# An Animated Visualization Method for Large-Scale Unstructured Unsteady Flow
## 2 Related Work
### Unsteady Data Compression  
Memory optimization is primarily focused on the spatial consistency within a single time step and the temporal consistency between continuous time steps in order to compress data for an unsteady flow field with temporal and spatial dimensions. [PERSON] et al. [7] designed a time-space partitioning (TSP) tree that divides the spatial domain into an octree as the primary structure, then divides the temporal domain into a binary time tree as the secondary structure and uses the data in the adjacent spatiotemporal domain to represent the current data based on the error tolerance. [PERSON] et al. [8] proposed a space-partitioning time (spt) tree, which first divides the temporal domain into a fully balanced binary time tree as a primary structure and then divides the spatial domain into a standard complete octree, obtaining a higher data reuse rate because unsteady data exhibits a stronger correlation in time. [PERSON] et al. [9] used temporal consistency to prune tree nodes by storing each time step of data in an octree form separately and then comparing the similarity of adjacent time step data for pruning. The kind of method that separates the temporal and spatial dimensions and uses differential coding and octree to compress unsteady data by using temporal and spatial correlation, respectively, can reorganize the original data into a multi-resolution hierarchy, which has a faster encoding and decoding speed and higher compression ratio. The accuracy loss caused by compression is small [10], so it is widely used in unsteady data visualization. Generalizing existing research to unstructured unsteady flow fields is challenging. Most existing research relies on structured unsteady data. Thus, the regular hexahedral mesh can use octree to represent the mesh distribution in eight directions accurately [11]. Moreover, it can efficiently calculate differential coding under a certain premise. The premise is that the flow field meshes do not change with time; only the flow field variables change with time. However, unstructured unsteady flow fields are different. They have some challenges that make it difficult to explicitly represent hierarchical structures. They have an irregular mesh distribution and multi-density characteristics. The meshes and variables of the flow field will change over time. If structured meshes are used to represent unstructured flow fields and then spatiotemporal domain partitioning is performed, there are issues such as mesh partitioning density affecting data accuracy, difficulty in fitting complex unstructured mesh structures, and an inability to correspond vertex data accurately. Therefore, compressing unstructured meshes into structured meshes is challenging. It is possible to attempt to design adaptive octrees using leaf nodes of different densities to represent an unstructured triangular mesh with an irregular mesh density distribution. But, it is challenging to design compression algorithms that correspond to mesh spatial positions in different time steps. In addition to the aforementioned compression techniques that separate the temporal and spatial dimensions, there are also compression techniques that regard the entire unsteady data set as four-dimensional data and extend the three-dimensional volume data compression techniques to four-dimensional space compression. [PERSON] et al. [12], for instance, proposed a high-dimensional data compression method that combines volume texture compression (VTC) and the Lorenzo high-dimensional parallelogram predictor, which uses the temporal and spatial correlation of time-varying data to predict the current voxel value from the decompressed adjacent voxel data values. [PERSON] et al. [13] proposed a partitioning method based on the fourth root of 2 to divide unsteady data into fine-grained hierarchical data, sampling and approximating each detail level with biquadratic B-spline wavelets. [PERSON] et al.