We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to existing methods. We achieve such data coherency by calculating a Hamiltonian path that approximately minimizes an objective function that describes the similarity of data values and location coherency in a neighborhood. Our extended variant even supports multiscale data via quadtrees and octrees. Our method is useful in many areas of visualization, including multivariate or comparative visualization, ensemble visualization of 2D and 3D data on regular grids, or multiscale visual analysis of particle simulations. The effectiveness of our method is evaluated with numerical comparisons to existing techniques and through examples of ensemble and multivariate datasets.

中文翻译：

---

数据驱动的空间填充曲线

我们提出了一种用于 2D 和 3D 可视化的数据驱动空间填充曲线方法。我们的灵活曲线以一种方式遍历空间域中的数据元素，与现有方法相比，由此产生的线性化可以更好地保留空间中的特征。我们通过计算哈密顿路径来实现这种数据一致性，该路径近似最小化描述数据值相似性和邻域中位置一致性的目标函数。我们的扩展变体甚至通过四叉树和八叉树支持多尺度数据。我们的方法在许多可视化领域都很有用，包括多变量或比较可视化、规则网格上 2D 和 3D 数据的整体可视化，或粒子模拟的多尺度可视化分析。