BSplineCurve
Current Versions
2
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).
Boolean
 
1 if the curve is periodic, 0 if it is not periodic.
integer
p
Degree.
integer
m
Length of knot vector.
double[m]
U
Knot vector.
double[n][k]
Pw
The control points of the curve. The number of control points, n, is given by n = m - p - 1. If the curve is rational, these are given in homogeneous coordinates and k = d + 1. If the curve is polynomial, these are given in Cartesian coordinates and k = d.
Description
The BSplineCurve describes a general spline curve using B-spline basis functions. Splines on this form are often referred to as B-splines.
A pth-degree spline curve is defined by
where Pi are the control points., the wi are the weights, and the Nip are the pth degree B-spline basis functions defined in the nonperiodic and nonuniform knot vector
For Nip(u), the following definition is used:
For nonrational B-splines, all weights are equal to 1 and the curve can be expressed as
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
12 BSplineCurve # class
2 # version
3 # sdim
0 # rational?
0 # periodic?
3 # degree
# knot vector
8 0 0 0 0 1 1 1 1
# control points
1 0 0
1 0.33333333333333333 0
1 0.66666666666666666 0.3333333333333333
1 1 1
See also
 BezierCurve