We present a novel algorithm for simplifying the topology of a 3D shape, which is characterized by the number of connected components, handles, and cavities. Existing methods either limit their modifications to be only cutting or only filling, or take a heuristic approach to decide where to cut or fill. We consider the problem of finding a globally optimal set of cuts and fills that achieve the simplest topology while minimizing geometric changes. We show that the problem can be formulated as graph labelling, and we solve it by a transformation to the Node-Weighted Steiner Tree problem. When tested on examples with varying levels of topological complexity, the algorithm shows notable improvement over existing simplification methods in both topological simplicity and geometric distortions.

中文翻译：

---

切割或填充

我们提出了一种用于简化 3D 形状拓扑的新算法，其特点是连接组件、手柄和空腔的数量。现有方法要么将其修改限制为仅切割或仅填充，要么采用启发式方法来决定切割或填充的位置。我们考虑找到一组全局最优的切割和填充的问题，以实现最简单的拓扑结构，同时最小化几何变化。我们证明了这个问题可以表述为图标注，我们通过转换到节点加权施泰纳树问题来解决它。在对具有不同拓扑复杂度级别的示例进行测试时，该算法在拓扑简单性和几何失真方面都比现有的简化方法有显着改进。