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Article

Locally RSD-Generated Parametrized G1-Spline Surfaces Interpolating First-Order Data over 3D Triangular Meshes

by
László L. Stachó
Bolyai Institute, University of Szeged, Aradi Vértanúk tere 1, 6725 Szeged, Hungary
AppliedMath 2025, 5(3), 83; https://doi.org/10.3390/appliedmath5030083
Submission received: 29 May 2025 / Revised: 22 June 2025 / Accepted: 27 June 2025 / Published: 2 July 2025
Versions Notes

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 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.
Keywords: triangular mesh in 3D; G1-spline; parametrized surface; reduced side derivatives; RSD interpolation; shape function; GCD cofactors triangular mesh in 3D; G1-spline; parametrized surface; reduced side derivatives; RSD interpolation; shape function; GCD cofactors

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MDPI and ACS Style

Stachó, L.L. Locally RSD-Generated Parametrized G1-Spline Surfaces Interpolating First-Order Data over 3D Triangular Meshes. AppliedMath 2025, 5, 83. https://doi.org/10.3390/appliedmath5030083

AMA Style

Stachó LL. Locally RSD-Generated Parametrized G1-Spline Surfaces Interpolating First-Order Data over 3D Triangular Meshes. AppliedMath. 2025; 5(3):83. https://doi.org/10.3390/appliedmath5030083

Chicago/Turabian Style

Stachó, László L. 2025. "Locally RSD-Generated Parametrized G1-Spline Surfaces Interpolating First-Order Data over 3D Triangular Meshes" AppliedMath 5, no. 3: 83. https://doi.org/10.3390/appliedmath5030083

APA Style

Stachó, L. L. (2025). Locally RSD-Generated Parametrized G1-Spline Surfaces Interpolating First-Order Data over 3D Triangular Meshes. AppliedMath, 5(3), 83. https://doi.org/10.3390/appliedmath5030083

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