We introduce a novel paradigm that simplifies the visualization and analysis of data that have a spatially/temporally varying frame of reference. The primary application driver is tokamak fusion plasma, where science variables (e.g., density and temperature) are interpolated in a complex magnetic field-line-following coordinate system. We also see a similar challenge in rotational fluid mechanics, cosmology, and Lagrangian ocean analysis; such physics implies a deforming spacetime and induces high complexity in volume rendering, isosurfacing, and feature tracking, among various visualization tasks. Without loss of generality, this paper proposes an algorithm to build a simplicial complex -- a tetrahedral mesh, for the deforming 3D spacetime derived from two 2D triangular meshes representing consecutive timesteps. Without introducing new nodes, the resulting mesh fills the gap between 2D meshes with tetrahedral cells while satisfying given constraints on how nodes connect between the two input meshes. In the algorithm we first divide the spacetime into smaller partitions to reduce complexity based on the input geometries and constraints. We then independently search for a feasible tessellation of each partition taking nonconvexity into consideration. We demonstrate multiple use cases for a simplified visualization analysis scheme with a synthetic case and fusion plasma applications.

翻译：我们引入了一种新范式，用于简化具有时空变化参考系数据的可视化与分析。其主要应用驱动是托卡马克聚变等离子体，其中科学变量（如密度和温度）需在复杂磁力线跟随坐标系中进行插值。我们在旋转流体力学、宇宙学和拉格朗日海洋分析中也观察到类似挑战；此类物理过程隐含变形时空，并导致体渲染、等值面提取和特征追踪等多种可视化任务的高度复杂性。在不失一般性的前提下，本文提出一种算法，用于构建基于连续两个时间步的二维三角形网格导出的三维变形时空的单形复形——四面体网格。该算法无需引入新节点，即可通过四面体单元填充二维网格间的间隙，同时满足关于两个输入网格节点连接方式的给定约束。在算法中，我们首先根据输入几何形状和约束将时空划分为更小的子区域以降低复杂度；随后独立搜索每个子区域的可行剖分方案，并考虑非凸性。我们通过合成案例和聚变等离子体应用，展示了简化可视化分析方案的多个用例。