The time-accurate value-scattering process (SCAP) is the bottleneck of the UFLIC (Unsteady Flow Line Integral Convolution) [60] pipeline while a large amount of Euler pathline integration is computationally expensive due to intensive temporal-spatial vector interpolation and line-segment clamping against pixels. In order to obtain a dense scattering coverage to exploit sufficient temporal-spatial coherence, UFLIC uses a conservative seeding scheme by which a seed is released from each pixel center at the first integer time step of each SCAP. Such a regular seed pattern does not take into account flow structures and particles are too dense in converging regions. Also, a pathline is always advected from scratch and is deleted when the life span expires. This simplistic use of pathlines ignores intra-SCAP and inter-SCAP correlations, which induces severe pathline redundancy. AUFLIC (Accelerated UFLIC) adopts a flow-driven seeding strategy (Figure 1) by introducing spatial flexibility (i.e., a seed may not necessarily be released exactly from a pixel center as long as the seed is within the pixel) and temporal flexibility (i.e., a seed may not necessarily be released exactly at an integer time step; instead it may be released at a fractional time shortly after the SCAP begins). Also, AUFLIC employs a fourth-order Runge-Kutta integrator with adaptive step size and error control in combination with cubic Hermite polynomial curve interpolation to achieve faster, more accurate pathline advection, and faster line convolution (due to evenly sampling the texture) than the Euler method.
The temporally-spatially flexible seeding strategy used in AUFLIC allows for a flow-aligned seed distribution by which only a few (sparsely placed) seeds need pathline integration while most seeds are placed along the pathlines advected at earlier times by other seeds upstream and therefore the known pathlines can be copied in the same SCAP and reused between SCAPs, with pathline integration substantially reduced, for fast value scattering. Pathline copying is an intra-SCAP operation by which a seed's trace in the life span is used, with only minor corrections, for those of other seeds successively released at several positions downstream along the known trace at fractional times shortly after the SCAP begins as long as they are released at the same time as the initial seed travels through their seeding positions. Each of these seeds travels through a different-length part of the same curve during the first time step of the SCAP, but they synchronously run though the same trace over the remaining time steps. Pathline reuse is an inter-SCAP operation by which the position a pathline passes through within a fractional time into the second time step of the previous SCAP is used to release a new seed at exactly the same global time, but in the first time step of the current SCAP. This seed's trace is obtained by reusing the latter part of the known pathline from the previous SCAP, appended with integration over an additional time step. Pathline copying applies whether a pathline is obtained by reuse or brute-force integration. To fulfill the flow-driven seeding strategy for a dense scattering coverage at a low computational cost and maintain a nearly constant frame rate, a dynamic seeding controller is used in AUFLIC to decide whether a pathline is advected from scratch, copied from that of another seed in the current SCAP, reused from the last SCAP, saved for the next SCAP, or finally deleted. Table 1 gives a comparison of UFLIC and AUFLIC.
Comparison of IBFV, LEA, UFAC, and AUFLIC / UFLIC in temporal-spatial coherence
Introduction to the AUFLIC paper published in IEEE Transactions on Visualization and Computer Graphics
Flow Visualization
Home Page