Using Line - Integral Convolution to Visualize Dense Vector Fields

of memory and disk space become more accessible, demands for more effective visualization methods that can analyze large-scale numerical data also continue to grow. Among many problems that are faced by visualization researchers, how to effectively visualize numerical vector field data is one of the most challenging research subjects. In 1993, Cabral and Leedom proposed an innovative approach called line-integral convolution (LIC), which can produce realistic visualizations of flow direction everywhere in a vector-field. This technique has drawn a lot of attention from researchers as well as practical users in the past several years. Generally, people are impressed by the results of using LIC to visualize vector-field data. In this article, I briefly review this new visualization technique, along with some recent extensions, in the hope that you will find it useful for your own applications. Visualizing dense vector-field data is a difficult problem. This is because the graphical icons that can naturally represent a vector tend to use up too much of the spatial resolution of the display. Suppose we were to draw a line segment representing a vector’s direction and make the length of the segment proportional to the vector magnitude. Unlike displaying a scalar quantity, in which we can just paint a color to a single pixel to illustrate its value, drawing a line segment inevitably requires more screen space. As a result, the display window quickly gets cluttered as the size of vector data increases. Another way to visualize the vector field is to specify seed locations and then compute streamlines, curves that are tangent everywhere to the flow direction in the field. This is one of the most popular visualization techniques in computational fluid dynamics. The disadvantage of using streamlines, however, is that in order not to miss any subtle features in the data, you have to know where to place those seed points. For large-scale simulations with complex geometric models, knowing for sure where the interesting features are is nontrivial. You probably will need to place a lot of streamlines, which again clutter the display, or you can probe around by trial-and-error, but you never know if you have missed anything. To solve the problems, visualization researchers have been working on “global techniques,” trying to image the flow direction everywhere in the field into a single picture. Such techniques attempt to represent the vector at every grid point by as little as one pixel display space and to pull out interesting features automatically. In this way, large data sets can be effectively visualized, and the amount of user interaction involved becomes minimal. In the following, I review the LIC algorithm and some of its extensions to show you how the technique realizes these goals.