Open CASCADE Technology
7.4.0

Describes a parabola in the plane (2D space). A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in the plane with a coordinate system (a gp_Ax22d object) where: More...
#include <gp_Parab2d.hxx>
Public Member Functions  
gp_Parab2d ()  
Creates an indefinite parabola. More...  
gp_Parab2d (const gp_Ax2d &theMirrorAxis, const Standard_Real theFocalLength, const Standard_Boolean theSense=Standard_True)  
Creates a parabola with its vertex point, its axis of symmetry ("XAxis") and its focal length. The sense of parametrization is given by theSense. If theSense == TRUE (by default) then righthanded coordinate system is used, otherwise  lefthanded. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetryaxis. Raises ConstructionError if FocalLength < 0.0. More...  
gp_Parab2d (const gp_Ax22d &theAxes, const Standard_Real theFocalLength)  
Creates a parabola with its vertex point, its axis of symmetry ("XAxis"), correspond Yaxis and its focal length. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetryaxis. Raises ConstructionError if Focal < 0.0. More...  
gp_Parab2d (const gp_Ax2d &theDirectrix, const gp_Pnt2d &theFocus, const Standard_Boolean theSense=Standard_True)  
Creates a parabola with the directrix and the focus point. Yaxis of the parabola (in User Coordinate System  UCS) is the direction of theDirectrix. Xaxis always directs from theDirectrix to theFocus point and always comes through theFocus. Apex of the parabola is a middle point between the theFocus and the intersection point of theDirectrix and the Xaxis. Warnings : It is possible to have FocalLength = 0 (when theFocus lies in theDirectrix). In this case, Xdirection of the parabola is defined by theSense parameter. If theSense == TRUE (by default) then righthanded coordinate system is used, otherwise  lefthanded. Result parabola will look like a line, which is perpendicular to the directrix. More...  
void  SetFocal (const Standard_Real Focal) 
Changes the focal distance of the parabola Warnings : It is possible to have Focal = 0. Raises ConstructionError if Focal < 0.0. More...  
void  SetLocation (const gp_Pnt2d &P) 
Changes the "Location" point of the parabola. It is the vertex of the parabola. More...  
void  SetMirrorAxis (const gp_Ax2d &A) 
Modifies this parabola, by redefining its local coordinate system so that its origin and "X Direction" become those of the axis MA. The "Y Direction" of the local coordinate system is then recomputed. The orientation of the local coordinate system is not modified. More...  
void  SetAxis (const gp_Ax22d &A) 
Changes the local coordinate system of the parabola. The "Location" point of A becomes the vertex of the parabola. More...  
void  Coefficients (Standard_Real &A, Standard_Real &B, Standard_Real &C, Standard_Real &D, Standard_Real &E, Standard_Real &F) const 
Computes the coefficients of the implicit equation of the parabola (in WCS  World Coordinate System). A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0. More...  
gp_Ax2d  Directrix () const 
Computes the directrix of the parabola. The directrix is: More...  
Standard_Real  Focal () const 
Returns the distance between the vertex and the focus of the parabola. More...  
gp_Pnt2d  Focus () const 
Returns the focus of the parabola. More...  
gp_Pnt2d  Location () const 
Returns the vertex of the parabola. More...  
gp_Ax2d  MirrorAxis () const 
Returns the symmetry axis of the parabola. The "Location" point of this axis is the vertex of the parabola. More...  
gp_Ax22d  Axis () const 
Returns the local coordinate system of the parabola. The "Location" point of this axis is the vertex of the parabola. More...  
Standard_Real  Parameter () const 
Returns the distance between the focus and the directrix of the parabola. More...  
void  Reverse () 
gp_Parab2d  Reversed () const 
Reverses the orientation of the local coordinate system of this parabola (the "Y Direction" is reversed). Therefore, the implicit orientation of this parabola is reversed. Note: More...  
