IEEE Trans Vis Comput Graph. 2011 Jul;17(7):1007-19. doi: 10.1109/TVCG.2010.90. Epub 2010 Jun 17.
Interactive visualization applications benefit from simplification techniques that generate good-quality coarse meshes from high-resolution meshes that represent the domain. These meshes often contain interesting substructures, called embedded structures, and it is desirable to preserve the topology of the embedded structures during simplification, in addition to preserving the topology of the domain. This paper describes a proof that link conditions, proposed earlier, are sufficient to ensure that edge contractions preserve the topology of the embedded structures and the domain. Excluding two specific configurations, the link conditions are also shown to be necessary for topology preservation. Repeated application of edge contraction on an extended complex produces a coarser representation of the domain and the embedded structures. An extension of the quadric error metric is used to schedule edge contractions, resulting in a good-quality coarse mesh that closely approximates the input domain and the embedded structures.
交互式可视化应用程序受益于简化技术，这些技术可以从表示域的高分辨率网格生成高质量的粗网格。这些网格通常包含有趣的子结构，称为嵌入式结构，除了保留域的拓扑结构外，还希望在简化过程中保留嵌入式结构的拓扑结构。本文证明了之前提出的链接条件足以确保边缘收缩保留嵌入式结构和域的拓扑结构。除了两种特定的配置外，还证明链接条件对于拓扑保留也是必要的。在扩展的复杂对象上重复应用边缘收缩会生成域和嵌入式结构的较粗表示。使用二次误差度量的扩展来安排边缘收缩，从而生成接近输入域和嵌入式结构的高质量粗网格。
