# Geom2d_Circle Class Reference

Describes a circle in the plane (2D space). A circle is defined by its radius and, as with any conic curve, is positioned in the plane with a coordinate system (gp_Ax22d object) where the origin is the center of the circle. The coordinate system is the local coordinate system of the circle. The orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the circle, determining the direction in which the parameter increases along the circle. The Geom2d_Circle circle is parameterized by an angle: P(U) = O + R*Cos(U)*XDir + R*Sin(U)*YDir where: More...

`#include <Geom2d_Circle.hxx>`

Inheritance diagram for Geom2d_Circle: [legend]

## Public Member Functions

Geom2d_Circle (const gp_Circ2d &C)
Constructs a circle by conversion of the gp_Circ2d circle C. More...

Geom2d_Circle (const gp_Ax2d &A, const Standard_Real Radius, const Standard_Boolean Sense=Standard_True)
Constructs a circle of radius Radius, whose center is the origin of axis A; A is the "X Axis" of the local coordinate system of the circle; this coordinate system is direct if Sense is true (default value) or indirect if Sense is false. Note: It is possible to create a circle where Radius is equal to 0.0. Exceptions Standard_ConstructionError if Radius is negative. More...

Geom2d_Circle (const gp_Ax22d &A, const Standard_Real Radius)
Constructs a circle of radius Radius, where the coordinate system A locates the circle and defines its orientation in the plane such that: More...

void SetCirc2d (const gp_Circ2d &C)
Converts the gp_Circ2d circle C into this circle. More...

gp_Circ2d Circ2d () const
Returns the non persistent circle from gp with the same geometric properties as <me>. More...

Returns the radius of this circle. More...

Standard_Real ReversedParameter (const Standard_Real U) const override
Computes the parameter on the reversed circle for the point of parameter U on this circle. For a circle, the returned value is: 2.*Pi - U. More...

Standard_Real Eccentricity () const override
Returns 0., which is the eccentricity of any circle. More...

Standard_Real FirstParameter () const override
Returns 0.0. More...

Standard_Real LastParameter () const override
Returns 2*PI. More...

Standard_Boolean IsClosed () const override
returns True. More...

Standard_Boolean IsPeriodic () const override
returns True. The period of a circle is 2.*Pi. More...

void D0 (const Standard_Real U, gp_Pnt2d &P) const override
Returns in P the point of parameter U. P = C + R * Cos (U) * XDir + R * Sin (U) * YDir where C is the center of the circle , XDir the XDirection and YDir the YDirection of the circle's local coordinate system. More...

void D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1) const override
Returns the point P of parameter U and the first derivative V1. More...

void D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const override
Returns the point P of parameter U, the first and second derivatives V1 and V2. More...

void D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const override
Returns the point P of parameter u, the first second and third derivatives V1 V2 and V3. More...

gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const override
For the point of parameter U of this circle, computes the vector corresponding to the Nth derivative. Exceptions: Standard_RangeError if N is less than 1. More...

void Transform (const gp_Trsf2d &T) override
Applies the transformation T to this circle. More...

Handle< Geom2d_GeometryCopy () const override
Creates a new object which is a copy of this circle. More... Public Member Functions inherited from Geom2d_Conic
void SetAxis (const gp_Ax22d &A)
Modifies this conic, redefining its local coordinate system partially, by assigning P as its origin. More...

void SetXAxis (const gp_Ax2d &A)

void SetYAxis (const gp_Ax2d &A)
Assigns the origin and unit vector of axis A to the origin of the local coordinate system of this conic and either: More...

void SetLocation (const gp_Pnt2d &P)
Modifies this conic, redefining its local coordinate system fully, by assigning A as this coordinate system. More...

gp_Ax2d XAxis () const
Returns the "XAxis" of the conic. This axis defines the origin of parametrization of the conic. This axis and the "Yaxis" define the local coordinate system of the conic. -C++: return const&. More...

gp_Ax2d YAxis () const
Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis". More...

gp_Pnt2d 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 vertex of the parabola. More...

const gp_Ax22dPosition () const
Returns the local coordinates system of the conic. More...

