Local bilinear computation of Jacobi sets
Local bilinear computation of Jacobi sets
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DOI：
10.1007/s00371-022-02557-4
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发表时间：
2022-06
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通讯作者：
Daniel Klötzl;Tim Krake;Youjia Zhou;I. Hotz;Bei Wang;D. Weiskopf
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作者：
Daniel Klötzl;Tim Krake;Youjia Zhou;I. Hotz;Bei Wang;D. Weiskopf
我们提出了一种新的方法计算雅可比集在2D域。雅可比集是一种基于莫尔斯理论的拓扑描述符，它捕获多个标量场之间的梯度对齐，这对于多场可视化非常有用。以前的Jacobi集计算在三角剖分上使用分段线性近似，这会导致像锯齿形图案这样的离散化工件。在本文中，我们利用局部双线性方法，通过保持拓扑结构和改进几何结构，得到了Jacobi集的一个更精确的近似。因此，避免了边缘上的锯齿形图案，从而产生更平滑的雅可比集表示。我们的实验表明，与分段线性方法相比，随着分辨率的增加，收敛性更好。我们利用这一优势，一个有效的局部细分方案。最后，我们的方法进行了定性和定量评估，与以前的方法相比，不同的网格分辨率，并在一些合成和现实世界的例子。
We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.