Question about periodic bspline

I do not understand the comments in geom_bsplinecurve.hxx:

1. On a periodic curve the first and the last multicities must be the same.

2. On periodic curves, Poles.Length() == Sum(Mults(i)) except the first or last

While from some intro to bspline, ( by Thomas W. Sederberg), the condition of knot and control vertices of periodic bspline are :

"This requires that the first n control points are
identical to the last n, and the first n parameter intervals in the knot vector are identical to the last n intervals as in Figure 9."

Are those statements for OpenCascade and Intro to Bspline equivalent?



wei guo's picture

Could anyone help me whether following set of periodic spline is valid for def in OCC:

degree = 3,
knots = [1 3 4 5 7 8 10 11 12 14]
Control points = P0 P1 P2 P3 P4 P5 P0 P1 P2

Thanks a lot