| | Describes a rational or non-rational Bezier curve
- a non-rational Bezier curve is defined by a table
of poles (also called control points),
- a rational Bezier curve is defined by a table of
poles with varying weights.
These data are manipulated by two parallel arrays:
- the poles table, which is an array of gp_Pnt2d points, and
- the weights table, which is an array of reals.
The bounds of these arrays are 1 and "the number of poles" of the curve.
The poles of the curve are "control points" used to deform the curve.
The first pole is the start point of the curve, and the
last pole is the end point of the curve. The segment
which joins the first pole to the second pole is the
tangent to the curve at its start point, and the
segment which joins the last pole to the
second-from-last pole is the tangent to the curve
at its end point.
It is more difficult to give a geometric signification
to the weights but they are useful for providing
exact representations of the arcs of a circle or
ellipse. Moreover, if the weights of all the poles are
equal, the curve is polynomial; it is therefore a
non-rational curve. The non-rational curve is a
special and frequently used case. The weights are
defined and used only in case of a rational curve.
The degree of a Bezier curve is equal to the
number of poles, minus 1. It must be greater than or
equal to 1. However, the degree of a
Geom2d_BezierCurve curve is limited to a value
(25) which is defined and controlled by the system.
This value is returned by the function MaxDegree.
The parameter range for a Bezier curve is [ 0, 1 ].
If the first and last control points of the Bezier
curve are the same point then the curve is closed.
For example, to create a closed Bezier curve with
four control points, you have to give a set of control
points P1, P2, P3 and P1.
The continuity of a Bezier curve is infinite.
It is not possible to build a Bezier curve with
negative weights. We consider that a weight value
is zero if it is less than or equal to
gp::Resolution(). We also consider that
two weight values W1 and W2 are equal if:
|W2 - W1| <= gp::Resolution().
Warning
- When considering the continuity of a closed
Bezier curve at the junction point, remember that
a curve of this type is never periodic. This means
that the derivatives for the parameter u = 0
have no reason to be the same as the
derivatives for the parameter u = 1 even if the curve is closed.
- The length of a Bezier curve can be null.
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1.6.3