The concept of multi-sided Coons patches was introduced to enhance the efficiency of surface'hole-filling',which leverage the Boolean sum methodology of bilinear Coons patches and serve as a direct extension of bilinear Coons patches within the polygonal domain.The bilinear Coons patches were reformulated by using bilinear coordinates.The parameter domain was expanded to encompass a convex polygonal domain.The bilinear coordinates on the rectangular domain were replaced by generalized barycentric coordinates on the convex polygonal domain,thereby facilitating the construction of the multi-sided Coons patches.Theoretical derivations and numerical examples demonstrate that the proposed multi-sided Coons patches possess boundary interpolation properties,offer straightforward construction methodologies,exhibit high computational efficiency,and provide a partial resolution to the hole-filling problem.
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