Describes a branch of a hyperbola in the plane (2D space). A hyperbola is defined by its major and minor radii, and positioned in the plane with a coordinate system (a gp_Ax22d object) of which:
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| gp_Hypr2d () |
| Creates of an indefinite hyperbola. More...
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| gp_Hypr2d (const gp_Ax2d &theMajorAxis, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius, const Standard_Boolean theIsSense=Standard_True) |
| Creates a hyperbola with radii theMajorRadius and theMinorRadius, centered on the origin of theMajorAxis and where the unit vector of theMajorAxis is the "X
Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if theIsSense is true (the default value), and indirect if theIsSense is false. Warnings : It is yet possible to create an Hyperbola with theMajorRadius <= theMinorRadius. Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0. More...
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| gp_Hypr2d (const gp_Ax22d &theA, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius) |
| a hyperbola with radii theMajorRadius and theMinorRadius, positioned in the plane by coordinate system theA where: More...
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void | SetLocation (const gp_Pnt2d &theP) |
| Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes theP. More...
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void | SetMajorRadius (const Standard_Real theMajorRadius) |
| Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if theMajorRadius or MinorRadius is negative. More...
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void | SetMinorRadius (const Standard_Real theMinorRadius) |
| Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or theMinorRadius is negative. More...
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void | SetAxis (const gp_Ax22d &theA) |
| Modifies this hyperbola, by redefining its local coordinate system so that it becomes theA. More...
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void | SetXAxis (const gp_Ax2d &theA) |
| Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too. More...
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void | SetYAxis (const gp_Ax2d &theA) |
| Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too. More...
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gp_Ax2d | Asymptote1 () const |
| In the local coordinate system of the hyperbola the equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the equation of the first asymptote is Y = (B/A)*X where A is the major radius of the hyperbola and B the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0. More...
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gp_Ax2d | Asymptote2 () const |
| In the local coordinate system of the hyperbola the equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the equation of the first asymptote is Y = -(B/A)*X where A is the major radius of the hyperbola and B the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0. More...
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void | Coefficients (Standard_Real &theA, Standard_Real &theB, Standard_Real &theC, Standard_Real &theD, Standard_Real &theE, Standard_Real &theF) const |
| Computes the coefficients of the implicit equation of the hyperbola : theA * (X**2) + theB * (Y**2) + 2*theC*(X*Y) + 2*theD*X + 2*theE*Y + theF = 0. More...
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gp_Hypr2d | ConjugateBranch1 () const |
| Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>. More...
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gp_Hypr2d | ConjugateBranch2 () const |
| Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>. More...
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gp_Ax2d | Directrix1 () const |
| Computes the directrix which is the line normal to the XAxis of the hyperbola in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the hyperbola, where e is the eccentricity of the hyperbola. This line is parallel to the "YAxis". The intersection point between the "Directrix1" and the "XAxis" is the "Location" point of the "Directrix1". This point is on the positive side of the "XAxis". More...
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gp_Ax2d | Directrix2 () const |
| This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the hyperbola. More...
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Standard_Real | Eccentricity () const |
| Returns the eccentricity of the hyperbola (e > 1). If f is the distance between the location of the hyperbola and the Focus1 then the eccentricity e = f / MajorRadius. Raises DomainError if MajorRadius = 0.0. More...
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Standard_Real | Focal () const |
| Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2". More...
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gp_Pnt2d | Focus1 () const |
| Returns the first focus of the hyperbola. This focus is on the positive side of the "XAxis" of the hyperbola. More...
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gp_Pnt2d | Focus2 () const |
| Returns the second focus of the hyperbola. This focus is on the negative side of the "XAxis" of the hyperbola. More...
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const gp_Pnt2d & | Location () const |
| Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis". More...
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Standard_Real | MajorRadius () const |
| Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola). More...
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Standard_Real | MinorRadius () const |
| Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola). More...
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gp_Hypr2d | OtherBranch () const |
| Returns the branch of hyperbola obtained by doing the symmetrical transformation of <me> with respect to the "YAxis" of <me>. More...
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Standard_Real | Parameter () const |
| Returns p = (e * e - 1) * MajorRadius where e is the eccentricity of the hyperbola. Raises DomainError if MajorRadius = 0.0. More...
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const gp_Ax22d & | Axis () const |
| Returns the axisplacement of the hyperbola. More...
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gp_Ax2d | XAxis () const |
| Computes an axis whose. More...
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gp_Ax2d | YAxis () const |
| Computes an axis whose. More...
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void | Reverse () |
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gp_Hypr2d | Reversed () const |
| Reverses the orientation of the local coordinate system of this hyperbola (the "Y Axis" is reversed). Therefore, the implicit orientation of this hyperbola is reversed. Note: More...
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Standard_Boolean | IsDirect () const |
| Returns true if the local coordinate system is direct and false in the other case. More...
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void | Mirror (const gp_Pnt2d &theP) |
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gp_Hypr2d | Mirrored (const gp_Pnt2d &theP) const |
| Performs the symmetrical transformation of an hyperbola with respect to the point theP which is the center of the symmetry. More...
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void | Mirror (const gp_Ax2d &theA) |
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gp_Hypr2d | Mirrored (const gp_Ax2d &theA) const |
| Performs the symmetrical transformation of an hyperbola with respect to an axis placement which is the axis of the symmetry. More...
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void | Rotate (const gp_Pnt2d &theP, const Standard_Real theAng) |
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gp_Hypr2d | Rotated (const gp_Pnt2d &theP, const Standard_Real theAng) const |
| Rotates an hyperbola. theP is the center of the rotation. theAng is the angular value of the rotation in radians. More...
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void | Scale (const gp_Pnt2d &theP, const Standard_Real theS) |
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gp_Hypr2d | Scaled (const gp_Pnt2d &theP, const Standard_Real theS) const |
| Scales an hyperbola. <theS> is the scaling value. If <theS> is positive only the location point is modified. But if <theS> is negative the "XAxis" is reversed and the "YAxis" too. More...
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void | Transform (const gp_Trsf2d &theT) |
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gp_Hypr2d | Transformed (const gp_Trsf2d &theT) const |
| Transforms an hyperbola with the transformation theT from class Trsf2d. More...
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void | Translate (const gp_Vec2d &theV) |
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gp_Hypr2d | Translated (const gp_Vec2d &theV) const |
| Translates an hyperbola 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_Pnt2d &theP1, const gp_Pnt2d &theP2) |
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gp_Hypr2d | Translated (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2) const |
| Translates an hyperbola from the point theP1 to the point theP2. More...
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Describes a branch of a hyperbola in the plane (2D space). A hyperbola is defined by its major and minor radii, and positioned in the plane with a coordinate system (a gp_Ax22d object) of which:
- the origin is the center of the hyperbola,
- the "X Direction" defines the major axis of the hyperbola, and
- the "Y Direction" defines the minor axis of the hyperbola. This coordinate system is the "local coordinate system" of the hyperbola. The orientation of this coordinate system (direct or indirect) gives an implicit orientation to the hyperbola. In this coordinate system, the equation of the hyperbola is: X*X/(MajorRadius**2)-Y*Y/(MinorRadius**2) = 1.0 The branch of the hyperbola described is the one located on the positive side of the major axis. The following schema shows the plane of the hyperbola, and in it, the respective positions of the three branches of hyperbolas constructed with the functions OtherBranch, ConjugateBranch1, and ConjugateBranch2:
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FirstConjugateBranch
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Other | Main
--------------------- C ------------------------------>XAxis
Branch | Branch
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SecondConjugateBranch
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Warning The major radius can be less than the minor radius. See Also gce_MakeHypr2d which provides functions for more complex hyperbola constructions Geom2d_Hyperbola which provides additional functions for constructing hyperbolas and works, in particular, with the parametric equations of hyperbolas