Describes a parabola in 3D space. A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in space with a coordinate system (gp_Ax2 object) where: More...
#include <Geom_Parabola.hxx>
Public Member Functions | |
| Geom_Parabola (const gp_Parab &Prb) | |
| Creates a parabola from a non transient one. More... | |
| Geom_Parabola (const gp_Ax2 &A2, const Standard_Real Focal) | |
| Creates a parabola with its local coordinate system "A2" and it's focal length "Focal". The XDirection of A2 defines the axis of symmetry of the parabola. The YDirection of A2 is parallel to the directrix of the parabola. The Location point of A2 is the vertex of the parabola Raised if Focal < 0.0. More... | |
| Geom_Parabola (const gp_Ax1 &D, const gp_Pnt &F) | |
| D is the directrix of the parabola and F the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point F, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to D and its location point is the vertex of the parabola. The normal to the plane of the parabola is the cross product between the XAxis and the YAxis. More... | |
| void | SetFocal (const Standard_Real Focal) |
| Assigns the value Focal to the focal distance of this parabola. Exceptions Standard_ConstructionError if Focal is negative. More... | |
| void | SetParab (const gp_Parab &Prb) |
| Converts the gp_Parab parabola Prb into this parabola. More... | |
| gp_Parab | Parab () const |
| Returns the non transient parabola from gp with the same geometric properties as <me>. More... | |
| Standard_Real | ReversedParameter (const Standard_Real U) const |
| Computes the parameter on the reversed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is: -U. More... | |
| Standard_Real | FirstParameter () const |
| Returns the value of the first or last parameter of this parabola. This is, respectively: More... | |
| Standard_Real | LastParameter () const |
| Returns the value of the first or last parameter of this parabola. This is, respectively: More... | |
| Standard_Boolean | IsClosed () const |
| Returns False. More... | |
| Standard_Boolean | IsPeriodic () const |
| Returns False. More... | |
| gp_Ax1 | Directrix () const |
| Computes the directrix of this parabola. This is a line normal to the axis of symmetry, in the plane of this parabola, located on the negative side of its axis of symmetry, at a distance from the apex equal to the focal length. The directrix is returned as an axis (gp_Ax1 object), where the origin is located on the "X Axis" of this parabola. More... | |
| Standard_Real | Eccentricity () const |
| Returns 1. (which is the eccentricity of any parabola). More... | |
| gp_Pnt | Focus () const |
| Computes the focus of this parabola. The focus is on the positive side of the "X Axis" of the local coordinate system of the parabola. More... | |
| Standard_Real | Focal () const |
| Computes the focal distance of this parabola The focal distance is the distance between the apex and the focus of the parabola. More... | |
| Standard_Real | Parameter () const |
| Computes the parameter of this parabola which is the distance between its focus and its directrix. This distance is twice the focal length. If P is the parameter of the parabola, the equation of the parabola in its local coordinate system is: Y**2 = 2.*P*X. More... | |
| void | D0 (const Standard_Real U, gp_Pnt &P) const |
| Returns in P the point of parameter U. If U = 0 the returned point is the origin of the XAxis and the YAxis of the parabola and it is the vertex of the parabola. P = S + F * (U * U * XDir + * U * YDir) where S is the vertex of the parabola, XDir the XDirection and YDir the YDirection of the parabola's local coordinate system. 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. 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 first and second derivatives V1 and V2. 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 parabola, 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 parabola. More... | |
| 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... | |
| 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_Geometry > | Copy () const |
| Creates a new object which is a copy of this parabola. 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 | |
| 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 a parabola in 3D space. A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in space with a coordinate system (gp_Ax2 object) where:
- the origin is the apex of the parabola,
- the "X Axis" defines the axis of symmetry; the parabola is on the positive side of this axis,
- the origin, "X Direction" and "Y Direction" define the plane of the parabola. This coordinate system is the local coordinate system of the parabola. The "main Direction" of this coordinate system is a vector normal to the plane of the parabola. 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 parabola. The "main Direction" of the local coordinate system gives an explicit orientation to the parabola, determining the direction in which the parameter increases along the parabola. The Geom_Parabola parabola is parameterized as follows: P(U) = O + U*U/(4.*F)*XDir + 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,
- F is the focal length of the parabola. The parameter of the parabola is therefore its Y coordinate in the local coordinate system, with the "X Axis" of the local coordinate system defining the origin of the parameter. The parameter range is ] -infinite, +infinite [.
