Describes an ellipse in the plane (2D space). An ellipse is defined by its major and minor radii and, as with any conic curve, is positioned in the plane with a coordinate system (gp_Ax22d object) where: More...
#include <Geom2d_Ellipse.hxx>
Public Member Functions | |
| Geom2d_Ellipse (const gp_Elips2d &E) | |
| Creates an ellipse by conversion of the gp_Elips2d ellipse E. More... | |
| Geom2d_Ellipse (const gp_Ax2d &MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense=Standard_True) | |
| Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, and positioned in the plane by its major axis MajorAxis; the center of the ellipse is the origin of MajorAxis and the unit vector of MajorAxis is the "X
Direction" of the local coordinate system of the ellipse; this coordinate system is direct if Sense is true (default value) or indirect if Sense is false. Warnings : It is not forbidden to create an ellipse with MajorRadius = MinorRadius. Exceptions Standard_ConstructionError if: More... | |
| Geom2d_Ellipse (const gp_Ax22d &Axis, const Standard_Real MajorRadius, const Standard_Real MinorRadius) | |
| Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where the coordinate system Axis locates the ellipse and defines its orientation in the plane such that: More... | |
| void | SetElips2d (const gp_Elips2d &E) |
| Converts the gp_Elips2d ellipse E into this ellipse. More... | |
| void | SetMajorRadius (const Standard_Real MajorRadius) |
| Assigns a value to the major radius of this ellipse. Exceptions Standard_ConstructionError if: More... | |
| void | SetMinorRadius (const Standard_Real MinorRadius) |
| Assigns a value to the minor radius of this ellipse. Exceptions Standard_ConstructionError if: More... | |
| gp_Elips2d | Elips2d () const |
| Converts this ellipse into a gp_Elips2d ellipse. More... | |
| Standard_Real | ReversedParameter (const Standard_Real U) const |
| Computes the parameter on the reversed ellipse for the point of parameter U on this ellipse. For an ellipse, the returned value is: 2.*Pi - U. More... | |
| gp_Ax2d | Directrix1 () const |
| Computes the directrices of this ellipse. This directrix is the line normal to the XAxis of the ellipse in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the ellipse, where e is the eccentricity of the ellipse. This line is parallel to the "YAxis". The intersection point between directrix1 and the "XAxis" is the "Location" point of the directrix1. This point is on the positive side of the "XAxis". Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a circle) More... | |
| gp_Ax2d | Directrix2 () const |
| This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a circle). More... | |
| Standard_Real | Eccentricity () const |
| Returns the eccentricity of the ellipse between 0.0 and 1.0 If f is the distance between the center of the ellipse and the Focus1 then the eccentricity e = f / MajorRadius. Returns 0 if MajorRadius = 0. More... | |
| Standard_Real | Focal () const |
| Computes the focal distance. The focal distance is the distance between the center and a focus of the ellipse. More... | |
| gp_Pnt2d | Focus1 () const |
| Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse. More... | |
| gp_Pnt2d | Focus2 () const |
| Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse. More... | |
| Standard_Real | MajorRadius () const |
| Returns the major radius of this ellipse. More... | |
| Standard_Real | MinorRadius () const |
| Returns the minor radius of this ellipse. More... | |
| Standard_Real | Parameter () const |
| Computes the parameter of this ellipse. This value is given by the formula p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0. More... | |
| Standard_Real | FirstParameter () const |
| Returns the value of the first parameter of this ellipse. This is 0.0, which gives the start point of this ellipse. The start point and end point of an ellipse are coincident. More... | |
| Standard_Real | LastParameter () const |
| Returns the value of the last parameter of this ellipse. This is 2.*Pi, which gives the end point of this ellipse. The start point and end point of an ellipse are coincident. More... | |
| Standard_Boolean | IsClosed () const |
| return True. More... | |
| Standard_Boolean | IsPeriodic () const |
| return True. More... | |
| void | D0 (const Standard_Real U, gp_Pnt2d &P) const |
| Returns in P the point of parameter U. P = C + MajorRadius * Cos (U) * XDir + MinorRadius * Sin (U) * YDir where C is the center of the ellipse , XDir the direction of the "XAxis" and "YDir" the "YAxis" of the ellipse. More... | |
| void | D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &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_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const |
