Does increasing the weight of control points have any effect on the continuity of a B-Spline?

Question

I have a basic question relating to NURBs Spline and tension splines like v-splines.

Does increasing the weight of a give control point or all control points have any effect on the continuity of the B-Spline ? For example in the case of a C2 continuous weighted B-Spline (NURBS) with uniform knotvector ? And also in the case of tension splines like v-Spline where tension values act similar to weights also with uniform knot vector.

Answer 1

Theoretically it does not decrease the continuity. However, it practical terms there is often a change in the radius of curvature. In the limit, when the weight is infinite, you will get parametric continuity but not geometric continuity (C but not G).

In this example, when the weight gets high enough, while if you zoom in enough you will still have a continuous curve, it's not going to be suitable for many applications that require smoothness. So, it depends on what you're using continuity for.