| | 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:
- the origin is the center of the hyperbola,
- the "X Direction" defines the major axis, and
- the "Y Direction" defines the minor axis.
The origin, "X Direction" and "Y Direction" of this
coordinate system define the plane of the hyperbola.
The 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 "main Direction" of the local coordinate system is
a vector normal to the plane of the hyperbola. The
axis, of which the origin and unit vector are
respectively the origin and "main Direction" of the
local coordinate system, is termed the "Axis" or "main <br>
Axis" of the hyperbola.
The "main Direction" of the local coordinate system
gives an explicit orientation to the hyperbola,
determining the direction in which the parameter
increases along the hyperbola.
The Geom_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: Defines the main branch of an hyperbola.
^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).
More...
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1.6.3