Describes an ellipse in 3D space. An ellipse is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 object) where: More...
#include <Geom_Ellipse.hxx>
Public Member Functions | |
| Geom_Ellipse (const gp_Elips &E) | |
| Constructs an ellipse by conversion of the gp_Elips ellipse E. More... | |
| Geom_Ellipse (const gp_Ax2 &A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius) | |
| Constructs an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the ellipse and defines its orientation in 3D space such that: More... | |
| void | SetElips (const gp_Elips &E) |
| Converts the gp_Elips ellipse E into this ellipse. More... | |
| void | SetMajorRadius (const Standard_Real MajorRadius) |
| Assigns a value to the major radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius. More... | |
| void | SetMinorRadius (const Standard_Real MinorRadius) |
| Assigns a value to the minor radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius or if MinorRadius < 0. More... | |
| gp_Elips | Elips () const |
| returns the non transient ellipse from gp with the same 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_Ax1 | Directrix1 () const |
| 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". Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle) More... | |
| gp_Ax1 | Directrix2 () const |
| This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. 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. It is the distance between the the two focus of the ellipse. More... | |
| gp_Pnt | Focus1 () const |
| Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse. More... | |
| gp_Pnt | 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 |
| Returns 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 respectively: More... | |
| Standard_Real | LastParameter () const |
| Returns the value of the last parameter of this ellipse. This is respectively: More... | |
| Standard_Boolean | IsClosed () const |
| return True. More... | |
| Standard_Boolean | IsPeriodic () const |
| return True. More... | |
| void | D0 (const Standard_Real U, gp_Pnt &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_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 vectors V1 and V2 are the first and second derivatives at this point. More... | |
| void | D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const |
| Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3. More... | |
| gp_Vec | 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_Trsf &T) |
| Applies the transformation T to this ellipse. More... | |
| Handle< Geom_Geometry > | Copy () const |
| Creates a new object which is a copy of this ellipse. More... | |
 Public Member Functions inherited from Geom_Conic | |
| void | SetAxis (const gp_Ax1 &A1) |
| Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed. 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 normal to the plane of the conic. 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... | |
| 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 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... | |
Additional Inherited Members | |
| Protected Attributes inherited from Geom_Conic | |
| gp_Ax2 | pos |
Detailed Description
Describes an ellipse in 3D space. An ellipse is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 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. The origin, "X Direction" and "Y Direction" of this coordinate system define the plane of the ellipse. The coordinate system is the local coordinate system of the ellipse. The "main Direction" of this coordinate system is the vector normal to the plane of the ellipse. 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 ellipse. The "main Direction" of the local coordinate system gives an explicit orientation to the ellipse (definition of the trigonometric sense), determining the direction in which the parameter increases along the ellipse. The Geom_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 [.
Constructor & Destructor Documentation
| Geom_Ellipse::Geom_Ellipse | ( | const gp_Elips & | E | ) |
Constructs an ellipse by conversion of the gp_Elips ellipse E.
| Geom_Ellipse::Geom_Ellipse | ( | const gp_Ax2 & | A2, |
| const Standard_Real | MajorRadius, | ||
| const Standard_Real | MinorRadius | ||
| ) |
Constructs an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the ellipse and defines its orientation in 3D space such that:
- the center of the ellipse is the origin of A2,
- the "X Direction" of A2 defines the major axis of the ellipse, i.e. the major radius MajorRadius is measured along this axis,
- the "Y Direction" of A2 defines the minor axis of the ellipse, i.e. the minor radius MinorRadius is measured along this axis,
- A2 is the local coordinate system of the ellipse. Exceptions Standard_ConstructionError if:
- MajorRadius is less than MinorRadius, or
- MinorRadius is less than 0. Warning The Geom package does not prevent the construction of an ellipse where MajorRadius and MinorRadius are equal.
Member Function Documentation
|
virtual |
Creates a new object which is a copy of this ellipse.
Implements Geom_Geometry.
|
virtual |
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 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 vectors V1 and V2 are the first and second derivatives at this point.
Implements Geom_Curve.
|
virtual |
Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.
Implements Geom_Curve.
| gp_Ax1 Geom_Ellipse::Directrix1 | ( | ) | const |
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". Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle)
| gp_Ax1 Geom_Ellipse::Directrix2 | ( | ) | const |
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse.
Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle).
|
virtual |
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 Geom_Curve.
|
virtual |
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 Geom_Conic.
| gp_Elips Geom_Ellipse::Elips | ( | ) | const |
returns the non transient ellipse from gp with the same
|
virtual |
Returns the value of the first parameter of this ellipse. This is respectively:
- 0.0, which gives the start point of this ellipse, or The start point and end point of an ellipse are coincident.
Implements Geom_Curve.
| Standard_Real Geom_Ellipse::Focal | ( | ) | const |
Computes the focal distance. It is the distance between the the two focus of the ellipse.
| gp_Pnt Geom_Ellipse::Focus1 | ( | ) | const |
Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse.
| gp_Pnt Geom_Ellipse::Focus2 | ( | ) | const |
Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse.
|
virtual |
return True.
Implements Geom_Curve.
|
virtual |
return True.
Implements Geom_Curve.
|
virtual |
Returns the value of the last parameter of this ellipse. This is respectively:
- 2.*Pi, which gives the end point of this ellipse. The start point and end point of an ellipse are coincident.
Implements Geom_Curve.
| Standard_Real Geom_Ellipse::MajorRadius | ( | ) | const |
Returns the major radius of this ellipse.
| Standard_Real Geom_Ellipse::MinorRadius | ( | ) | const |
Returns the minor radius of this ellipse.
| Standard_Real Geom_Ellipse::Parameter | ( | ) | const |
Returns p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0.
|
virtual |
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 Geom_Conic.
| void Geom_Ellipse::SetElips | ( | const gp_Elips & | E | ) |
Converts the gp_Elips ellipse E into this ellipse.
| void Geom_Ellipse::SetMajorRadius | ( | const Standard_Real | MajorRadius | ) |
Assigns a value to the major radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius.
| void Geom_Ellipse::SetMinorRadius | ( | const Standard_Real | MinorRadius | ) |
Assigns a value to the minor radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius or if MinorRadius < 0.
|
virtual |
Applies the transformation T to this ellipse.
Implements Geom_Geometry.
The documentation for this class was generated from the following file:
