Open CASCADE Technology  7.4.1.dev
Public Member Functions
gp_Hypr2d Class Reference

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: More...

#include <gp_Hypr2d.hxx>

Public Member Functions

 gp_Hypr2d ()
 Creates of an indefinite hyperbola. More...
 
 gp_Hypr2d (const gp_Ax2d &MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense=Standard_True)
 Creates a hyperbola with radii MajorRadius and MinorRadius, centered on the origin of MajorAxis and where the unit vector of MajorAxis is the "X Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if Sense is true (the default value), and indirect if Sense is false. Warnings : It is yet possible to create an Hyperbola with MajorRadius <= MinorRadius. Raises ConstructionError if MajorRadius < 0.0 or MinorRadius < 0.0. More...
 
 gp_Hypr2d (const gp_Ax22d &A, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
 a hyperbola with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where: More...
 
void SetLocation (const gp_Pnt2d &P)
 Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes P. More...
 
void SetMajorRadius (const Standard_Real MajorRadius)
 Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative. More...
 
void SetMinorRadius (const Standard_Real MinorRadius)
 Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative. More...
 
void SetAxis (const gp_Ax22d &A)
 Modifies this hyperbola, by redefining its local coordinate system so that it becomes A. More...
 
void SetXAxis (const gp_Ax2d &A)
 Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too. More...
 
void SetYAxis (const gp_Ax2d &A)
 Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too. More...
 
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...
 
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...
 
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 hyperbola : A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0. More...
 
gp_Hypr2d ConjugateBranch1 () const
 Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>. More...
 
gp_Hypr2d ConjugateBranch2 () const
 Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>. More...
 
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...
 
gp_Ax2d Directrix2 () const
 This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the hyperbola. More...
 
Standard_Real Eccentricity () const
 Returns the excentricity 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...
 
Standard_Real Focal () const
 Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2". More...
 
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...
 
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...
 
const gp_Pnt2dLocation () const
 Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis". More...
 
Standard_Real MajorRadius () const
 Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola). More...
 
Standard_Real MinorRadius () const
 Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola). More...
 
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...
 
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...
 
const gp_Ax22dAxis () const
 Returns the axisplacement of the hyperbola. More...
 
gp_Ax2d XAxis () const
 Computes an axis whose. More...
 
gp_Ax2d YAxis () const
 Computes an axis whose. More...
 
void Reverse ()
 
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...
 
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_Hypr2d Mirrored (const gp_Pnt2d &P) const
 Performs the symmetrical transformation of an hyperbola with respect to the point P which is the center of the symmetry. More...
 
void Mirror (const gp_Ax2d &A)
 
gp_Hypr2d Mirrored (const gp_Ax2d &A) const
 Performs the symmetrical transformation of an hyperbola 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_Hypr2d Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const
 Rotates an hyperbola. 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_Hypr2d Scaled (const gp_Pnt2d &P, const Standard_Real S) const
 Scales an hyperbola. <S> is the scaling value. If <S> is positive only the location point is modified. But if <S> is negative the "XAxis" is reversed and the "YAxis" too. More...
 
void Transform (const gp_Trsf2d &T)
 
gp_Hypr2d Transformed (const gp_Trsf2d &T) const
 Transforms an hyperbola with the transformation T from class Trsf2d. More...
 
void Translate (const gp_Vec2d &V)
 
gp_Hypr2d Translated (const gp_Vec2d &V) const
 Translates an hyperbola 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_Hypr2d Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const
 Translates an hyperbola from the point P1 to the point P2. More...
 

Detailed Description

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:

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

Constructor & Destructor Documentation

◆ gp_Hypr2d() [1/3]

gp_Hypr2d::gp_Hypr2d ( )

Creates of an indefinite hyperbola.

