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.
翻译:三角表面映射为 2D 空间( 或四面网格到 3D 空间) 是几何处理中最根本的问题。 在计算物理学中, 解剖在网状一代中起着重要作用: 将网状作为输入, 并移动脊椎以摆脱折叠。 事实上, 网状解剖可以被视为一个特殊的映射案例, 地图空间中要界定对象的几何, 而几何域并不明确, 假设每个元素都是正常的。 在本文件中, 我们提议了一个受未切开的问题启发的映射方法, 并将其性能与艺术状态进行比较。 我们方法的主要优势是, 将本地喷射图的不切切图作为输入, 这是绘图的主要挑战 。 实际上, 我们的方法在非常困难的环境下, 并且与先前的工作相比, 在 2D 和 3D 中, 生成了本地的导射图, 并且不那么扭曲 。 我们用一个大型的参考数据库来展示它, 以及更困难的压力测试。 为了更好的重新解读, 我们用一个更先进的代码在 Cyst 应用程序中, 我们出版一个更高级的代码 。