Constructing continuous, smooth surfaces remains a key challenge in geometric modeling, especially when working with complex configurations such as extraordinary vertices [1]. In this talk, we investigate various approaches for constructing smooth surfaces, focusing on methods such as approximate C1 constructions, and the almost-C1 formulation [2]. Almost-C1 splines are a type of bi-quadratic spline that operates on fully unstructured quadrilateral meshes, with no restrictions on the placement or quantity of extraordinary vertices. Another approach is bi-cubic Coons patches with Hermite interpolation curves [3]. This construction is based on cubic Hermite curves and bi-linear Coons interpolation, ensuring G1-continuity at the nodes and C0 along edges. These approaches demonstrate varying limitations, particularly in maintaining continuity and handling unstructured meshes to create splines for surface modeling. We propose a bi-cubic surface construction designed to achieve exact C1 continuity in regular regions while maintaining G1 continuity at extraordinary vertices. It is designed to operate on unstructured quadrilateral meshes. The construction can be applied to fourth-order problems, such as Kirchhoff--Love shells. Note that this talk is based on ongoing research within the project "Isogeometric multi-patch shells and multigrid solvers".