Open CASCADE Technology
6.5.4
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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>
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. |
Geom_Hyperbola::Geom_Hyperbola | ( | const gp_Ax2 & | A2, |
const Standard_Real | MajorRadius, | ||
const Standard_Real | MinorRadius | ||
) |
MajorRadius is less than 0.0,
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 | ) |
void Geom_Hyperbola::SetMinorRadius | ( | const Standard_Real | MinorRadius | ) |
void Geom_Hyperbola::Transform | ( | const gp_Trsf & | T | ) | [virtual] |
Implements Geom_Geometry.