Differential geometry analysis demonstrates curvature derivations for generalized Darboux curves in Euclidean space, highlighting computational geometric methods.
In this paper, we introduce the W-direction curve constructed from the unit generalized Darboux vector of a Frenet curve in n-dimensional Euclidean space Eⁿ. 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.
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Bedia Merih Özçetin (2026) studied this question.
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