Weighted transfinite interpolation for slightly unstructured curvilinear patches

This paper presents an extension of the classical transfinite interpolation formula originally developed by Gordon and Hall, aimed at improving geometric modeling over slightly unstructured curvilinear patches. While traditional transfinite schemes rely on structured boundary data and cardinal blending functions, the proposed method introduces a weighted framework that accommodates irregularities in the layout of interpolation stations. By assigning suitable weights to both the blending and trial functions—such as Bernstein polynomials, B-splines, or NURBS—the interpolation scheme gains flexibility while preserving smoothness and continuity across the patch. The approach maintains the intuitive geometric structure of the original formulation, but significantly expands its applicability to more general domains encountered in computer-aided geometric design (CAGD), mesh generation, and isogeometric analysis. With the cylindrical patch serving as the primary benchmark and the spherical cap as the secondary, various combinations of blending and trial functions are investigated to illustrate the method’s capability to accurately represent mild irregularities in data distribution.