We present a novel method to construct short cuts for parameterizations with low isometric distortion. The algorithm contains two steps: (i) detect feature points, where the distortion is usually concentrated; and (ii) construct a cut by connecting the detected feature points. Central to each step is a greedy method. After generating a redundant feature point set, a greedy filtering process is performed to identify the feature points required for low isometric distortion parameterizations. This filtering process discards the feature points that are useless for distortion reduction while still enabling us to obtain low isometric distortion. Next, we formulate the process of connecting the detected feature points as a Steiner tree problem. To find an approximate solution, we first successively and greedily produce a collection of auxiliary points. Then, a cut is constructed by connecting the feature points and auxiliary points. In the 26,299 test cases in which an exact solution to the Steiner tree problem is available, the length of the cut obtained by our method is on average 0.17% longer than optimal. Compared to state‐of‐the‐art cut construction methods, our method is one order of magnitude faster and generates shorter cuts while achieving similar isometric distortion.

中文翻译：

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参数化的贪婪切割构造

我们提出了一种新的方法来构造具有低等距失真的参数化的捷径。该算法包含两个步骤： (i) 检测特征点，其中通常失真比较集中；(ii) 通过连接检测到的特征点构造一个切口。每个步骤的核心是贪心方法。在生成冗余特征点集后，执行贪婪过滤过程以识别低等距失真参数化所需的特征点。这个过滤过程丢弃了对减少失真无用的特征点，同时仍然使我们能够获得低等距失真。接下来，我们将连接检测到的特征点的过程表述为一个 Steiner 树问题。为了找到一个近似解，我们首先连续贪婪地产生一组辅助点。然后，通过连接特征点和辅助点来构造一个切口。在提供 Steiner 树问题精确解的 26,299 个测试用例中，通过我们的方法获得的切割长度平均比最佳长度长 0.17%。与最先进的切割构造方法相比，我们的方法要快一个数量级，并生成更短的切割，同时实现类似的等距失真。