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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2601.11677 |
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| _version_ | 1866911381948727296 |
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| author | Ammad, Muhammad Misro, Md Yushalify Bibi, Samia Ramli, Ahmad |
| author_facet | Ammad, Muhammad Misro, Md Yushalify Bibi, Samia Ramli, Ahmad |
| contents | We study a discrete analogue of the parametric Plateau problem in a non-polynomial tensor-product surface spaces generated by the generalized trigonometric (GT)--Bézier basis. Boundary interpolation is imposed by prescribing the boundary rows and columns of the control net, while the interior control points are selected by a Dirichlet principle: for each admissible choice of Bézier basis shape parameters, we compute the unique Dirichlet-energy extremal within the corresponding GT--Bézier patch space, which yields a parameter-dependent symmetric linear system for the interior control net under standard nondegeneracy assumptions. The remaining design freedom is thereby reduced to a four-parameter optimization problem, which we solve by particle swarm optimization. Numerical experiments show that the resulting two-level procedure consistently decreases the Dirichlet energy and, in our tests, often reduces the realized surface area relative to classical Bernstein--Bézier Dirichlet patches and representative quasi-harmonic and bending-energy constructions under identical boundary control data. We further adapt the same Dirichlet-extremal methodology to a hybrid tensor-product/bilinear Coons framework, obtaining minimality-biased TB--Coons patches from sparse boundary specifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11677 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dirichlet Extremals for Discrete Plateau Problems in GT-Bezier Spaces via PSO Ammad, Muhammad Misro, Md Yushalify Bibi, Samia Ramli, Ahmad Numerical Analysis We study a discrete analogue of the parametric Plateau problem in a non-polynomial tensor-product surface spaces generated by the generalized trigonometric (GT)--Bézier basis. Boundary interpolation is imposed by prescribing the boundary rows and columns of the control net, while the interior control points are selected by a Dirichlet principle: for each admissible choice of Bézier basis shape parameters, we compute the unique Dirichlet-energy extremal within the corresponding GT--Bézier patch space, which yields a parameter-dependent symmetric linear system for the interior control net under standard nondegeneracy assumptions. The remaining design freedom is thereby reduced to a four-parameter optimization problem, which we solve by particle swarm optimization. Numerical experiments show that the resulting two-level procedure consistently decreases the Dirichlet energy and, in our tests, often reduces the realized surface area relative to classical Bernstein--Bézier Dirichlet patches and representative quasi-harmonic and bending-energy constructions under identical boundary control data. We further adapt the same Dirichlet-extremal methodology to a hybrid tensor-product/bilinear Coons framework, obtaining minimality-biased TB--Coons patches from sparse boundary specifications. |
| title | Dirichlet Extremals for Discrete Plateau Problems in GT-Bezier Spaces via PSO |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.11677 |