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Keywords = RSD interpolation

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16 pages, 335 KB  
Article
Locally RSD-Generated Parametrized G1-Spline Surfaces Interpolating First-Order Data over 3D Triangular Meshes
by László L. Stachó
AppliedMath 2025, 5(3), 83; https://doi.org/10.3390/appliedmath5030083 - 2 Jul 2025
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Abstract
Given a triangular mesh in R3 with a family of points associated with its vertices along with vectors associated with its edges, we propose a novel technique for the construction of locally generated fitting parametrized G1-spline interpolation surfaces. The method consists of [...] Read more.
Given a triangular mesh in R3 with a family of points associated with its vertices along with vectors associated with its edges, we propose a novel technique for the construction of locally generated fitting parametrized G1-spline interpolation surfaces. The method consists of a G1 correction over the mesh edges of the mesh triangles, produced using reduced side derivatives (RSDs) introduced earlier by the author in terms of the barycentric weight functions. In the case of polynomial RSD shape functions, we establish polynomial edge corrections via an algorithm with an independent interest in determining the optimal GCD cofactors with the lowest degree for arbitrary families of polynomials. Full article
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