| Returns the point P of parameter U. The vectors V1 and V2 are the first and second derivatives at this point. More... | |
| void | D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const |
| 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 |
| For the point of parameter U of this ellipse, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1. More... | |
| void | Transform (const gp_Trsf2d &T) |
| Applies the transformation T to this ellipse. More... | |
| Handle< Geom2d_Geometry > | Copy () const |
| Creates a new object which is a copy of this ellipse. 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_Ax22d & | Position () const |
| Returns the local coordinates system of the conic. More... | |
| void | Reverse () |
| Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. More... | |
| GeomAbs_Shape | Continuity () const |
| Returns GeomAbs_CN which is the global continuity of any conic. More... | |
| Standard_Boolean | IsCN (const Standard_Integer N) const |
| 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_Curve > | Reversed () 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_Geometry > | Mirrored (const gp_Pnt2d &P) const |
| Handle< Geom2d_Geometry > | Mirrored (const gp_Ax2d &A) const |
| Handle< Geom2d_Geometry > | Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const |
| Handle< Geom2d_Geometry > | Scaled (const gp_Pnt2d &P, const Standard_Real S) const |
| Handle< Geom2d_Geometry > | Transformed (const gp_Trsf2d &T) const |
| Handle< Geom2d_Geometry > | Translated (const gp_Vec2d &V) const |
| Handle< Geom2d_Geometry > | Translated (const gp_Pnt2d &P1, const gp_Pnt2d &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... | |
Additional Inherited Members | |
| Protected Attributes inherited from Geom2d_Conic | |
| gp_Ax22d | pos |
Detailed Description
Describes an ellipse in the plane (2D space). An ellipse is defined by its major and minor radii 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 ellipse,
- the "X Direction" defines the major axis, and
- the "Y Direction" defines the minor axis. This coordinate system is the local coordinate system of the ellipse. The orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the ellipse, determining the direction in which the parameter increases along the ellipse. The Geom2d_Ellipse ellipse is parameterized by an angle: P(U) = O + MajorRad*Cos(U)*XDir + MinorRad*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,
- MajorRad and MinorRad are the major and minor radii of the ellipse. The "X Axis" of the local coordinate system therefore defines the origin of the parameter of the ellipse. An ellipse is a closed and periodic curve. The period is 2.*Pi and the parameter range is [ 0,2.*Pi [. See Also GCE2d_MakeEllipse which provides functions for more complex ellipse constructions gp_Ax22d gp_Elips2d for an equivalent, non-parameterized data structure
Constructor & Destructor Documentation
| Geom2d_Ellipse::Geom2d_Ellipse | ( | const gp_Elips2d & | E | ) |
Creates an ellipse by conversion of the gp_Elips2d ellipse E.
| Geom2d_Ellipse::Geom2d_Ellipse | ( | const gp_Ax2d & | MajorAxis, |
| const Standard_Real | MajorRadius, | ||
| const Standard_Real | MinorRadius, | ||
| const Standard_Boolean | Sense = Standard_True |
||
| ) |
Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, and positioned in the plane by its major axis MajorAxis; the center of the ellipse is the origin of MajorAxis and the unit vector of MajorAxis is the "X Direction" of the local coordinate system of the ellipse; this coordinate system is direct if Sense is true (default value) or indirect if Sense is false. Warnings : It is not forbidden to create an ellipse with MajorRadius = MinorRadius. Exceptions Standard_ConstructionError if:
- MajorRadius is less than MinorRadius, or
- MinorRadius is less than 0.
| Geom2d_Ellipse::Geom2d_Ellipse | ( | const gp_Ax22d & | Axis, |
| const Standard_Real | MajorRadius, | ||
| const Standard_Real | MinorRadius | ||
| ) |
Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where the coordinate system Axis locates the ellipse and defines its orientation in the plane such that:
- the center of the ellipse is the origin of Axis,
- the "X Direction" of Axis defines the major axis of the ellipse,
- the "Y Direction" of Axis defines the minor axis of the ellipse,
- the orientation of Axis (direct or indirect) gives the orientation of the ellipse. Warnings : It is not forbidden to create an ellipse with MajorRadius = MinorRadius. Exceptions Standard_ConstructionError if:
- MajorRadius is less than MinorRadius, or
- MinorRadius is less than 0.
