On Novel Associated Curves of a Generalized Darboux Vector in $\mathbb{E}^n$

In this paper, we introduce the $\mathcal{W}$-direction curve constructed from the unit generalized Darboux vector of a Frenet curve in $n$-dimensional Euclidean space $\mathbb{E}^n$. We derive the higher-order derivatives of the associated curve and determine its Frenet vectors and curvatures. The computational procedure is implemented via an algorithm developed in MATLAB. Finally, a representative example is provided to illustrate the applicability of the proposed method.