Translations:B-Splines/108/en

The derivative until which continuity exists is given by the multiplicity $$m$$. Therefore we can specify a vector with the multiplicity for every knot: $$\{m_0, m_1,\dots, m_k\}$$. A knot on a spline with degree d and the multiplicity m tells that the curve left and right to the knot has at least an equal n order derivative (called Cn continuity) whereas $$n=d-m$$.