Continuity Level

Levels of curve continuity:

Left: C⁰, because of the angle at the top

Middle: C¹, at the top a semicircle joins a semicircle of smaller radius

Right: C², the difference is subtle but the right side is not semicircular and blends with the left

The level of continuity is a way to describe curvature. A curve with an angular cusp is C⁰ continuous. The curve is continuous but its derivative is not. A curve whose curvature changes has C¹ continuity. The curve and its derivative are both continuous but its second derivative is not. A curve with uninterrupted, unchanging curvature has C² continuity. NURBS curves must have at least C⁰ continuity; a continuity level greater than C² is unnecessary for most 3D computer modeling.