Interactive 3D Force‐Directed Edge Bundling

Abstract

Figure 1: Node-link diagram of an almost fully connected, bidirectional graph, originating from a NEST simulation based on a macaque's brain [GD07]. These images depict 32 vertices each of which represents a brain region. The edges are the regions' interconnectivity. Left: original graph; Right: the same graph after edge bundling; the edges are directed from purple to yellow. AbstractInteractive analysis of 3D relational data is challenging. A common way of representing such data are node-link diagrams as they support analysts in achieving a mental model of the data. However, naïve 3D depictions of complex graphs tend to be visually cluttered, even more than in a 2D layout. This makes graph exploration and data analysis less efficient. This problem can be addressed by edge bundling. We introduce a 3D cluster-based edge bundling algorithm that is inspired by the force-directed edge bundling (FDEB) algorithm [HvW09b] and fulfills the requirements to be embedded in an interactive framework for spatial data analysis. It is parallelized and scales with the size of the graph regarding the runtime. Furthermore, it maintains the edge's model and thus supports rendering the graph in different structural styles. We demonstrate this with a graph originating from a simulation of the function of a macaque brain.

State of the Art in Edge and Trail Bundling Techniques

“…The method produces convincing results, but is relatively slow, due to the high complexity of 3D kernel density estimation. A similar method is proposed in [ZWHK16]. Here, FDEB is used instead of KDEEB for bundling, and bundling speed is increased by adding a similar edge pre‐clustering step, thereby reducing the number of pairs ( p i , p j ) on which the compatibility κ needs to be computed (Eqn.…”

“…1 and related text). In turn, this distance can be computed as the sum of distances of the closest endpoints of d i and d j [GHNS11]; or the distance between the midpoints of d i and d j (see FDEB [HVW09] and its refinements [NEH12, NHE11, BSL*14, ZWHK16], and WR [LBA10b]). However simple, such similarities cannot be used for trail bundling, as trails are usualy not straight lines.…”

MLSEB: Edge Bundling Using Moving Least Squares Approximation

“…Energy-based minimization methods have been also used in many studies. Examples include ink-minimization methods [8,9] and force-directed methods [12,31,38,44,45]. Most of these methods used compatibility criteria to measure the similarity of different edges based on spatial information (i.e., length, position, angle, and visibility), and then moved the similar edges with ink-minimization or force-directed strategies.…”

An Information-Theoretic Framework for Evaluating Edge Bundling Visualization

“…Holten et al [ 33 ] further developed the force model in general graphs, namely, force-directed edge bundling (FDEB). A set of methods and applications [ 34 , 35 , 36 ] follow a similar idea. Some methods [ 37 , 38 , 39 , 40 ] use geometric control meshes to guide bundling process.…”