Standard_Boolean  IsDirect () const 
Returns true if the local coordinate system is direct and false in the other case. More...  
void  Mirror (const gp_Pnt2d &P) 
gp_Parab2d  Mirrored (const gp_Pnt2d &P) const 
Performs the symmetrical transformation of a parabola with respect to the point P which is the center of the symmetry. More...  
void  Mirror (const gp_Ax2d &A) 
gp_Parab2d  Mirrored (const gp_Ax2d &A) const 
Performs the symmetrical transformation of a parabola with respect to an axis placement which is the axis of the symmetry. More...  
void  Rotate (const gp_Pnt2d &P, const Standard_Real Ang) 
gp_Parab2d  Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const 
Rotates a parabola. 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) 
gp_Parab2d  Scaled (const gp_Pnt2d &P, const Standard_Real S) const 
Scales a parabola. S is the scaling value. If S is negative the direction of the symmetry axis "XAxis" is reversed and the direction of the "YAxis" too. More...  
void  Transform (const gp_Trsf2d &T) 
gp_Parab2d  Transformed (const gp_Trsf2d &T) const 
Transforms an parabola with the transformation T from class Trsf2d. More...  
void  Translate (const gp_Vec2d &V) 
gp_Parab2d  Translated (const gp_Vec2d &V) const 
Translates a parabola in the direction of the vector V. The magnitude of the translation is the vector's magnitude. More...  
void  Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2) 
gp_Parab2d  Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const 
Translates a parabola from the point P1 to the point P2. More...  
Describes a parabola in the plane (2D space). A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in the plane with a coordinate system (a gp_Ax22d object) where:
gp_Parab2d::gp_Parab2d  (  ) 
Creates an indefinite parabola.
gp_Parab2d::gp_Parab2d  (  const gp_Ax2d &  theMirrorAxis, 
const Standard_Real  theFocalLength,  
const Standard_Boolean  theSense = Standard_True 

) 
Creates a parabola with its vertex point, its axis of symmetry ("XAxis") and its focal length. The sense of parametrization is given by theSense. If theSense == TRUE (by default) then righthanded coordinate system is used, otherwise  lefthanded. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetryaxis. Raises ConstructionError if FocalLength < 0.0.
gp_Parab2d::gp_Parab2d  (  const gp_Ax22d &  theAxes, 
const Standard_Real  theFocalLength  
) 
Creates a parabola with its vertex point, its axis of symmetry ("XAxis"), correspond Yaxis and its focal length. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetryaxis. Raises ConstructionError if Focal < 0.0.
gp_Parab2d::gp_Parab2d  (  const gp_Ax2d &  theDirectrix, 
const gp_Pnt2d &  theFocus,  
const Standard_Boolean  theSense = Standard_True 

) 
Creates a parabola with the directrix and the focus point. Yaxis of the parabola (in User Coordinate System  UCS) is the direction of theDirectrix. Xaxis always directs from theDirectrix to theFocus point and always comes through theFocus. Apex of the parabola is a middle point between the theFocus and the intersection point of theDirectrix and the Xaxis. Warnings : It is possible to have FocalLength = 0 (when theFocus lies in theDirectrix). In this case, Xdirection of the parabola is defined by theSense parameter. If theSense == TRUE (by default) then righthanded coordinate system is used, otherwise  lefthanded. Result parabola will look like a line, which is perpendicular to the directrix.
gp_Ax22d gp_Parab2d::Axis  (  )  const 
Returns the local coordinate system of the parabola. The "Location" point of this axis is the vertex of the parabola.
void gp_Parab2d::Coefficients  (  Standard_Real &  A, 
Standard_Real &  B,  
Standard_Real &  C,  
Standard_Real &  D,  
Standard_Real &  E,  
Standard_Real &  F  
)  const 
Computes the coefficients of the implicit equation of the parabola (in WCS  World Coordinate System). A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0.
gp_Ax2d gp_Parab2d::Directrix  (  )  const 
Computes the directrix of the parabola. The directrix is:
Standard_Real gp_Parab2d::Focal  (  )  const 
Returns the distance between the vertex and the focus of the parabola.
gp_Pnt2d gp_Parab2d::Focus  (  )  const 
Returns the focus of the parabola.
