Hello .Thanks for your replies.
Basically ,I’m following a research paper and trying to understand the way they have parametrized the stent center line. The image that I had posted is the one from that particular literature. In short ,they have fixed the control points,the knot vector, and the degree and only used the weights of the three control points ( the other part being the reflection of the first part ) as decision variables,for the design optimization problem in hand .The below is the para from the said literature:
“The centerline of a single stent segment is represented
as a NURBS curve. A control polygon with eight nodes is
developed from the stent dimensions detailed above (Fig.).
Further exploitation of the anti-symmetry of an individual
stent segment means that control points 4−7 may be generated
by reflecting nodes 3−0 through the central reflection
point. Furthermore, the weights associated with the control
nodes 0−4 are numerically equal to weights 7−4, thereby
reducing the number of weights to be specified for a given
curve to four.”
Now, it seems like the curve does pass through the mid-point (229,458) .So,if we first draw the lower half n reflect it than we will have to make (229,458) as an end point(i.e control point)