论文标题
局部双线雅各比集的连通性降低
Reduced Connectivity for Local Bilinear Jacobi Sets
论文作者
论文摘要
我们提出了一种新的拓扑连接方法，用于对Jacobi集的局部双线性计算，该方法在保留拓扑结构和几何配置的同时改善了视觉表示。为此，利用了局部双线性方法的拓扑结构，这是由传统分段线性方法的神经复合物给出的。由于神经复合物由高维的简单组成，因此局部双线方法（以神经复合物的1骨骨骼表示）导致通过线段的交叉点使杂乱无章。因此，我们提出了一种同质的等效表示，该表示使用不同的崩溃和边缘收缩来去除此类伪影。我们的新连接方法易于实现，只有很少的开销，并且导致杂乱无章的表示。
We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological structure of the local bilinear method is utilized, which is given by the nerve complex of the traditional piecewise linear method. Since the nerve complex consists of higher-dimensional simplices, the local bilinear method (visually represented by the 1-skeleton of the nerve complex) leads to clutter via crossings of line segments. Therefore, we propose a homotopy-equivalent representation that uses different collapses and edge contractions to remove such artifacts. Our new connectivity method is easy to implement, comes with only little overhead, and results in a less cluttered representation.
