Open CASCADE Technology 7.7.2
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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. | |
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: | |
void | SetElips (const gp_Elips &E) |
Converts the gp_Elips ellipse E into this ellipse. | |
void | SetMajorRadius (const Standard_Real MajorRadius) |
Assigns a value to the major radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius. | |
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. | |
gp_Elips | Elips () const |
returns the non transient ellipse from gp with the same | |
Standard_Real | ReversedParameter (const Standard_Real U) const override |
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. | |
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) | |
gp_Ax1 | Directrix2 () const |
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. | |
Standard_Real | Eccentricity () const override |
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. | |
Standard_Real | Focal () const |
Computes the focal distance. It is the distance between the the two focus of the ellipse. | |
gp_Pnt | Focus1 () const |
Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse. | |
gp_Pnt | Focus2 () const |
Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse. | |
Standard_Real | MajorRadius () const |
Returns the major radius of this ellipse. | |
Standard_Real | MinorRadius () const |
Returns the minor radius of this ellipse. | |
Standard_Real | Parameter () const |
Returns p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0. | |
Standard_Real | FirstParameter () const override |
Returns the value of the first parameter of this ellipse. This is respectively: | |
Standard_Real | LastParameter () const override |
Returns the value of the last parameter of this ellipse. This is respectively: | |
Standard_Boolean | IsClosed () const override |
return True. | |
Standard_Boolean | IsPeriodic () const override |
return True. | |
void | D0 (const Standard_Real U, gp_Pnt &P) const override |
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. | |
void | D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const override |
Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1. | |
void | D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const override |
Returns the point P of parameter U. The vectors V1 and V2 are the first and second derivatives at this point. | |
void | D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const override |
Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3. | |
gp_Vec | DN (const Standard_Real U, const Standard_Integer N) const override |
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. | |
void | Transform (const gp_Trsf &T) override |
Applies the transformation T to this ellipse. | |
Handle< Geom_Geometry > | Copy () const override |
Creates a new object which is a copy of this ellipse. | |
virtual void | DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override |
Dumps the content of me into the stream. | |
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void | SetAxis (const gp_Ax1 &theA1) |
Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed. | |
void | SetLocation (const gp_Pnt &theP) |
changes the location point of the conic. | |
void | SetPosition (const gp_Ax2 &theA2) |
changes the local coordinate system of the conic. | |
const gp_Ax1 & | Axis () const |
Returns the "main Axis" of this conic. This axis is normal to the plane of the conic. | |
const 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. | |
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. | |
virtual Standard_Real | Eccentricity () const =0 |
Returns the eccentricity value of the conic e. 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. | |
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. | |
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. | |
void | Reverse () override |
Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. | |
virtual Standard_Real | ReversedParameter (const Standard_Real U) const override=0 |
Returns the parameter on the reversed curve for the point of parameter U on <me>. | |
GeomAbs_Shape | Continuity () const override |
The continuity of the conic is Cn. | |
Standard_Boolean | IsCN (const Standard_Integer N) const override |
Returns True. Raised if N < 0. | |
virtual void | DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override |
Dumps the content of me into the stream. | |
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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. | |
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>. | |
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>. | |
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>. | |
Handle< Geom_Curve > | Reversed () const |
Returns a copy of <me> reversed. | |
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. | |
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. | |
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 which is a fixed criterion independent of the application. | |
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. | |
virtual Standard_Real | Period () const |
Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic. | |
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. | |
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. | |
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. | |
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. | |
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. | |
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. | |
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. | |
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. | |
virtual void | DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override |
Dumps the content of me into the stream. | |
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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. | |
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. | |
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). | |
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. | |
void | Scale (const gp_Pnt &P, const Standard_Real S) |
Scales a Geometry. S is the scaling value. | |
void | Translate (const gp_Vec &V) |
Translates a Geometry. V is the vector of the translation. | |
void | Translate (const gp_Pnt &P1, const gp_Pnt &P2) |
Translates a Geometry from the point P1 to the point P2. | |
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). | |
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. | |
virtual void | DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const |
Dumps the content of me into the stream. | |
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Standard_Transient () | |
Empty constructor. | |
Standard_Transient (const Standard_Transient &) | |
Copy constructor – does nothing. | |
Standard_Transient & | operator= (const Standard_Transient &) |
Assignment operator, needed to avoid copying reference counter. | |
virtual | ~Standard_Transient () |
Destructor must be virtual. | |
virtual void | Delete () const |
Memory deallocator for transient classes. | |
virtual const opencascade::handle< Standard_Type > & | DynamicType () const |
Returns a type descriptor about this object. | |
Standard_Boolean | IsInstance (const opencascade::handle< Standard_Type > &theType) const |
Returns a true value if this is an instance of Type. | |
Standard_Boolean | IsInstance (const Standard_CString theTypeName) const |
Returns a true value if this is an instance of TypeName. | |
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. | |
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. | |
Standard_Transient * | This () 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. | |
Standard_Integer | GetRefCount () const |
Get the reference counter of this object. | |
void | IncrementRefCounter () const |
Increments the reference counter of this object. | |
Standard_Integer | DecrementRefCounter () const |
Decrements the reference counter of this object; returns the decremented value. | |
Additional Inherited Members | |
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typedef void | base_type |
Returns a type descriptor about this object. | |
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static const char * | get_type_name () |
Returns a type descriptor about this object. | |
static const opencascade::handle< Standard_Type > & | get_type_descriptor () |
Returns type descriptor of Standard_Transient class. | |
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gp_Ax2 | pos |
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:
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 | ||
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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:
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Creates a new object which is a copy of this ellipse.
Implements Geom_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 Geom_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 Geom_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 Geom_Curve.
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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).
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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 Geom_Curve.
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Dumps the content of me into the stream.
Reimplemented from Geom_Conic.
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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 Geom_Conic.
gp_Elips Geom_Ellipse::Elips | ( | ) | const |
returns the non transient ellipse from gp with the same
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Returns the value of the first parameter of this ellipse. This is respectively:
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.
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return True.
Implements Geom_Curve.
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return True.
Implements Geom_Curve.
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Returns the value of the last parameter of this ellipse. This is respectively:
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.
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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 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.
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Applies the transformation T to this ellipse.
Implements Geom_Geometry.