This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. 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-intersection. Moreover, the algorithm is adaptable to various scenarios, such as preserving convexity, interpolating sharp corners, and ensuring sphere preservation. The paper substantiates the efficacy of the proposed method through the presentation of numerous numerical examples, offering a practical demonstration of its capabilities.

翻译：本文提出了一种在$\mathbb{R}^d$（$d\ge 2$）中构造几何光滑插值曲线的方法，适用于带方向且可展平的点。该构造包含四个基本组成部分：局部函数、混合函数、重分布函数和粘合函数。所得曲线具有多项优良特性，包括$G^2$几何光滑性、局部性、无尖点且无自交。此外，该算法可适应多种场景，如保持凸性、插值尖锐拐角以及保证球面保持性。本文通过大量数值算例验证了所提方法的有效性，并对其实际能力进行了实证演示。