Visualizing 3D Flow

49 A n elegant and versatile technique, line integral convolution (LIC) 1,2 represents directional information via patterns of correlation in a texture. Although most commonly used to depict 2D flow, or flow over a surface in 3D, LIC methods can also portray 3D flow through a volume. 1,3 However, the popularity of LIC as a device for illustrating 3D flow has historically been limited by the computational expense of generating and rendering such a 3D texture and by the difficulties inherent in clearly and effectively conveying the directional information embodied in the resulting volumetric output textures. Here we discuss some factors that may underlie some of the perceptual difficulties encountered with dense 3D displays and describe strategies for more effectively visualizing 3D flow with volume LIC. Specifically, we suggest techniques for s selectively emphasizing critical regions of interest in a flow; s facilitating the accurate perception of the 3D depth and orientation of overlapping streamlines; s efficiently incorporating an indication of orientation into a flow representation; and s conveying additional information about related scalar quantities such as temperature or vorticity over a flow via subtle, continuous line width and color variations. Applying LIC to a solid noise texture using a 3D vector field results in a solid 3D output texture—as shown in Figure 1—in which the values of the voxels are everywhere locally correlated in the direction of the 3D flow. The mechanics of the computation are straightforward, but how can you effectively visualize such data? It can be difficult to mentally reconstruct an accurate perception of the 3D flow from any series of 2D slices viewed sequentially. Defining an appropriate set of surfaces across which the 3D flow information can meaningfully be shown can prove problematic and imaging the data as a set of partial opacity values via direct-volume rendering sacrifices the inner details of the 3D texture. We believe that if appropriately defined and rendered, a 3D LIC texture has considerable potential to provide a full, immediate, and intuitive impression of a 3D flow's global and local characteristics. The challenge is to determine how to achieve such a representation. Shen et al. 3 suggested complementing a volume-rendered LIC texture with simulated dye advection. Here we look at some other options. In certain cases, you can use a scalar function such as temperature or vorticity to identify, a priori, specific critical regions in a flow volume within which (or …