Suppose I have a cubic B-spline curve, it has $57$ knots vectors and $53$ control points. The knot vector is like $(0,0,0,0,1,2,…,50,50,50,50)$
The curve is like this
If we want to generate the following curve (repeated three times)
What I think is repeat knot in knot vectors and control points. Of course, I need to delete some internal knot and control points in order to make the number of knots equals number of control points + $4$. But is there any rule?
Best Answer
Cubic basis function are determined by 5 knots each. I.e. your basis functions can be represented as
$(0,0,0,0,1),\ (0,0,0,1,2),\ (0,0,1,2,3)\ .......\ (49,50,50,50,50)$
When translating all basis functions by 50, their representatives change to
$(50,50,50,50,51),\ (50,50,50,51,52),\ (50,50,51,52,53)\ .......\ (99,100,100,100,100)$
Now there is twice as many and you also repeat your control points getting twice as many.
Since $(49,50,50,50,50)$ is followed by $(50,50,50,50,51)$, you should not add any more knots equal to $50$ than those you had already.