In this paper, we propose a novel space partitioning strategy for implicit hierarchy visualization such that the new plot not only has a tidy layout similar to the treemap, but also is flexible to data changes similar to the Voronoi treemap. To achieve this, we define a new distance function and neighborhood relationship between sites so that space will be divided by axis-aligned segments. Then a sweepline+skyline based heuristic algorithm is proposed to allocate the partitioned spaces to form an orthogonal Voronoi diagram with orthogonal rectangles. To the best of our knowledge, it is the first time to use a sweepline-based strategy for the Voronoi treemap. Moreover, we design a novel strategy to initialize the diagram status and modify the status update procedure so that the generation of our plot is more effective and efficient. We show that the proposed algorithm has an O(nlog(n)) complexity which is the same as the state-of-the-art Voronoi treemap. To this end, we show via experiments on the artificial dataset and real-world dataset the performance of our algorithm in terms of computation time, converge rate, and aspect ratio. Finally, we discuss the pros and cons of our method and make a conclusion.
Non-rectangular treemaps are also designed in the literature. Jigsaw map has nicely shaped regions and stable layout by considering Hilbert curves or H curves @cite_7 . They generate irregular shapes which are not easy to be compared with. A modification then was proposed by splitting the space into rectangles @cite_32 . To relax rectangular constraint, angular treemaps describe a divide-and-conquer method to partition the space into various shapes @cite_13 . Besides that, the treemap layout that produces irregular nested shapes by subdividing the Gosper curve @cite_28 was also proposed.
@cite_28 @cite_13 @cite_32 @cite_7
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The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map. Space-filling visualization techniques have proved their capability in visualizing large hierarchical structured data. However, most existing techniques restrict their partitioning process in vertical and horizontal direction only, which cause problem with identifying hierarchical structures. This paper presents a new space-filling method named Angular Treemaps that relax the constraint of the rectangular subdivision. The approach of Angular Treemaps utilizes divide and conquer paradigm to visualize and emphasize large hierarchical structures within a compact and limited display area with better interpretability. Angular Treemaps generate various layouts to highlight hierarchical sub-structure based on user's preferences or system recommendations. It offers flexibility to be adopted into a wider range of applications, regarding different enclosing shapes. Preliminary usability results suggest user's performance by using this technique is improved in locating and identifying categorized analysis tasks. Treemaps are a well known and powerful space-filling visualisation method for displaying hierarchical data. Many alternative treemap algorithms have been proposed, often with the aim being to optimise performance across several criteria, including spatial stability to assist users in locating and monitoring items of interest. In this paper, we demonstrate that spatial stability is not fully captured by the commonly used "distance change” (DC) metric, and we introduce a new "location drift” (LD) metric to more fully capture spatial stability. An empirical study examines the validity and usefulness of the location drift metric, showing that it explains some effects on user performance that distance change does not. Next, we introduce "Hilbert” and "Moore” treemap algorithms, which are designed to achieve high spatial stability. We assess their performance in comparison to other treemaps, showing that Hilbert and Moore treemaps perform well across all stability metrics. A recent line of treemap research has focused on layout algorithms that optimize properties such as stability, preservation of ordering information, and aspect ratio of rectangles. No ideal treemap layout algorithm has been found, and so it is natural to explore layouts that produce nonrectangular regions. This note describes a connection between space-filling visualizations and the mathematics of space-filling curves, and uses that connection to characterize a family of layout algorithms which produce nonrectangular regions but enjoy geometric continuity under changes to the data and legibility even for highly unbalanced trees.