PolyChopper：一种多面体分割方案
PolyChopper: a Polyhedron Splitting Scheme
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中文总结 AI 辅助
介绍PolyChopper方案，用平面切割凸多面体，通过调整相交顶点控制生成元素质量，实验表明该方法稳健，能生成更优子多面体，递归应用可产生层次结构，元素渐小且保持凸性和四面体为主。
中文摘要 AI 辅助
我们引入并实现了一种名为PolyChopper的新颖方案，用于将凸多面体分割成有限个不相交的凸子多面体。该算法用平面切割多面体，平面既可以作为外部约束给定，也可由惯性张量自动确定。然后根据用户定义的质量参数调整所得的相交顶点，以控制生成元素的复杂性和质量，引入额外的“缺口楔体”、四面体和棱锥。实验结果表明，该方法稳健，能持续生成比原始多面体更简单且质量更高的子多面体。此外，递归应用该算法可生成元素逐渐变小的多面体细分层次结构，所有这些都保证保持凸性且主要为四面体。
英文摘要
We introduce and implement a novel scheme, called \textit{PolyChopper}, for splitting a convex polyhedron into a finite set of disjoint convex sub-polyhedra. The algorithm cuts the polyhedron with a plane, which can either be prescribed as an external constraint or automatically determined from the inertia tensor. The resulting intersection vertices are then adjusted to control the complexity and quality of the generated elements, introducing additional ``notch wedges'', tetrahedra and pyramids, according to a user-defined quality parameter. Experimental results demonstrate that the proposed approach is robust and consistently produces sub-polyhedra that are both simpler and of higher quality than the original polyhedron. Furthermore, recursively applying the algorithm generates a hierarchy of polyhedral subdivisions with progressively smaller elements, all guaranteed to remain convex and predominantly tetrahedral.
