Types of Continuities:

Different types of curve segments may be utilized to construct synthetic curves, with certain continuity requirements. Continuity refers the smoothness of the connection of two curves or surfaces at the connection points or edges. Usually, three types of continuity, called as C ^o, C¹, and C², are described to characterize the smoothness of connection of two curves. C ^o continuity implies simply associating two curves. It means that the gradients of these curves at the point of joining in addition to their curvatures can be different (Figure (a)). In C¹ continuity, the gradients at the point of joining should be same (Figure (b)). However, C² implies curvature continuity; that is, not only the gradient but also the centre of curvature is the similar, as shown in Figure (c).

First-order Continuity and Second-order Continuity :

Figure: Types of Continuities