raised if N < 0.

Implements Geom_Curve.

gp_Pnt Geom_Conic::Location ( ) const

Returns the location point of the conic.
For the circle, the ellipse and the hyperbola it is the center of
the conic. For the parabola it is the Apex of the parabola.

const gp_Ax2& Geom_Conic::Position ( ) const

Returns the local coordinates system of the conic.
The main direction of the Axis2Placement is normal to the
plane of the conic. The X direction of the Axis2placement
is in the plane of the conic and corresponds to the origin
for the conic's parametric value u.

void Geom_Conic::Reverse ( )

virtual

Reverses the direction of parameterization of <me>.
The local coordinate system of the conic is modified.

Implements Geom_Curve.

virtual Standard_Real Geom_Conic::ReversedParameter ( const Standard_Real U ) const

pure virtual

 Returns the  parameter on the  reversed  curve for <br>
     the point of parameter U on <me>. <br>

Implements Geom_Curve.

Implemented in Geom_Hyperbola, Geom_Ellipse, Geom_Parabola, and Geom_Circle.

void Geom_Conic::SetAxis ( const gp_Ax1 & A1 )

Changes the orientation of the conic's plane. The normal <br>

axis to the plane is A1. The XAxis and the YAxis are recomputed.
raised if the A1 is parallel to the XAxis of the conic.

void Geom_Conic::SetLocation ( const gp_Pnt & P )

changes the location point of the conic.

void Geom_Conic::SetPosition ( const gp_Ax2 & A2 )

changes the local coordinate system of the conic.

gp_Ax1 Geom_Conic::XAxis ( ) const

Returns the XAxis of the conic.
This axis defines the origin of parametrization of the conic.
This axis is perpendicular to the Axis of the conic.
This axis and the Yaxis define the plane of the conic.

gp_Ax1 Geom_Conic::YAxis ( ) const

Returns the YAxis of the conic.
The YAxis is perpendicular to the Xaxis.
This axis and the Xaxis define the plane of the conic.

Field Documentation

gp_Ax2 Geom_Conic::pos

protected

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

Geom_Conic.hxx

Public Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

Field Documentation