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中文摘要：
针对目前大多数二维流形建模系统不能保证二维流形结构的问题，通过对基于网格结构的二维流形建模系统进行深入研究，提出一种新的基于顶点的表示方法，并证明其能够精确表示二维流形结构．在此基础上，确定了一组简单的有效性测试规则，并证明了这组规则能在大部分现有的网格建模数据结构中测试二维流形结构的有效性．
英文摘要：
Most existing 2-manifold modeling systems cannot guarantee manifold structures. This paper gives a thorough study on manifold modeling techniques, proposes a vertex-based representation, and proves that this representation precisely characterizes the manifold structures. Based on the theoretical results, a set of topology validating rules are given, which can be adopted to design testing algorithms for most existing 2-manifold modeling systems.
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