The level of continuity is a way to describe curvature. A curve with an angular cusp is C 0 continuous. The curve is continuous but its derivative is not. A curve whose curvature changes has C 1 continuity. The curve and its derivative are both continuous but its second derivative is not. A curve with uninterrupted, unchanging curvature has C 2 continuity. NURBS curves must have at least C 0 continuity; a continuity level greater than C 2 is unnecessary for most 3D computer modeling.
Levels of curve continuity:
Left: C 0 , because of the angle at the top
Middle: C 1 , at the top a semicircle joins a semicircle of smaller radius
Right: C 2 , the difference is subtle but the right side is not semicircular and blends with the left
