多片拼接NURBS曲面上平纹织物铺覆仿真算法

Draping Simulation Algorithms of Plain Woven Fabrics over Multi-Patch NURBS Surfaces

  • 摘要: 本文针对多片拼接NURBS曲面上平纹织物铺覆仿真,提出了一套限制最大剪切角与分片数量的铺覆仿真整体优化方案。首先,本文改进了基于变形能量的渔网算法,以双二次Bézier映射取代传统双线性映射提升了网格拟合自由度;在球壳铺覆实验中,铺覆结果与标准值的均方误差(MSE)由改进前的0.7615降至0.0467;针对传统算法单片曲面铺覆不完整问题,设计了边界扩张策略,通过递归延伸测地线生成子区域网格,消除了测地线延伸受限导致的铺覆盲区。其次,本文提出多片拼接NURBS曲面整体参数化方法,采用双线性映射将各单片曲面独立参数域映射至0,1×0,1全局参数域,实现多片拼接NURBS曲面上铺覆网格的跨边界生成;将其铺覆结果与不同算法和商业软件结果进行对比分析,验证了算法的精确性与可靠性。再次,针对限制网格剪切角的实际需求,提出基于Voronoi图算法控制种子点实现参数域划分,结合遗传算法优化子区域初始铺覆参数,分区铺覆案例的最大剪切角从初始46.29°降至22.16°。本研究提出的整体优化方案有效实现了多片拼接NURBS曲面的铺覆仿真,为平纹织物预成型体制备及铺覆工艺优化提供了可靠的技术支撑。

     

    Abstract: This study investigates the draping simulation of plain-woven fabrics over multi-patch NURBS surfaces and proposes an integrated optimization framework that simultaneously constrains the maximum shear angle and the number of cut patches. First, an improved deformation-energy-based fishnet algorithm is developed, where a biquadratic Bézier mapping replaces the conventional bilinear mapping to increase the degrees of freedom for surface fitting. In the spherical-shell benchmark, the mean squared error (MSE) between the predicted shear-angle distribution and the reference solution is reduced from 0.7615 to 0.0467. To overcome the incomplete coverage commonly observed in traditional fishnet approaches on single curved surfaces, a boundary expansion strategy is introduced, in which geodesics are recursively extended to generate meshes over residual subregions, thereby eliminating draping blind zones caused by limited geodesic extend ability. Second, a global parameterization method for multi-patch NURBS assemblies is proposed. By employing a bilinear mapping, the independent parametric domains of individual patches are unified into a global 0,1×0,1 parametric space, enabling continuous mesh generation across patch interfaces. The proposed method is further validated through comparative studies against alternative algorithms and commercial software, demonstrating its accuracy and robustness. Third, to satisfy practical requirements on shear-angle limitations, a Voronoi-diagram-based parametric-domain partitioning scheme is presented, where seed locations control the partition boundaries. A genetic algorithm is then used to optimize the initial draping parameters within each subregion; in a representative cut-pattern optimization case, the maximum shear angle is reduced from an initially over-limit value of 46.29° to 22.16°. Overall, the proposed approach enables reliable draping simulation on multi-patch NURBS surfaces and provides practical support for plain-woven preform manufacturing and draping-process optimization.

     

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