We present an efficient B-spline finite element method (FEM) for cloth simulation. While higher-order FEM has long promised higher accuracy, its adoption in cloth simulators has been limited by its larger computational costs while generating results with similar visual quality. Our contribution is a full algorithmic pipeline that makes cloth simulation using quadratic B-spline surfaces faster than standard linear FEM in practice while consistently improving accuracy and visual fidelity. Using quadratic B-spline basis functions, we obtain a globally $C^1$-continuous displacement field that supports consistent discretization of both membrane and bending energies, effectively reducing locking artifacts and mesh dependence common to linear elements. To close the performance gap, we introduce a reduced integration scheme that separately optimizes quadrature rules for membrane and bending energies, an accelerated Hessian assembly procedure tailored to the spline structure, and an optimized linear solver based on partial factorization. Together, these optimizations make high-order, smooth cloth simulation competitive at scale, yielding an average $2\times$ speedup over highly-optimized linear FEM in our tests. Extensive experiments demonstrate improved accuracy, wrinkle detail, and robustness, including contact-rich scenarios, relative to linear FEM and recent higher-order approaches. Our method enables realistic wrinkling dynamics across a wide range of material parameters and supports practical garment animation, providing a new promising spatial discretization for high-quality cloth simulation.

翻译：本文提出一种高效的B样条有限元方法（FEM）用于布料模拟。尽管高阶有限元法长期以来被认为具有更高的精度，但由于其计算成本较高且生成的视觉效果相似，在布料模拟器中的应用一直受限。我们的贡献在于提出了一套完整的算法流程，使得在实际应用中采用二次B样条曲面的布料模拟比标准线性有限元法更快，同时持续提升精度与视觉保真度。通过使用二次B样条基函数，我们获得了全局$C^1$连续的位移场，该位移场支持薄膜能量与弯曲能量的一致离散化，有效减少了线性单元常见的自锁现象与网格依赖性。为弥补性能差距，我们引入了分别针对薄膜能量与弯曲能量优化积分法则的降阶积分方案、针对样条结构定制的加速Hessian矩阵组装流程，以及基于部分分解的优化线性求解器。这些优化措施共同使得高阶平滑布料模拟在大规模场景中具备竞争力，在我们的测试中相比高度优化的线性有限元法平均实现$2\times$的加速。大量实验证明，相较于线性有限元法及近期的高阶方法，本方法在精度、褶皱细节和鲁棒性（包括密集接触场景）方面均有提升。该方法能够在广泛材料参数范围内实现逼真的褶皱动力学，并支持实用的服装动画，为高质量布料模拟提供了一种前景广阔的新型空间离散化方案。