In order for the continuity to occur across two connected curves, all prior conditions for those curves must be met. Continuity of curves are important for surface reflection lines.

In order for two curves to be tangent, they must be connected at their endpoints. Tangent-continuity means that line, tangent at the beginning of one curve, is parallel to the tangent of the other curve and both tangent lines must be the same length. The control polygon is also tangent to the curve at the start and end point.