| | Describes a branch of a hyperbola in the plane (2D space).
A hyperbola is defined by its major and minor radii
and, as with any conic curve, is positioned in the
plane with a coordinate system (gp_Ax22d object) where:
- the origin is the center of the hyperbola,
- the "X Direction" defines the major axis, and
- the "Y Direction" defines the minor axis.
This coordinate system is the local coordinate
system of the hyperbola.
The branch of the hyperbola described is the one
located on the positive side of the major axis.
The orientation (direct or indirect) of the local
coordinate system gives an explicit orientation to the
hyperbola, determining the direction in which the
parameter increases along the hyperbola.
The Geom2d_Hyperbola hyperbola is parameterized as follows:
P(U) = O + MajRad*Cosh(U)*XDir + MinRad*Sinh(U)*YDir
where:
- P is the point of parameter U,
- O, XDir and YDir are respectively the origin, "X <br>
Direction" and "Y Direction" of its local coordinate system,
- MajRad and MinRad are the major and minor radii of the hyperbola.
The "X Axis" of the local coordinate system therefore
defines the origin of the parameter of the hyperbola.
The parameter range is ] -infinite,+infinite [.
The following diagram illustrates the respective
positions, in the plane of the hyperbola, of the three
branches of hyperbolas constructed using the
functions OtherBranch, ConjugateBranch1 and
ConjugateBranch2:
^YAxis
|
FirstConjugateBranch
|
Other | Main
--------------------- C
--------------------->XAxis
Branch |
Branch
|
SecondConjugateBranch
|
Warning
The value of the major radius (on the major axis) can
be less than the value of the minor radius (on the minor axis).
See Also
GCE2d_MakeHyperbola which provides functions for
more complex hyperbola constructions
gp_Ax22d
gp_Hypr2d for an equivalent, non-parameterized data structure
More...
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1.6.3