◆ gp_Hypr2d() [2/3]

gp_Hypr2d::gp_Hypr2d ( const gp_Ax2d MajorAxis,
const Standard_Real  MajorRadius,
const Standard_Real  MinorRadius,
const Standard_Boolean  Sense = Standard_True 
)

Creates a hyperbola with radii MajorRadius and MinorRadius, centered on the origin of MajorAxis and where the unit vector of MajorAxis is the "X Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if Sense is true (the default value), and indirect if Sense is false. Warnings : It is yet possible to create an Hyperbola with MajorRadius <= MinorRadius. Raises ConstructionError if MajorRadius < 0.0 or MinorRadius < 0.0.

◆ gp_Hypr2d() [3/3]

gp_Hypr2d::gp_Hypr2d ( const gp_Ax22d A,
const Standard_Real  MajorRadius,
const Standard_Real  MinorRadius 
)

a hyperbola with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where:

  • the origin of A is the center of the hyperbola,
  • the "X Direction" of A defines the major axis of the hyperbola, that is, the major radius MajorRadius is measured along this axis, and
  • the "Y Direction" of A defines the minor axis of the hyperbola, that is, the minor radius MinorRadius is measured along this axis, and
  • the orientation (direct or indirect sense) of A gives the implicit orientation of the hyperbola. Warnings : It is yet possible to create an Hyperbola with MajorRadius <= MinorRadius. Raises ConstructionError if MajorRadius < 0.0 or MinorRadius < 0.0

Member Function Documentation

◆ Asymptote1()

gp_Ax2d gp_Hypr2d::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.

◆ Asymptote2()

gp_Ax2d gp_Hypr2d::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.

◆ Axis()

const gp_Ax22d& gp_Hypr2d::Axis ( ) const

Returns the axisplacement of the hyperbola.

◆ Coefficients()

void gp_Hypr2d::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 hyperbola : A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0.

◆ ConjugateBranch1()

gp_Hypr2d gp_Hypr2d::ConjugateBranch1 ( ) const

Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>.

◆ ConjugateBranch2()

gp_Hypr2d gp_Hypr2d::ConjugateBranch2 ( ) const

Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>.

◆ Directrix1()

gp_Ax2d gp_Hypr2d::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".

◆ Directrix2()

gp_Ax2d gp_Hypr2d::Directrix2 ( ) const

This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the hyperbola.

◆ Eccentricity()

Standard_Real gp_Hypr2d::Eccentricity ( ) const

Returns the excentricity 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.

◆ Focal()

Standard_Real gp_Hypr2d::Focal ( ) const

Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2".

◆ Focus1()

gp_Pnt2d gp_Hypr2d::Focus1 ( ) const

Returns the first focus of the hyperbola. This focus is on the positive side of the "XAxis" of the hyperbola.

◆ Focus2()

gp_Pnt2d gp_Hypr2d::Focus2 ( ) const

Returns the second focus of the hyperbola. This focus is on the negative side of the "XAxis" of the hyperbola.

◆ IsDirect()

Standard_Boolean gp_Hypr2d::IsDirect ( ) const

Returns true if the local coordinate system is direct and false in the other case.

◆ Location()

const gp_Pnt2d& gp_Hypr2d::Location ( ) const

Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis".

◆ MajorRadius()

Standard_Real gp_Hypr2d::MajorRadius ( ) const

Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola).

◆ MinorRadius()

Standard_Real gp_Hypr2d::MinorRadius ( ) const

Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola).

◆ Mirror() [1/2]

void gp_Hypr2d::Mirror ( const gp_Pnt2d P)

◆ Mirror() [2/2]

void gp_Hypr2d::Mirror ( const gp_Ax2d A)

◆ Mirrored() [1/2]

gp_Hypr2d gp_Hypr2d::Mirrored ( const gp_Pnt2d P) const

Performs the symmetrical transformation of an hyperbola with respect to the point P which is the center of the symmetry.

◆ Mirrored() [2/2]

gp_Hypr2d gp_Hypr2d::Mirrored ( const gp_Ax2d A) const

Performs the symmetrical transformation of an hyperbola with respect to an axis placement which is the axis of the symmetry.

