Notes on the Simplification of the Morse-Smale Complex
Notes on the Simplification of the Morse-Smale Complex
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关于 Morse-Smale 复合体简化的注释
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
T. Weinkauf
中科院分区：
文献类型：
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作者：
D. Günther;Jan Reininghaus;H. Seidel;T. Weinkauf
可以明确或隐式代表摩尔斯 - 摩尔复合体。根据表示的类型，简化Morse-Sale络合物的作用不同。在显式表示中，通过在简化过程中明确重新连接临界点，直接简化了摩尔斯 - 摩尔群。另一方面，在隐式表示中，组合梯度场给出了摩尔斯 - 男性复合体。在这种情况下，简化会改变组合流，从而使莫尔斯 - 摩尔复合物的间接简化。在两种表示中，莫尔斯 - 摩尔复合物的拓扑复杂性均降低。但是，简化通常会产生不同的结果。在本章中，我们强调了引起这些差异的两种表示的属性。我们还提供了有关运行时间和内存消耗的两个方案的复杂性分析。
The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption.