UFLIC (Unsteady Flow Line Integral Convolution) [60] is an object-space texture synthesis technique designed to visualize unsteady flow fields. The two important components, the time-accurate value scattering scheme and the successive texture feed-forward strategy, are based on the observation that particles leave their footprints, i.e., deposit their properties (e.g., texture values) at downstream positions, as the flow runs over time. At each time step a scattering process (SCAP, Figure 1) occurs for which a seed is released, i.e., discharged, from each pixel as a contributor to scatter the texture value to the downstream pixels along the newly advected pathline in its life span that usually ranges through several time steps. On the other hand, as a receiver, each pixel keeps several stamped buckets in a ring buffer to accumulate deposited values. A frame is obtained by convolving the values that each pixel has received and stored in the bucket stamped with the frame index, creating spatial coherence in the output image. To enhance temporal coherence, the resulting texture is high-pass filtered with noise jittering and then fed forward as the input texture to the next SCAP. Figure 2 shows the UFLIC pipeline.
(© Zhanping Liu)
UFLIC possesses the advantage of conveying very high temporal-spatial coherence by scattering fed-forward texture values. Value scattering along a long pathline over several time steps not only correlates a considerable number of intra-frame pixels to establish strong spatial coherence, but also correlates sufficient inter-frame pixels to build tight temporal coherence. Texture feed-forward that takes an output frame, after noise-jittered high-pass filtering, as the input texture for the next frame constructs an even closer correlation between the two consecutive frames to enhance temporal coherence. Flow directions are clearly depicted in individual images for instantaneous flow investigation and the animation is also quite smooth. The inconsistency between temporal and spatial patterns in IBFV, LEA, and UFAC is successfully resolved by scattering fed-forward texture values in UFLIC. In addition, UFLIC can be easily extended to time-varying 3D flows. The low performance of UFLIC is primarily due to intensive pathline computation that typically needs over 100 steps of integration for each pathline. In fact, there is a huge amount of redundancy between the SCAPs of different seed particles in terms of pathline integration. As shown in Figure 3, different particles may leave their footprints or scatter their property values to a large number of common downstream pixels. Thus there is a significant potential to accelerate UFLIC by exploiting the pathline redundancy. In fact, we may consider releasing a particle simply at point P instead of at exactly the pixel center B such that the red pathline can be reused to avoid the from-scratch integration of the green pathline. This strategy indicates that a particle may be released only at an integer time step but unnecessarily at a pixel center. That is how our AUFLIC version 1.0 works. We may adopt an even more ambitious mechanism by which a particle may be released unnecessarily at an integer time step and unnecessarily at a pixel center. That is how our AUFLIC version 2.0 works. It is worth mentioning that version 2.0 differs from version 1.0 far more than in the seeding flexibility aspect. Here is a table that compares UFLIC and AUFLIC 2.0 to reveal why the latter is an order-of-magnitude faster than the former, compared to AUFLIC 1.0 that achieves 2X speedup over UFLIC.
Figure 3. A huge amount of redundancy between the SCAPs of different seed particles in terms of pathline integration (© Zhanping Liu).
Flow Visualization
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