◆ OtherBranch()

gp_Hypr2d gp_Hypr2d::OtherBranch ( ) const

Returns the branch of hyperbola obtained by doing the symmetrical transformation of <me> with respect to the "YAxis" of <me>.

◆ Parameter()

Standard_Real gp_Hypr2d::Parameter ( ) const

Returns p = (e * e - 1) * MajorRadius where e is the eccentricity of the hyperbola. Raises DomainError if MajorRadius = 0.0.

◆ Reverse()

void gp_Hypr2d::Reverse ( )

◆ Reversed()

gp_Hypr2d 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:

  • Reverse assigns the result to this hyperbola, while
  • Reversed creates a new one.

◆ Rotate()

void gp_Hypr2d::Rotate ( const gp_Pnt2d P,
const Standard_Real  Ang 
)

◆ Rotated()

gp_Hypr2d gp_Hypr2d::Rotated ( const gp_Pnt2d P,
const Standard_Real  Ang 
) const

Rotates an hyperbola. P is the center of the rotation. Ang is the angular value of the rotation in radians.

◆ Scale()

void gp_Hypr2d::Scale ( const gp_Pnt2d P,
const Standard_Real  S 
)

◆ Scaled()

gp_Hypr2d gp_Hypr2d::Scaled ( const gp_Pnt2d P,
const Standard_Real  S 
) const

Scales an hyperbola. <S> is the scaling value. If <S> is positive only the location point is modified. But if <S> is negative the "XAxis" is reversed and the "YAxis" too.

◆ SetAxis()

void gp_Hypr2d::SetAxis ( const gp_Ax22d A)

Modifies this hyperbola, by redefining its local coordinate system so that it becomes A.

◆ SetLocation()

void gp_Hypr2d::SetLocation ( const gp_Pnt2d P)

Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes P.

◆ SetMajorRadius()

void gp_Hypr2d::SetMajorRadius ( const Standard_Real  MajorRadius)

Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative.

◆ SetMinorRadius()

void gp_Hypr2d::SetMinorRadius ( const Standard_Real  MinorRadius)

Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative.

◆ SetXAxis()

void gp_Hypr2d::SetXAxis ( const gp_Ax2d A)

Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too.

◆ SetYAxis()

void gp_Hypr2d::SetYAxis ( const gp_Ax2d A)

Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too.

◆ Transform()

void gp_Hypr2d::Transform ( const gp_Trsf2d T)

◆ Transformed()

gp_Hypr2d gp_Hypr2d::Transformed ( const gp_Trsf2d T) const

Transforms an hyperbola with the transformation T from class Trsf2d.

◆ Translate() [1/2]

void gp_Hypr2d::Translate ( const gp_Vec2d V)

◆ Translate() [2/2]

void gp_Hypr2d::Translate ( const gp_Pnt2d P1,
const gp_Pnt2d P2 
)

◆ Translated() [1/2]

gp_Hypr2d gp_Hypr2d::Translated ( const gp_Vec2d V) const

Translates an hyperbola in the direction of the vector V. The magnitude of the translation is the vector's magnitude.

◆ Translated() [2/2]

gp_Hypr2d gp_Hypr2d::Translated ( const gp_Pnt2d P1,
const gp_Pnt2d P2 
) const

Translates an hyperbola from the point P1 to the point P2.

◆ XAxis()

gp_Ax2d gp_Hypr2d::XAxis ( ) const

Computes an axis whose.

  • the origin is the center of this hyperbola, and
  • the unit vector is the "X Direction" or "Y Direction" respectively of the local coordinate system of this hyperbola Returns the major axis of the hyperbola.

◆ YAxis()

gp_Ax2d gp_Hypr2d::YAxis ( ) const

Computes an axis whose.

  • the origin is the center of this hyperbola, and
  • the unit vector is the "X Direction" or "Y Direction" respectively of the local coordinate system of this hyperbola Returns the minor axis of the hyperbola.

The documentation for this class was generated from the following file: