I have circle described via NURBS. Now, I can calculate line intersection, because equation can be reduced and I got "classic" circle equation. However, when I change weights of my control points, I have no longer circle. I have tried to calculate intersection with line, but I am stucked in brain-development phase (meaning on paper).

Is it even possible ? Because in certain configuration, I can get 3 intersection points (but for circle, there will be max. 2 -> equation is of 2 degree). I limited my solution so that weights will create convex shape. In that case, there should be still 2 intersection tops.

And the same later on in 3D with plane / sphere (again, with weightened knots)