2D Vector field approximation using linear neighborhoods
2D Vector field approximation using linear neighborhoods
复制标题
使用线性邻域的 2D 矢量场近似
DOI：
10.1007/s00371-015-1140-9
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Hlawitschka
中科院分区：
文献类型：
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作者：
Stefan Koch;Jens Kasten;Alexander Wiebel;G. Scheuermann;M. Hlawitschka
我们提出了一种二维向量场的向量场近似方法，该方法保留了向量场的拓扑结构，并显著减少了内存占用。这种近似基于一种分割。每个分割区域内的流由一个仿射线性函数近似。该实现由四个目标驱动：（1）近似保留原始拓扑结构；（2）在所有区域中，最大近似误差低于用户定义的阈值；（3）区域数量尽可能少；（4）每个点具有最小近似误差。生成最优解在计算上是不可行的。我们讨论了这个问题，并提供了一种贪心策略，以有效地计算一种考虑这四个目标的合理分割。最后，我们使用区域仿射线性近似来为向量场计算一个简化的网格。
We present a vector field approximation for two-dimensional vector fields that preserves their topology and significantly reduces the memory footprint. This approximation is based on a segmentation. The flow within each segmentation region is approximated by an affine linear function. The implementation is driven by four aims: (1) the approximation preserves the original topology; (2) the maximal approximation error is below a user-defined threshold in all regions; (3) the number of regions is as small as possible; and (4) each point has the minimal approximation error. The generation of an optimal solution is computationally infeasible. We discuss this problem and provide a greedy strategy to efficiently compute a sensible segmentation that considers the four aims. Finally, we use the region-wise affine linear approximation to compute a simplified grid for the vector field.