Member Function Documentation
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Creates a new object which is a copy of this ellipse.
Implements Geom2d_Geometry.
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Returns in P the point of parameter U. P = C + MajorRadius * Cos (U) * XDir + MinorRadius * Sin (U) * YDir where C is the center of the ellipse , XDir the direction of the "XAxis" and "YDir" the "YAxis" of the ellipse.
Implements Geom2d_Curve.
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Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1.
Implements Geom2d_Curve.
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Returns the point P of parameter U. The vectors V1 and V2 are the first and second derivatives at this point.
Implements Geom2d_Curve.
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Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.
Implements Geom2d_Curve.
| gp_Ax2d Geom2d_Ellipse::Directrix1 | ( | ) | const |
Computes the directrices of this ellipse. This directrix is the line normal to the XAxis of the ellipse in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the ellipse, where e is the eccentricity of the ellipse. This line is parallel to the "YAxis". The intersection point between directrix1 and the "XAxis" is the "Location" point of the directrix1. This point is on the positive side of the "XAxis". Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a circle)
| gp_Ax2d Geom2d_Ellipse::Directrix2 | ( | ) | const |
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a circle).
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For the point of parameter U of this ellipse, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.
Implements Geom2d_Curve.
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Returns the eccentricity of the ellipse between 0.0 and 1.0 If f is the distance between the center of the ellipse and the Focus1 then the eccentricity e = f / MajorRadius. Returns 0 if MajorRadius = 0.
Implements Geom2d_Conic.
| gp_Elips2d Geom2d_Ellipse::Elips2d | ( | ) | const |
Converts this ellipse into a gp_Elips2d ellipse.
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Returns the value of the first parameter of this ellipse. This is 0.0, which gives the start point of this ellipse. The start point and end point of an ellipse are coincident.
Implements Geom2d_Curve.
| Standard_Real Geom2d_Ellipse::Focal | ( | ) | const |
Computes the focal distance. The focal distance is the distance between the center and a focus of the ellipse.
| gp_Pnt2d Geom2d_Ellipse::Focus1 | ( | ) | const |
Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse.
| gp_Pnt2d Geom2d_Ellipse::Focus2 | ( | ) | const |
Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse.
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return True.
Implements Geom2d_Curve.
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return True.
Implements Geom2d_Curve.
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Returns the value of the last parameter of this ellipse. This is 2.*Pi, which gives the end point of this ellipse. The start point and end point of an ellipse are coincident.
Implements Geom2d_Curve.
| Standard_Real Geom2d_Ellipse::MajorRadius | ( | ) | const |
Returns the major radius of this ellipse.
| Standard_Real Geom2d_Ellipse::MinorRadius | ( | ) | const |
Returns the minor radius of this ellipse.
| Standard_Real Geom2d_Ellipse::Parameter | ( | ) | const |
Computes the parameter of this ellipse. This value is given by the formula p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0.
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Computes the parameter on the reversed ellipse for the point of parameter U on this ellipse. For an ellipse, the returned value is: 2.*Pi - U.
Implements Geom2d_Conic.
| void Geom2d_Ellipse::SetElips2d | ( | const gp_Elips2d & | E | ) |
Converts the gp_Elips2d ellipse E into this ellipse.
| void Geom2d_Ellipse::SetMajorRadius | ( | const Standard_Real | MajorRadius | ) |
Assigns a value to the major radius of this ellipse. Exceptions Standard_ConstructionError if:
- the major radius of this ellipse becomes less than the minor radius, or
- MinorRadius is less than 0.
| void Geom2d_Ellipse::SetMinorRadius | ( | const Standard_Real | MinorRadius | ) |
Assigns a value to the minor radius of this ellipse. Exceptions Standard_ConstructionError if:
- the major radius of this ellipse becomes less than the minor radius, or
- MinorRadius is less than 0.
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Applies the transformation T to this ellipse.
Implements Geom2d_Geometry.
The documentation for this class was generated from the following file:
