用拓扑图融合几何与拓扑特征，实现灵活的网格分割。
Flexible Mesh Segmentation via Reeb Graph Representation of Geometrical and Topological Features
- 基于改进的拓扑骨架构建柔性黎曼图
- 通过保留关键特征简化图结构，提升分割精度
- 适合需要几何拓扑联合分析的三维建模任务
本文提出一种新的网格分割方法，通过灵活的黎曼图表示，整合几何与拓扑特征。算法分为三步：利用改进的拓扑骨架法构建黎曼图；通过消去临界点进行拓扑简化，同时保留关键特征；最后基于自适应区域生长生成连通分段，综合考虑几何与拓扑条件。该方法对n个顶点的网格具有O(n log n)的计算复杂度，兼具高效性与可扩展性。案例研究验证了其在基于形状直径函数的部件分解和基于形状指数的地形分析中的有效性，表明该方法是处理复杂网格几何分析的稳健框架，有效连接了形状的几何与拓扑特性。
原文摘要 · Abstract (English)
This paper presents a new mesh segmentation method that integrates geometrical and topological features through a flexible Reeb graph representation. The algorithm consists of three phases: construction of the Reeb graph using the improved topological skeleton approach, topological simplification of the graph by cancelling critical points while preserving essential features, and generation of contiguous segments via an adaptive region-growth process that takes geometric and topological criteria into account. Operating with a computational complexity of O(n log(n)) for a mesh of n vertices, the method demonstrates both efficiency and scalability. An evaluation through case studies, including part-based decomposition with Shape Diameter Function and terrain analysis with Shape Index, validates the effectiveness of the method in completely different applications. The results establish this approach as a robust framework for advanced geometric analysis of meshes, connecting the geometric and topological features of shapes.
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