A Flow-guided Streamline Seeding Strategy Vivek Verma , David Kao , and Alex Pang Computer Science Department, UCSC NASA Ames Research Center vivek@cse.ucsc.edu, davidkao@nas.nasa.gov, pang@cse.ucsc.edu www.cse.ucsc.edu/research/avis/seed.html Abstract This paper presents a seed placement strategy for streamlines based on flow features in the dataset. The primary goal of our seeding strategy is to capture flow patterns in the vicinity of critical points in the flow field, even as the density of streamlines is reduced. Sec- ondary goals are to place streamlines such that there is sufficient coverage in non-critical regions, and to vary the streamline place- ments and lengths so that the overall presentation is aesthetically pleasing (avoid clustering of streamlines, avoid sharp discontinu- ities across several streamlines, etc.). The procedure is straight for- ward and non-iterative. First, critical points are identified. Next, the flow field is segmented into regions, each containing a single critical point. The critical point in each region is then seeded with a template depending on the type of critical point. Finally, additional seed points are randomly distributed around the field using a Pois- son disk distribution to minimize closely spaced seed points. The main advantage of this approach is that it does not miss the features around critical points. Since the strategy is not image-guided, and hence not view dependent, significant savings are possible when examining flow fields from different viewpoints, especially for 3D flow fields. Key Words and Phrases: seed placement, streamline, critical point, Voronoi diagram, Poisson disk distribution. 1 INTRODUCTION There are a number of methods for streamline placement that mostly address the aesthetic aspects of a flow visualization using streamlines. These methods [10, 16] describe how the streamlines should be placed in a flow field so that the visualization does not appear to be cluttered and there are no artifacts introduced in the visualization process that might lead to a misinterpretation of the flow field. In our work we address an important issue that has been largely neglected by these methods. Namely, whether the stream- lines placed by these methods result in a visualization that captures all the important features (e.g. critical points) of the flow field. Our streamline seeding strategy guarantees that important features like critical points are not missed. If the streamlines are not seeded ap- propriately (e.g. using regular or random seeding), or using image- guided streamline placement alone, important details of the flow can be missed. This problem is illustrated in Figure 1. We can see that without proper seed placement, some details of the flow can be missed by the streamline visualization. The saddle critical point is not sufficiently captured by the streamlines in Figure 1a and Figure 1b. Streamlines generated using our method adequately highlights the critical points as shown in Figure 1c. There are some important goals to consider in order to generate an effective streamline visualization. In particular, a good seeding strategy should have the following characteristics: Coverage: The streamlines should not miss any interesting re- gions in the vector field. The interesting regions are those that we would like to study in the vector field, e.g. critical points, separation, and re-attachment lines. In addition, streamlines should cover the entire region of the field. Hence, even if the field is more or less uniform in a region, some streamlines should indicate the uniform nature of the flow in these regions. This goal is easier to achieve than other goals because one can always generate a lot of streamlines such that nothing im- portant is missed. However, simply populating the field with more streamlines is not acceptable because some areas in the flow field, such as convergent regions, will force streamlines to cluster together, making it difficult to distinguish among individual streamlines. More importantly, it defeats the char- acteristic of uniformity as described next. Uniformity: The streamlines should be more or less uniformly distributed over the field. This is a more challenging goal to achieve because while we can control where to place the seeds, we do not know how the resulting streamlines will be- have. Uniformity is directly related to the density of stream- lines crossing a unit area of the flow field. Hence, density of streamlines is an important parameter. Continuity: It is desirable from the point of view of aesthetics that the streamlines show continuity in the flow. Hence, one would prefer fewer long streamlines over many short stream- lines. The latter tend to give the impression of “choppiness” while the former tend to give an impression of smooth contin- uous flow. In general, given an arbitrary flow field, the longer the streamlines, the higher the likelihood that they will tend to crowd together in some areas and disperse in other areas, thereby making it difficult to meet both the uniformity and continuity criteria simultaneously. Therefore, this parameter needs to be balanced against the uniformity criterion. Since most flow fields are defined over a grid, a popular seeding strategy is to seed at the grid points so that no important features are missed. This is usually an overkill and requires that more stream- lines be traced than is necessary to capture all the desired details of the flow. Furthermore, the streamlines tend to clutter in ways that are difficult to predict. Even if the grid is sub-sampled to reduce the density of streamlines, cluttering is still difficult to avoid. Finally, regular seeding may also produce visualization artifacts that are not present in the flow field. Figure 2 shows streamlines with regu- lar seed placement for two datasets. These images show that the streamlines placed on a regular grid can generate artifacts because the underlying regular grid can be perceived in the visualization (top image in Figure 2) and also create clutter if the streamlines are too long (bottom image in Figure 2). Cluttering is of course dependent on the flow field. Blindly seed- ing on a regular grid results in a streamline visualization where the individual streamlines can be difficult to distinguish in important regions (e.g. regions where a critical point is present). If one does not seed all the grid locations and seed only every other grid point