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

GeomAbs_Shape Continuity () const override
Returns GeomAbs_CN which is the global continuity of any conic. More...

Standard_Boolean IsCN (const Standard_Integer N) const override
Returns True, the order of continuity of a conic is infinite. More... Public Member Functions inherited from Geom2d_Curve
virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const
Computes the parameter on the curve transformed by T for the point of parameter U on this curve. Note: this function generally returns U but it can be redefined (for example, on a line). More...

virtual Standard_Real ParametricTransformation (const gp_Trsf2d &T) const
Returns the coefficient required to compute the parametric transformation of this curve when transformation T is applied. This coefficient is the ratio between the parameter of a point on this curve and the parameter of the transformed point on the new curve transformed by T. Note: this function generally returns 1. but it can be redefined (for example, on a line). More...

Handle< Geom2d_CurveReversed () const
Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded: More...

virtual Standard_Real Period () const
Returns thne period of this curve. raises if the curve is not periodic. More...

gp_Pnt2d 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. More... Public Member Functions inherited from Geom2d_Geometry
void Mirror (const gp_Pnt2d &P)
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object. More...

void Mirror (const gp_Ax2d &A)
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void Rotate (const gp_Pnt2d &P, const Standard_Real Ang)
Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians. More...

void Scale (const gp_Pnt2d &P, const Standard_Real S)
Scales a Geometry. S is the scaling value. More...

void Translate (const gp_Vec2d &V)
Translates a Geometry. V is the vector of the tanslation. More...

void Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)
Translates a Geometry from the point P1 to the point P2. More...

Handle< Geom2d_GeometryMirrored (const gp_Pnt2d &P) const

Handle< Geom2d_GeometryMirrored (const gp_Ax2d &A) const

Handle< Geom2d_GeometryRotated (const gp_Pnt2d &P, const Standard_Real Ang) const

Handle< Geom2d_GeometryScaled (const gp_Pnt2d &P, const Standard_Real S) const

Handle< Geom2d_GeometryTransformed (const gp_Trsf2d &T) const

Handle< Geom2d_GeometryTranslated (const gp_Vec2d &V) const

Handle< Geom2d_GeometryTranslated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const Public Member Functions inherited from MMgt_TShared
virtual void Delete () const override
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_Transientoperator= (const Standard_Transient &)
Assignment operator, needed to avoid copying reference counter. More...

virtual ~Standard_Transient ()
Destructor must be virtual. More...

virtual const opencascade::handle< Standard_Type > & DynamicType () const

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_TransientThis () const
Returns non-const 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... Public Types inherited from Standard_Transient
typedef void base_type Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()

static const opencascade::handle< Standard_Type > & get_type_descriptor ()
Returns type descriptor of Standard_Transient class. More... Protected Attributes inherited from Geom2d_Conic
gp_Ax22d pos

## Detailed Description

Describes a circle in the plane (2D space). A circle is defined by its radius and, as with any conic curve, is positioned in the plane with a coordinate system (gp_Ax22d object) where the origin is the center of the circle. The coordinate system is the local coordinate system of the circle. The orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the circle, determining the direction in which the parameter increases along the circle. The Geom2d_Circle circle is parameterized by an angle: P(U) = O + R*Cos(U)*XDir + R*Sin(U)*YDir where:

• P is the point of parameter U,
• O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
• R is the radius of the circle. The "X Axis" of the local coordinate system therefore defines the origin of the parameter of the circle. The parameter is the angle with this "X Direction". A circle is a closed and periodic curve. The period is 2.*Pi and the parameter range is [ 0,2.*Pi [. See Also GCE2d_MakeCircle which provides functions for more complex circle constructions gp_Ax22d and gp_Circ2d for an equivalent, non-parameterized data structure.

