A third domain we examined is algorithm visualization. In the past, algorithm visualizations have used animation techniques and sequential layouts to show successive steps. In Section 5, we show how a spreadsheet can be used to easily construct both animations and tabular layouts of steps for 3D Delaunay triangulation. We also show how we can utilize multiple visual representations to enhance the comprehensibility of the visualization. We use this algorithm as an example of how algorithm visualization can be supported in our visualization spreadsheet.
The algorithm generates 3D random points using random number generators, and then forms tetrahedra from the points using Delaunay triangulation. Delaunay triangulation has been used in scientific and information visualization domains to generate structures around points. 2D Delaunay triangulation is an optimal triangulation and has a number of interesting properties, such as maximizing the minimum angles. However, 3D Delaunay triangulation is much more complicated than 2D, and is a more complex algorithm. Even though the problem of 3D triangulation is well studied, it is still non-intuitive for many people. So visualization techniques can help in gaining better insights into the algorithm.
Figure 3 shows the SIV spreadsheet system loaded with this data. The columns show the results of the algorithm after 5, 6, 25, and 50 steps, from left to right respectively. Row 1 shows the point set using 3D scatter-plots. Row 2 shows the same data using transparent tetrahedra after 3D Delaunay triangulation has been performed on the point sets. Row 3 represents the tetrahedra using edges between vertices. The last row aggregates several cells together to form new visualizations. The combination of geometries from several cells results in visualizations that show differences between successive steps of the algorithm.
Figure 3:
