Abstract

Geometrical and topological inconsistencies, such as self-intersections and non-manifold elements, are common in triangular meshes, causing various problems across all stages of geometry processing. In this paper, we propose a method to resolve these inconsistencies using a graph-based approach. We first convert geometrical inconsistencies into topological inconsistencies and construct a topology graph. We then define local pairing operations on the topology graph, which is guaranteed not to introduce new inconsistencies. The final output of our method is an oriented manifold with all geometrical and topological inconsistencies fixed. Validated against a large data set, our method overcomes chronic problems in the relevant literature. First, our method preserves the original geometry and it does not introduce a negative volume or false new data, as we do not impose any heuristic assumption (e.g. watertight mesh). Moreover, our method does not introduce new geometric inconsistencies, guaranteeing inconsistency-free outcome.

中文翻译：

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使用拓扑图修复网格

摘要

几何和拓扑上的不一致性，例如自相交和非流形元素，在三角形网格中很常见，从而在几何处理的所有阶段均引起各种问题。在本文中，我们提出了一种使用基于图的方法来解决这些不一致的方法。我们首先将几何不一致性转换为拓扑不一致性，然后构建拓扑图。然后，我们在拓扑图上定义本地配对操作，以确保不会引入新的不一致之处。我们方法的最终输出是定向的流形，其中所有几何和拓扑上的不一致性都得到了修复。经过大量数据验证，我们的方法克服了相关文献中的长期问题。首先，我们的方法保留了原始几何图形，并且不会引入负数或错误的新数据，因为我们不施加任何启发式假设（例如，水密网格）。而且，我们的方法不会引入新的几何不一致，从而保证了无不一致的结果。