## Constructor & Destructor Documentation

 Geom2d_Circle::Geom2d_Circle ( const gp_Circ2d & C )

Constructs a circle by conversion of the gp_Circ2d circle C.

 Geom2d_Circle::Geom2d_Circle ( const gp_Ax2d & A, const Standard_Real Radius, const Standard_Boolean Sense = `Standard_True` )

Constructs a circle of radius Radius, whose center is the origin of axis A; A is the "X Axis" of the local coordinate system of the circle; this coordinate system is direct if Sense is true (default value) or indirect if Sense is false. Note: It is possible to create a circle where Radius is equal to 0.0. Exceptions Standard_ConstructionError if Radius is negative.

 Geom2d_Circle::Geom2d_Circle ( const gp_Ax22d & A, const Standard_Real Radius )

Constructs a circle of radius Radius, where the coordinate system A locates the circle and defines its orientation in the plane such that:

• the center of the circle is the origin of A,
• the orientation (direct or indirect) of A gives the orientation of the circle.

## Member Function Documentation

 gp_Circ2d Geom2d_Circle::Circ2d ( ) const

Returns the non persistent circle from gp with the same geometric properties as <me>.

 Handle< Geom2d_Geometry > Geom2d_Circle::Copy ( ) const
overridevirtual

Creates a new object which is a copy of this circle.

Implements Geom2d_Geometry.

 void Geom2d_Circle::D0 ( const Standard_Real U, gp_Pnt2d & P ) const
overridevirtual

Returns in P the point of parameter U. P = C + R * Cos (U) * XDir + R * Sin (U) * YDir where C is the center of the circle , XDir the XDirection and YDir the YDirection of the circle's local coordinate system.

Implements Geom2d_Curve.

 void Geom2d_Circle::D1 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1 ) const
overridevirtual

Returns the point P of parameter U and the first derivative V1.

Implements Geom2d_Curve.

 void Geom2d_Circle::D2 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 ) const
overridevirtual

Returns the point P of parameter U, the first and second derivatives V1 and V2.

Implements Geom2d_Curve.

 void Geom2d_Circle::D3 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 ) const
overridevirtual

Returns the point P of parameter u, the first second and third derivatives V1 V2 and V3.

Implements Geom2d_Curve.

 gp_Vec2d Geom2d_Circle::DN ( const Standard_Real U, const Standard_Integer N ) const
overridevirtual

For the point of parameter U of this circle, computes the vector corresponding to the Nth derivative. Exceptions: Standard_RangeError if N is less than 1.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Circle::Eccentricity ( ) const
overridevirtual

Returns 0., which is the eccentricity of any circle.

Implements Geom2d_Conic.

 Standard_Real Geom2d_Circle::FirstParameter ( ) const
overridevirtual

Returns 0.0.

Implements Geom2d_Curve.

 Standard_Boolean Geom2d_Circle::IsClosed ( ) const
overridevirtual

returns True.

Implements Geom2d_Curve.

 Standard_Boolean Geom2d_Circle::IsPeriodic ( ) const
overridevirtual

returns True. The period of a circle is 2.*Pi.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Circle::LastParameter ( ) const
overridevirtual

Returns 2*PI.

Implements Geom2d_Curve.

Returns the radius of this circle.

 Standard_Real Geom2d_Circle::ReversedParameter ( const Standard_Real U ) const
overridevirtual

Computes the parameter on the reversed circle for the point of parameter U on this circle. For a circle, the returned value is: 2.*Pi - U.

Implements Geom2d_Conic.

 void Geom2d_Circle::SetCirc2d ( const gp_Circ2d & C )

Converts the gp_Circ2d circle C into this circle.

 void Geom2d_Circle::SetRadius ( const Standard_Real R )
 void Geom2d_Circle::Transform ( const gp_Trsf2d & T )
overridevirtual

Applies the transformation T to this circle.

Implements Geom2d_Geometry.

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