Constructor & Destructor Documentation
| Geom_Parabola::Geom_Parabola | ( | const gp_Parab & | Prb | ) |
Creates a parabola from a non transient one.
| Geom_Parabola::Geom_Parabola | ( | const gp_Ax2 & | A2, |
| const Standard_Real | Focal | ||
| ) |
Creates a parabola with its local coordinate system "A2" and it's focal length "Focal". The XDirection of A2 defines the axis of symmetry of the parabola. The YDirection of A2 is parallel to the directrix of the parabola. The Location point of A2 is the vertex of the parabola Raised if Focal < 0.0.
D is the directrix of the parabola and F the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point F, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to D and its location point is the vertex of the parabola. The normal to the plane of the parabola is the cross product between the XAxis and the YAxis.
Member Function Documentation
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Creates a new object which is a copy of this parabola.
Implements Geom_Geometry.
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Returns in P the point of parameter U. If U = 0 the returned point is the origin of the XAxis and the YAxis of the parabola and it is the vertex of the parabola. P = S + F * (U * U * XDir + * U * YDir) where S is the vertex of the parabola, XDir the XDirection and YDir the YDirection of the parabola's local coordinate system.
Implements Geom_Curve.
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Returns the point P of parameter U and the first derivative V1.
Implements Geom_Curve.
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Returns the point P of parameter U, the first and second derivatives V1 and V2.
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_Parabola::Directrix | ( | ) | const |
Computes the directrix of this parabola. This is a line normal to the axis of symmetry, in the plane of this parabola, located on the negative side of its axis of symmetry, at a distance from the apex equal to the focal length. The directrix is returned as an axis (gp_Ax1 object), where the origin is located on the "X Axis" of this parabola.
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For the point of parameter U of this parabola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.
Implements Geom_Curve.
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Returns 1. (which is the eccentricity of any parabola).
Implements Geom_Conic.
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Returns the value of the first or last parameter of this parabola. This is, respectively:
- Standard_Real::RealFirst(), or
- Standard_Real::RealLast().
Implements Geom_Curve.
| Standard_Real Geom_Parabola::Focal | ( | ) | const |
Computes the focal distance of this parabola The focal distance is the distance between the apex and the focus of the parabola.
| gp_Pnt Geom_Parabola::Focus | ( | ) | const |
Computes the focus of this parabola. The focus is on the positive side of the "X Axis" of the local coordinate system of the parabola.
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Returns False.
Implements Geom_Curve.
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Returns False.
Implements Geom_Curve.
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Returns the value of the first or last parameter of this parabola. This is, respectively:
- Standard_Real::RealFirst(), or
- Standard_Real::RealLast().
Implements Geom_Curve.
| gp_Parab Geom_Parabola::Parab | ( | ) | const |
Returns the non transient parabola from gp with the same geometric properties as <me>.
| Standard_Real Geom_Parabola::Parameter | ( | ) | const |
Computes the parameter of this parabola which is the distance between its focus and its directrix. This distance is twice the focal length. If P is the parameter of the parabola, the equation of the parabola in its local coordinate system is: Y**2 = 2.*P*X.
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Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
Transformed(T)->Value(U * ParametricTransformation(T))
is the same point as
Value(U).Transformed(T)
This methods returns T.ScaleFactor()
Reimplemented from Geom_Curve.
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Computes the parameter on the reversed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is: -U.
Implements Geom_Conic.
| void Geom_Parabola::SetFocal | ( | const Standard_Real | Focal | ) |
Assigns the value Focal to the focal distance of this parabola. Exceptions Standard_ConstructionError if Focal is negative.
| void Geom_Parabola::SetParab | ( | const gp_Parab & | Prb | ) |
Converts the gp_Parab parabola Prb into this parabola.
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Applies the transformation T to this parabola.
Implements Geom_Geometry.
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Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.
me->Transformed(T)->Value(me->TransformedParameter(U,T))
is the same point as
me->Value(U).Transformed(T)
This methods returns <U> * T.ScaleFactor()
Reimplemented from Geom_Curve.
The documentation for this class was generated from the following file:
