Open CASCADE Technology 6.6.0
Public Member Functions
Geom_Hyperbola Class Reference

Describes a branch of a hyperbola in 3D space.
A hyperbola is defined by its major and minor radii
and, as with any conic curve, is positioned in space
with a right-handed coordinate system (gp_Ax2 object) where:
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#include <Geom_Hyperbola.hxx>

Inheritance diagram for Geom_Hyperbola:
Inheritance graph
[legend]

Public Member Functions

 Geom_Hyperbola (const gp_Hypr &H)
 Constructs a hyperbola by conversion of the gp_Hypr hyperbola H.

 Geom_Hyperbola (const gp_Ax2 &A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
 Constructs a hyperbola defined by its major and
minor radii, MajorRadius and MinorRadius, where A2 locates the
hyperbola and defines its orientation in 3D space such that:

void SetHypr (const gp_Hypr &H)
 Converts the gp_Hypr hyperbola H into this hyperbola.

void SetMajorRadius (const Standard_Real MajorRadius)
 Assigns a value to the major radius of this hyperbola.
Exceptions
Standard_ConstructionError if:

void SetMinorRadius (const Standard_Real MinorRadius)
 Assigns a value to the minor radius of this hyperbola.
Exceptions
Standard_ConstructionError if:

gp_Hypr Hypr () const
 returns the non transient parabola from gp with the same
geometric properties as <me>.

Standard_Real ReversedParameter (const Standard_Real U) const
 Computes the parameter on the reversed hyperbola,
for the point of parameter U on this hyperbola.
For a hyperbola, the returned value is: -U.

Standard_Real FirstParameter () const
 Returns RealFirst from Standard.

Standard_Real LastParameter () const
 returns RealLast from Standard.

Standard_Boolean IsClosed () const
 Returns False.

Standard_Boolean IsPeriodic () const
 return False for an hyperbola.

gp_Ax1 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.
Raises ConstructionError if MajorRadius = 0.0

gp_Ax1 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.
Raises ConstructionError if MajorRadius = 0.0

gp_Hypr ConjugateBranch1 () const
 This branch of hyperbola is on the positive side of the
YAxis of <me>.

gp_Hypr ConjugateBranch2 () const
 This branch of hyperbola is on the negative side of the
YAxis of <me>.
Note: The diagram given under the class purpose
indicates where these two branches of hyperbola are
positioned in relation to this branch of hyperbola.

gp_Ax1 Directrix1 () const
 This directrix 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
directrix1 and the XAxis is the location point of the directrix1.
This point is on the positive side of the XAxis.

gp_Ax1 Directrix2 () const
 This line is obtained by the symmetrical transformation
of "directrix1" with respect to the YAxis of the hyperbola.

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.
//! raised if MajorRadius = 0.0

Standard_Real Focal () const
 Computes the focal distance. It is the distance between the
two focus of the hyperbola.

gp_Pnt Focus1 () const
 Returns the first focus of the hyperbola. This focus is on the
positive side of the XAxis of the hyperbola.

gp_Pnt Focus2 () const
 Returns the second focus of the hyperbola. This focus is on the
negative side of the XAxis of the hyperbola.

Standard_Real MajorRadius () const
 Returns the major or minor radius of this hyperbola.
The major radius is also the distance between the
center of the hyperbola and the apex of the main
branch (located on the "X Axis" of the hyperbola).

Standard_Real MinorRadius () const
 Returns the major or minor radius of this hyperbola.
The minor radius is also the distance between the
center of the hyperbola and the apex of a conjugate
branch (located on the "Y Axis" of the hyperbola).

gp_Hypr OtherBranch () const
 Computes the "other" branch of this hyperbola. This
is the symmetrical branch with respect to the center of this hyperbola.
Note: The diagram given under the class purpose
indicates where the "other" branch is positioned in
relation to this branch of the hyperbola.

Standard_Real Parameter () const
 Returns p = (e * e - 1) * MajorRadius where e is the
eccentricity of the hyperbola.
//! raised if MajorRadius = 0.0

void D0 (const Standard_Real U, gp_Pnt &P) const
 Returns in P the point of parameter U.
P = C + MajorRadius * Cosh (U) * XDir +
MinorRadius * Sinh (U) * YDir
where C is the center of the hyperbola , XDir the XDirection and
YDir the YDirection of the hyperbola's local coordinate system.

void D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const
 Returns the point P of parameter U and the first derivative V1.

void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const
 Returns the point P of parameter U, the first and second
derivatives V1 and V2.

void D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
 Returns the point P of parameter U, the first second and
third derivatives V1 V2 and V3.

gp_Vec DN (const Standard_Real U, const Standard_Integer N) const
 The returned vector gives the value of the derivative for the
order of derivation N.
//! Raised if N < 1.

void Transform (const gp_Trsf &T)
 Applies the transformation T to this hyperbola.

Handle_Geom_Geometry Copy () const
 Creates a new object which is a copy of this hyperbola.


Detailed Description


Constructor & Destructor Documentation

Geom_Hyperbola::Geom_Hyperbola ( const gp_Hypr H)
Geom_Hyperbola::Geom_Hyperbola ( const gp_Ax2 A2,
const Standard_Real  MajorRadius,
const Standard_Real  MinorRadius 
)
  • the center of the hyperbola is the origin of A2,
  • the "X Direction" of A2 defines the major axis
    of the hyperbola, i.e. the major radius
    MajorRadius is measured along this axis,
  • the "Y Direction" of A2 defines the minor axis
    of the hyperbola, i.e. the minor radius
    MinorRadius is measured along this axis,
  • A2 is the local coordinate system of the hyperbola.
    Exceptions
    Standard_ConstructionError if:

MajorRadius is less than 0.0,

  • MinorRadius is less than 0.0.

Member Function Documentation

gp_Ax1 Geom_Hyperbola::Asymptote1 ( ) const
gp_Ax1 Geom_Hyperbola::Asymptote2 ( ) const
gp_Hypr Geom_Hyperbola::ConjugateBranch1 ( ) const
gp_Hypr Geom_Hyperbola::ConjugateBranch2 ( ) const
Handle_Geom_Geometry Geom_Hyperbola::Copy ( ) const [virtual]

Implements Geom_Geometry.

void Geom_Hyperbola::D0 ( const Standard_Real  U,
gp_Pnt P 
) const [virtual]

Implements Geom_Curve.

void Geom_Hyperbola::D1 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1 
) const [virtual]

Implements Geom_Curve.

void Geom_Hyperbola::D2 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1,
gp_Vec V2 
) const [virtual]

Implements Geom_Curve.

void Geom_Hyperbola::D3 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1,
gp_Vec V2,
gp_Vec V3 
) const [virtual]

Implements Geom_Curve.

gp_Ax1 Geom_Hyperbola::Directrix1 ( ) const
gp_Ax1 Geom_Hyperbola::Directrix2 ( ) const
gp_Vec Geom_Hyperbola::DN ( const Standard_Real  U,
const Standard_Integer  N 
) const [virtual]

Implements Geom_Curve.

Standard_Real Geom_Hyperbola::Eccentricity ( ) const [virtual]

Implements Geom_Conic.

Standard_Real Geom_Hyperbola::FirstParameter ( ) const [virtual]

Implements Geom_Curve.

Standard_Real Geom_Hyperbola::Focal ( ) const
gp_Pnt Geom_Hyperbola::Focus1 ( ) const
gp_Pnt Geom_Hyperbola::Focus2 ( ) const
gp_Hypr Geom_Hyperbola::Hypr ( ) const
Standard_Boolean Geom_Hyperbola::IsClosed ( ) const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_Hyperbola::IsPeriodic ( ) const [virtual]

Implements Geom_Curve.

Standard_Real Geom_Hyperbola::LastParameter ( ) const [virtual]

Implements Geom_Curve.

Standard_Real Geom_Hyperbola::MajorRadius ( ) const
Standard_Real Geom_Hyperbola::MinorRadius ( ) const
gp_Hypr Geom_Hyperbola::OtherBranch ( ) const
Standard_Real Geom_Hyperbola::Parameter ( ) const
Standard_Real Geom_Hyperbola::ReversedParameter ( const Standard_Real  U) const [virtual]

Implements Geom_Conic.

void Geom_Hyperbola::SetHypr ( const gp_Hypr H)
void Geom_Hyperbola::SetMajorRadius ( const Standard_Real  MajorRadius)
  • MajorRadius is less than 0.0, or
  • MinorRadius is less than 0.0.Raised if MajorRadius < 0.0
void Geom_Hyperbola::SetMinorRadius ( const Standard_Real  MinorRadius)
  • MajorRadius is less than 0.0, or
  • MinorRadius is less than 0.0.Raised if MajorRadius < 0.0
void Geom_Hyperbola::Transform ( const gp_Trsf T) [virtual]

Implements Geom_Geometry.


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