  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.