Standard_Boolean gp_Parab2d::IsDirect  (  )  const 
Returns true if the local coordinate system is direct and false in the other case.
gp_Pnt2d gp_Parab2d::Location  (  )  const 
Returns the vertex of the parabola.
void gp_Parab2d::Mirror  (  const gp_Pnt2d &  P  ) 
void gp_Parab2d::Mirror  (  const gp_Ax2d &  A  ) 
gp_Ax2d gp_Parab2d::MirrorAxis  (  )  const 
Returns the symmetry axis of the parabola. The "Location" point of this axis is the vertex of the parabola.
gp_Parab2d gp_Parab2d::Mirrored  (  const gp_Pnt2d &  P  )  const 
Performs the symmetrical transformation of a parabola with respect to the point P which is the center of the symmetry.
gp_Parab2d gp_Parab2d::Mirrored  (  const gp_Ax2d &  A  )  const 
Performs the symmetrical transformation of a parabola with respect to an axis placement which is the axis of the symmetry.
Standard_Real gp_Parab2d::Parameter  (  )  const 
Returns the distance between the focus and the directrix of the parabola.
void gp_Parab2d::Reverse  (  ) 
gp_Parab2d gp_Parab2d::Reversed  (  )  const 
Reverses the orientation of the local coordinate system of this parabola (the "Y Direction" is reversed). Therefore, the implicit orientation of this parabola is reversed. Note:
void gp_Parab2d::Rotate  (  const gp_Pnt2d &  P, 
const Standard_Real  Ang  
) 
gp_Parab2d gp_Parab2d::Rotated  (  const gp_Pnt2d &  P, 
const Standard_Real  Ang  
)  const 
Rotates a parabola. P is the center of the rotation. Ang is the angular value of the rotation in radians.
void gp_Parab2d::Scale  (  const gp_Pnt2d &  P, 
const Standard_Real  S  
) 
gp_Parab2d gp_Parab2d::Scaled  (  const gp_Pnt2d &  P, 
const Standard_Real  S  
)  const 
Scales a parabola. S is the scaling value. If S is negative the direction of the symmetry axis "XAxis" is reversed and the direction of the "YAxis" too.
void gp_Parab2d::SetAxis  (  const gp_Ax22d &  A  ) 
Changes the local coordinate system of the parabola. The "Location" point of A becomes the vertex of the parabola.
void gp_Parab2d::SetFocal  (  const Standard_Real  Focal  ) 
Changes the focal distance of the parabola Warnings : It is possible to have Focal = 0. Raises ConstructionError if Focal < 0.0.
void gp_Parab2d::SetLocation  (  const gp_Pnt2d &  P  ) 
Changes the "Location" point of the parabola. It is the vertex of the parabola.
void gp_Parab2d::SetMirrorAxis  (  const gp_Ax2d &  A  ) 
Modifies this parabola, by redefining its local coordinate system so that its origin and "X Direction" become those of the axis MA. The "Y Direction" of the local coordinate system is then recomputed. The orientation of the local coordinate system is not modified.
void gp_Parab2d::Transform  (  const gp_Trsf2d &  T  ) 
gp_Parab2d gp_Parab2d::Transformed  (  const gp_Trsf2d &  T  )  const 
Transforms an parabola with the transformation T from class Trsf2d.
void gp_Parab2d::Translate  (  const gp_Vec2d &  V  ) 
gp_Parab2d gp_Parab2d::Translated  (  const gp_Vec2d &  V  )  const 
Translates a parabola in the direction of the vector V. The magnitude of the translation is the vector's magnitude.
gp_Parab2d gp_Parab2d::Translated  (  const gp_Pnt2d &  P1, 
const gp_Pnt2d &  P2  
)  const 
Translates a parabola from the point P1 to the point P2.