In this study, we present the bicubic Hermite element method (BHEM), a new computational framework devised for the elastodynamic simulation of parametric thin-shell structures. The BHEM is constructed based on parametric quadrilateral Hermite patches, which serve as a unified representation for shell geometry, simulation, collision avoidance, as well as rendering. Compared with the commonly utilized linear FEM, the BHEM offers higher-order solution spaces, enabling the capture of more intricate and smoother geometries while employing significantly fewer finite elements. In comparison to other high-order methods, the BHEM achieves conforming $\mathcal{C}^1$ continuity for Kirchhoff-Love (KL) shells with minimal complexity. Furthermore, by leveraging the subdivision and convex hull properties of Hermite patches, we develop an efficient algorithm for ray-patch intersections, facilitating collision handling in simulations and ray tracing in rendering. This eliminates the need for laborious remodeling of the pre-existing parametric surface as the conventional approaches do. We substantiate our claims with comprehensive experiments, which demonstrate the high accuracy and versatility of the proposed method.

翻译：本研究提出了双三次埃尔米特单元方法（BHEM），这是一种专为参数化薄壳结构的弹性动力学仿真设计的新计算框架。BHEM基于参数化四边形埃尔米特面片构建，该面片作为壳结构几何、仿真、碰撞避免及渲染的统一表示形式。与常用的线性有限元法相比，BHEM提供了更高阶的解空间，能够以显著更少的有限单元捕捉更复杂且更平滑的几何形状。与其他高阶方法相比，BHEM以最低复杂度实现了基尔霍夫-乐夫（KL）壳的共形$\mathcal{C}^1$连续性。此外，利用埃尔米特面片的细分与凸包性质，我们开发了一种高效的光线与面片相交检测算法，从而促进了仿真中的碰撞处理与渲染中的光线追踪。这消除了传统方法中对既有参数化曲面进行繁琐重建的需求。我们通过大量实验验证了该方法的高精度性与广泛适用性。