Thin Plate Spline Surface Reconstruction via the Method of Matched Sections
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917453797261312 |
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| author | Orynyak, Igor Danylenko, Kirill Tavrov, Danylo |
| author_facet | Orynyak, Igor Danylenko, Kirill Tavrov, Danylo |
| contents | This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the challenges of surface modeling, which lie at the intersection of computational mechanics and computer graphics. This work shows how the MMS successfully bridges this gap. By decomposing the domain into an assembly of 1D directional components matched along their entire boundaries, the method inherently enforces the continuity of all variational parameters, including second-order (curvature) and third-order (shear) derivatives. We demonstrate the method's advanced capabilities in high-fidelity surface reconstruction and blending, showing that it consistently generates energetically optimal, fair surfaces even from complex boundary conditions or sparse internal data points. By advancing the application of the MMS, this research establishes it as a powerful, physics-informed geometric tool that satisfies the dual demands of rigorous numerical analysis and aesthetic computer-aided design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thin Plate Spline Surface Reconstruction via the Method of Matched Sections Orynyak, Igor Danylenko, Kirill Tavrov, Danylo Graphics Numerical Analysis I.3.5 This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the challenges of surface modeling, which lie at the intersection of computational mechanics and computer graphics. This work shows how the MMS successfully bridges this gap. By decomposing the domain into an assembly of 1D directional components matched along their entire boundaries, the method inherently enforces the continuity of all variational parameters, including second-order (curvature) and third-order (shear) derivatives. We demonstrate the method's advanced capabilities in high-fidelity surface reconstruction and blending, showing that it consistently generates energetically optimal, fair surfaces even from complex boundary conditions or sparse internal data points. By advancing the application of the MMS, this research establishes it as a powerful, physics-informed geometric tool that satisfies the dual demands of rigorous numerical analysis and aesthetic computer-aided design. |
| title | Thin Plate Spline Surface Reconstruction via the Method of Matched Sections |
| topic | Graphics Numerical Analysis I.3.5 |
| url | https://arxiv.org/abs/2602.19182 |