Estimation of maximum isometric distortion in mappings between Bézier hexahedrons(Bézier六面体间映射的最大等距扭曲估计)
Abstrak
A novel method for estimating bounds of the maximum isometric distortion between two hexahedral elements is proposed in this paper. Given two hexahedral elements with geometric injections, the proposed approach applies Lipschitz continuity analysis combined with extremum estimation of polynomials. By decomposing the Jacobian matrices of the composite mapping into a combination of Bézier rational polynomials, we establish sufficiency criteria for extrema attainment at parametric domain corners, and construct tight upper and lower bounds for mapping distortion by integrating. Lipschitz bounds of derivatives. Through rigorous testing on extensive datasets, we demonstrate the effectiveness and reliability of our algorithm.提出了一种可估计两个六面体单元之间映射的最大等距扭曲上下界的方法。给定具有几何单射的两个六面体单元，基于Lipschitz连续性分析与多项式最值估计，通过将复合映射的雅可比矩阵分解为Bézier有理多项式的组合形式，建立了参数域在角点处取最值的充分性判据，并结合导数的Lipschitz界构建了映射扭曲的紧致上下界。通过在大量数据集上的严格测试，证明了本文算法的有效性和可靠性。
Topik & Kata Kunci
Penulis (2)
NI Yuheng(倪宇恒)
FU Xiaoming(傅孝明)
Akses Cepat
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Cek di sumber asli →- Tahun Terbit
- 2026
- Sumber Database
- DOAJ
- DOI
- 10.3785/j.issn.1008-9497.25109
- Akses
- Open Access ✓