This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in \(\mathbb{R}^n\) , applicable to any given set of ordered points in \(\mathbb{R}^n, n\ge 2\) . The construction involves four essential components: local functions, blending functions, redistributing functions, and gluing functions. The resulting curve possesses favorable attributes, including \(G^2\) geometric smoothness, locality, the absence of cusps, and no self-intersections. Numerical examples show that the curve interpolates the given points without overshooting or undershooting. Moreover, the algorithm is adaptable to various scenarios, such as preserving convexity, interpolating sharp corners, and ensuring sphere preservation. This paper substantiates the efficacy of the proposed method through the presentation of numerous examples, offering a practical demonstration of its capabilities.
