In the field of physically based simulation, high quality of the simulation model is crucial for the correctness of the simulation results and the performance of the simulation algorithm. When working with spline or subdivision models in the context of isogeometric analysis, the quality of the parameterization has to be considered in addition to the geometric quality of the control mesh. Following Cohen et al.’s concept of model quality in addition to mesh quality, we present a parameterization quality metric tailored for Catmull–Clark (CC) solids. It measures the quality of the limit volume based on a quality measure for conformal mappings, revealing local distortions and singularities. We present topological operations that resolve these singularities by splitting certain types of boundary cells that typically occur in interactively designed CC-solid models. The improved models provide higher parameterization quality that positively affects the simulation results without additional computational costs for the solver.

中文翻译：

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用于等几何分析的 Catmull-Clark 固体参数化质量的分析和改进

在基于物理的仿真领域，仿真模型的高质量对于仿真结果的正确性和仿真算法的性能至关重要。在等几何分析的上下文中使用样条或细分模型时，除了控制网格的几何质量外，还必须考虑参数化的质量。遵循 Cohen 等人关于模型质量和网格质量的概念，我们提出了一个为 Catmull-Clark (CC) 实体量身定制的参数化质量度量。它基于保形映射的质量度量来测量极限体积的质量，揭示局部失真和奇异性。我们提出了通过拆分某些类型的边界单元来解决这些奇点的拓扑操作，这些边界单元通常出现在交互式设计的 CC 实体模型中。改进后的模型提供了更高的参数化质量，从而对仿真结果产生积极影响，而无需为求解器增加额外的计算成本。