# differential geometry – Conditions for two B-Splines to represent the same curve

What will be the weakest constraint for two B-Spline curves? $$S_1 (t)$$ Y $$S_2 (u)$$ Represent the same curve in space?

Suppose your orders are $$k_1$$ Y $$k_2$$ respectively, the node vectors are ($$t_0, t_1, t_2, dots, t_ {m_1}$$) Y$$u_0, u_1, u_2, dots, u_ {m_2}$$) respectively, and the control points are $$P_0, P_1, dots, P_ {n_1}$$ Y $$Q_0, Q_1, dots, Q_ {n_2}$$ respectively.