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首页> 外文期刊>Journal of Zhejiang University Science: An international applied physics & engineering journal >Intersections of two offset parametric surfaces based on topology analysis
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Intersections of two offset parametric surfaces based on topology analysis

机译：基于拓扑分析的两个偏移参数曲面的相交

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Conventional methods for solving intersections between two offset parametric surfaces often include iteratively using computationally expensive SSI (surface/surface intersections) algorithm. In addition, these methods ignore the relations between the intersection curves of parametric surfaces with different offset distances. The algorithm presented in this paper, makes full use of the topological relations between different intersection loops and calculates intersection loops with the help of previously calculated intersection loops. It first pre-processes two parametric surfaces to obtain the characteristic points, called topology transition points (TTPs), which can help in the subsequent finding of the topologies of the intersection curves. Then these points are categorized into several distinct groups, and we can determine the calculation strategy for searching initial points by analyzing the properties of these TTPs on the surfaces. Hence, all intersection curves can be marched from initial points by the tracing algorithm. The proposed algorithm could calculate intersection curves robustly and effectively, and has been tested to be capable of overcoming the degenerate conditions such as loop and singularities leaking that occur frequently in conventional algorithms.
机译：解决两个偏移参数曲面之间的相交的常规方法通常包括迭代地使用计算上昂贵的SSI（曲面/曲面相交）算法。此外，这些方法忽略了具有不同偏移距离的参数曲面的相交曲线之间的关系。本文提出的算法充分利用了不同相交环之间的拓扑关系，并借助先前计算出的相交环来计算相交环。它首先对两个参数曲面进行预处理，以获得称为拓扑过渡点（TTP）的特征点，这可以帮助后续找到相交曲线的拓扑。然后将这些点分为几个不同的组，我们可以通过分析表面上这些TTP的属性来确定搜索初始点的计算策略。因此，可以通过跟踪算法从初始点开始行进所有交点曲线。所提出的算法可以鲁棒而有效地计算出相交曲线，并且已经过测试，能够克服传统算法中经常发生的退化条件，例如回路和奇异性泄漏。

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