| | Describes a cone.
A cone is defined by the half-angle at its apex, and
is positioned in space by a coordinate system (a
gp_Ax3 object) and a reference radius as follows:
- The "main Axis" of the coordinate system is the
axis of revolution of the cone.
- The plane defined by the origin, the "X Direction"
and the "Y Direction" of the coordinate system is
the reference plane of the cone. The intersection
of the cone with this reference plane is a circle of
radius equal to the reference radius.
- The apex of the cone is on the negative side of
the "main Axis" of the coordinate system if the
half-angle is positive, and on the positive side if
the half-angle is negative.
This coordinate system is the "local coordinate <br>
system" of the cone. The following apply:
- Rotation around its "main Axis", in the
trigonometric sense given by the "X Direction"
and the "Y Direction", defines the u parametric direction.
- Its "X Axis" gives the origin for the u parameter.
- Its "main Direction" is the v parametric direction of the cone.
- Its origin is the origin of the v parameter.
The parametric range of the two parameters is:
- [ 0, 2.*Pi ] for u, and - ] -infinity, +infinity [ for v
The parametric equation of the cone is: P(u, v) =
O + (R + v*sin(Ang)) * (cos(u)*XDir + sin(u)*YDir) + v*cos(Ang)*ZDir where:
- O, XDir, YDir and ZDir are respectively
the origin, the "X Direction", the "Y Direction" and
the "Z Direction" of the cone's local coordinate system,
- Ang is the half-angle at the apex of the cone, and
- R is the reference radius.
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1.6.3