Open CASCADE Technology  7.7.0.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 &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...
 
 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...
 
void SetLocation (const gp_Pnt2d &theP)
 Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes theP. More...
 
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...
 
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...
 
void SetAxis (const gp_Ax22d &theA)
 Modifies this hyperbola, by redefining its local coordinate system so that it becomes theA. More...
 
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...
 
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...
 
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 &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...
 
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 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...
 
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 &theP)
 
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...
 
void Mirror (const gp_Ax2d &theA)
 
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...
 
void Rotate (const gp_Pnt2d &theP, const Standard_Real theAng)
 
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...
 
void Scale (const gp_Pnt2d &theP, const Standard_Real theS)
 
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...
 
void Transform (const gp_Trsf2d &theT)
 
gp_Hypr2d Transformed (const gp_Trsf2d &theT) const
 Transforms an hyperbola with the transformation theT from class Trsf2d. More...
 
void Translate (const gp_Vec2d &theV)
 
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...
 
void Translate (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2)
 
gp_Hypr2d Translated (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2) const
 Translates an hyperbola from the point theP1 to the point theP2. 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:

Constructor & Destructor Documentation

◆ gp_Hypr2d() [1/3]

gp_Hypr2d::gp_Hypr2d ( )
inline

Creates of an indefinite hyperbola.

◆ gp_Hypr2d() [2/3]

gp_Hypr2d::gp_Hypr2d ( const gp_Ax2d theMajorAxis,
const Standard_Real  theMajorRadius,
const Standard_Real  theMinorRadius,
const Standard_Boolean  theIsSense = Standard_True 
)
inline

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.

◆ gp_Hypr2d() [3/3]

gp_Hypr2d::gp_Hypr2d ( const gp_Ax22d theA,
const Standard_Real  theMajorRadius,
const Standard_Real  theMinorRadius 
)
inline

a hyperbola with radii theMajorRadius and theMinorRadius, positioned in the plane by coordinate system theA where:

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

Member Function Documentation

◆ Asymptote1()

gp_Ax2d gp_Hypr2d::Asymptote1 ( ) const
inline

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
inline

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
inline

Returns the axisplacement of the hyperbola.

◆ Coefficients()

void gp_Hypr2d::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.

◆ ConjugateBranch1()

gp_Hypr2d gp_Hypr2d::ConjugateBranch1 ( ) const
inline

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

◆ ConjugateBranch2()

gp_Hypr2d gp_Hypr2d::ConjugateBranch2 ( ) const
inline

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

◆ Directrix1()

gp_Ax2d gp_Hypr2d::Directrix1 ( ) const
inline

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
inline

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
inline

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.

◆ Focal()

Standard_Real gp_Hypr2d::Focal ( ) const
inline

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
inline

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
inline

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
inline

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

◆ Location()

const gp_Pnt2d& gp_Hypr2d::Location ( ) const
inline

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
inline

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
inline

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_Ax2d theA)

◆ Mirror() [2/2]

void gp_Hypr2d::Mirror ( const gp_Pnt2d theP)

◆ Mirrored() [1/2]

gp_Hypr2d 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.

◆ Mirrored() [2/2]

gp_Hypr2d 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.

◆ OtherBranch()

gp_Hypr2d gp_Hypr2d::OtherBranch ( ) const
inline

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
inline

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 ( )
inline

◆ Reversed()

gp_Hypr2d gp_Hypr2d::Reversed ( ) const
inline

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 theP,
const Standard_Real  theAng 
)
inline

◆ Rotated()

gp_Hypr2d gp_Hypr2d::Rotated ( const gp_Pnt2d theP,
const Standard_Real  theAng 
) const
inline

Rotates an hyperbola. theP is the center of the rotation. theAng is the angular value of the rotation in radians.

◆ Scale()

void gp_Hypr2d::Scale ( const gp_Pnt2d theP,
const Standard_Real  theS 
)
inline

◆ Scaled()

gp_Hypr2d gp_Hypr2d::Scaled ( const gp_Pnt2d theP,
const Standard_Real  theS 
) const
inline

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.

◆ SetAxis()

void gp_Hypr2d::SetAxis ( const gp_Ax22d theA)
inline

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

◆ SetLocation()

void gp_Hypr2d::SetLocation ( const gp_Pnt2d theP)
inline

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

◆ SetMajorRadius()

void gp_Hypr2d::SetMajorRadius ( const Standard_Real  theMajorRadius)
inline

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

◆ SetMinorRadius()

void gp_Hypr2d::SetMinorRadius ( const Standard_Real  theMinorRadius)
inline

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

◆ SetXAxis()

void gp_Hypr2d::SetXAxis ( const gp_Ax2d theA)
inline

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 theA)
inline

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 theT)
inline

◆ Transformed()

gp_Hypr2d gp_Hypr2d::Transformed ( const gp_Trsf2d theT) const
inline

Transforms an hyperbola with the transformation theT from class Trsf2d.

◆ Translate() [1/2]

void gp_Hypr2d::Translate ( const gp_Pnt2d theP1,
const gp_Pnt2d theP2 
)
inline

◆ Translate() [2/2]

void gp_Hypr2d::Translate ( const gp_Vec2d theV)
inline

◆ Translated() [1/2]

gp_Hypr2d gp_Hypr2d::Translated ( const gp_Pnt2d theP1,
const gp_Pnt2d theP2 
) const
inline

Translates an hyperbola from the point theP1 to the point theP2.

◆ Translated() [2/2]

gp_Hypr2d gp_Hypr2d::Translated ( const gp_Vec2d theV) const
inline

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

◆ XAxis()

gp_Ax2d gp_Hypr2d::XAxis ( ) const
inline

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
inline

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: