Mapping a triangulated surface to 2D space (or a tetrahedral mesh to 3D space) is the most fundamental problem in geometry processing.In computational physics, untangling plays an important role in mesh generation: it takes a mesh as an input, and moves the vertices to get rid of foldovers.In fact, mesh untangling can be considered as a special case of mapping where the geometry of the object is to be defined in the map space and the geometric domain is not explicit, supposing that each element is regular.In this paper, we propose a mapping method inspired by the untangling problem and compare its performance to the state of the art.The main advantage of our method is that the untangling aims at producing locally injective maps, which is the major challenge of mapping.In practice, our method produces locally injective maps in very difficult settings, and with less distortion than the previous work, both in 2D and 3D. We demonstrate it on a large reference database as well as on more difficult stress tests.For a better reproducibility, we publish the code in Python for a basic evaluation, and in C++ for more advanced applications.

中文翻译：

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50行代码的无折叠地图

我们的方法可以在非常困难的环境中生成局部内射图，并且在2D和3D中都比以前的工作失真小。我们在大型参考数据库以及更困难的压力测试中进行了演示。为了获得更好的可重复性，我们将代码发布在Python中进行基本评估，并在C ++中发布用于更高级的应用程序。