BezierCurve
Current Version
1
Subtype of
GeomCurve
Fields
Entity/Object
Variable
Description
integer
 
Version.
integer
d
Space dimension.
Boolean
 
1 if the curve is rational, 0 if the curve is polynomial (nonrational).
integer
p
Degree.
double[p+1][k]
Pw
The control points. If the curve is rational, then the points are given in homogeneous coordinates and k = d+1. If the curve is polynomial, the points are given in Cartesian coordinates and k = d.
Description
A rational Bézier curve is a parameterized curve of the form
where the functions
are the Bernstein basis functions of degree p, Pi = ( x1, …,  xd) are the control points in the d-dimensional space, and wi are the weights, which should always be positive real numbers to get a properly defined rational Bézier curve. A rational Bézier curve has a direction defined by the parameter t. The homogeneous control points Pw[i] used in the serialization of a rational curve have the components:
A polynomial curve has all weights equal to 1.
Example
The following example illustrates a Bézier curve:
11 BezierCurve # class
1 # version
3 # sdim
1 # rational?
2 # degree
# homogeneous control points
-1 0 0 1
-0.70710678118654757 -0.70710678118654757 0 0.70710678118654757
0 -1 0 1
See also
BSplineCurve