Describes a parabola in 3D space. A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in space with a coordinate system (a gp_Ax2 object) where:
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| gp_Parab () |
| Creates an indefinite Parabola. More...
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| gp_Parab (const gp_Ax2 &theA2, const Standard_Real theFocal) |
| Creates a parabola with its local coordinate system "theA2" and it's focal length "Focal". The XDirection of theA2 defines the axis of symmetry of the parabola. The YDirection of theA2 is parallel to the directrix of the parabola. The Location point of theA2 is the vertex of the parabola Raises ConstructionError if theFocal < 0.0 Raised if theFocal < 0.0. More...
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| gp_Parab (const gp_Ax1 &theD, const gp_Pnt &theF) |
| theD is the directrix of the parabola and theF the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point theF, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to theD 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...
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void | SetAxis (const gp_Ax1 &theA1) |
| Modifies this parabola by redefining its local coordinate system so that. More...
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void | SetFocal (const Standard_Real theFocal) |
| Changes the focal distance of the parabola. Raises ConstructionError if theFocal < 0.0. More...
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void | SetLocation (const gp_Pnt &theP) |
| Changes the location of the parabola. It is the vertex of the parabola. More...
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void | SetPosition (const gp_Ax2 &theA2) |
| Changes the local coordinate system of the parabola. More...
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const gp_Ax1 & | Axis () const |
| Returns the main axis of the parabola. It is the axis normal to the plane of the parabola passing through the vertex of the parabola. More...
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gp_Ax1 | Directrix () const |
| Computes the directrix of this parabola. The directrix is: More...
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Standard_Real | Focal () const |
| Returns the distance between the vertex and the focus of the parabola. More...
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gp_Pnt | Focus () const |
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const gp_Pnt & | Location () const |
| Returns the vertex of the parabola. It is the "Location" point of the coordinate system of the parabola. More...
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Standard_Real | Parameter () const |
| Computes the parameter of the parabola. It is the distance between the focus and the directrix of the parabola. This distance is twice the focal length. More...
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const gp_Ax2 & | Position () const |
| Returns the local coordinate system of the parabola. More...
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gp_Ax1 | XAxis () const |
| Returns the symmetry axis of the parabola. The location point of the axis is the vertex of the parabola. More...
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gp_Ax1 | YAxis () const |
| It is an axis parallel to the directrix of the parabola. The location point of this axis is the vertex of the parabola. More...
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void | Mirror (const gp_Pnt &theP) |
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gp_Parab | Mirrored (const gp_Pnt &theP) const |
| Performs the symmetrical transformation of a parabola with respect to the point theP which is the center of the symmetry. More...
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void | Mirror (const gp_Ax1 &theA1) |
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gp_Parab | Mirrored (const gp_Ax1 &theA1) const |
| Performs the symmetrical transformation of a parabola with respect to an axis placement which is the axis of the symmetry. More...
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void | Mirror (const gp_Ax2 &theA2) |
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gp_Parab | Mirrored (const gp_Ax2 &theA2) const |
| Performs the symmetrical transformation of a parabola with respect to a plane. The axis placement theA2 locates the plane of the symmetry (Location, XDirection, YDirection). More...
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void | Rotate (const gp_Ax1 &theA1, const Standard_Real theAng) |
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gp_Parab | Rotated (const gp_Ax1 &theA1, const Standard_Real theAng) const |
| Rotates a parabola. theA1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...
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void | Scale (const gp_Pnt &theP, const Standard_Real theS) |
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gp_Parab | Scaled (const gp_Pnt &theP, const Standard_Real theS) const |
| Scales a parabola. theS is the scaling value. If theS is negative the direction of the symmetry axis XAxis is reversed and the direction of the YAxis too. More...
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void | Transform (const gp_Trsf &theT) |
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gp_Parab | Transformed (const gp_Trsf &theT) const |
| Transforms a parabola with the transformation theT from class Trsf. More...
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void | Translate (const gp_Vec &theV) |
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gp_Parab | Translated (const gp_Vec &theV) const |
| Translates a parabola in the direction of the vector theV. The magnitude of the translation is the vector's magnitude. More...
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void | Translate (const gp_Pnt &theP1, const gp_Pnt &theP2) |
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gp_Parab | Translated (const gp_Pnt &theP1, const gp_Pnt &theP2) const |
| Translates a parabola from the point theP1 to the point theP2. More...
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Describes a parabola in 3D space. A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in space with a coordinate system (a gp_Ax2 object) where:
- the origin of the coordinate system is on the apex of the parabola,
- the "X Axis" of the coordinate system is the axis of symmetry; the parabola is on the positive side of this axis, and
- the origin, "X Direction" and "Y Direction" of the coordinate system define the plane of the parabola. The equation of the parabola in this coordinate system, which is the "local coordinate system" of the parabola, is: where P, referred to as the parameter of the parabola, is the distance between the focus and the directrix (P is twice the focal length). The "main Direction" of the local coordinate system gives the normal vector to the plane of the parabola. See Also gce_MakeParab which provides functions for more complex parabola constructions Geom_Parabola which provides additional functions for constructing parabolas and works, in particular, with the parametric equations of parabolas