Vector Map Constrained Path Bundling in 3D Environments

Abstract

Dense line graphs and polyline maps are challenging for interactive visualization in geographic information systems (GIS). Bundling techniques are a common approach to reduce clutter and have successfully been demonstrated for the display of complex planar graphs. Previous techniques typically employed some form of attraction or repulsion forces to bundle edges in two dimensions, and while in principle extensible to 3D they do not directly support hard intersection constraints in a 3D environment. In geographic visualization systems, e.g. such as interactive virtual globes or 3D GIS viewers, it is often necessary to take the 3D environment into account and to: (1) bundle lines and paths in 3D, (2) constrain path bundles to follow some reference network vector map, as well as (3) avoid intersections with the digital elevation model (DEM). In this paper we introduce a novel method which uses geographic vector map reference information to route, visualize and simplify path bundles along their network paths in a constrained 3D environment using adaptive B-splines. Moreover, we describe an efficient rendering architecture to flexibly display bundled paths within a 3D rendering pipeline at varying level of detail (LOD).

State of the Art in Edge and Trail Bundling Techniques

“…3.3.1.1 ) is used to bundle DTI fibers by constraining motion to follow the DTI field anisotropy. Trail bundling is also used to bundle 3D streamlines for multiscale flow visualization [YWSC12] and 3D geographical routes over a height map [TP15]. A salient difference of this use‐case as compared to most other bundling cases discussed here is that a streamline's endpoints are not fixed, as they do not represent important spatial information that needs to be preserved in the visualization.…”

“…Vehicle trajectory analysis is important in many applications such as air‐traffic [WHS90], nautical vessel [SWvdW*11, SWvdWvW11, SHVDWVW16], and roadmap [TP15] planning and control. Early on, bundling was used to simplify the depiction of large trail‐sets so as to help inferring the main vehicle routes over a country [HVW09].…”

“…3D bundling of 2000 worldwide flight trails (a), and detail (b) [LBA10a]; Bundling commuter trails along the Swiss road network [TP15] (detail top‐right).…”

“…a,b). Finally, Vector Maps [TP15] bundle commuter paths on the 3D Swiss road network. The key parts of the road network are used as a ‘skeleton’ to attract bundles.…”

Faster Edge‐Path Bundling through Graph Spanners

“…Here, a secondary data structure is used to constrain the bundling. For example, vector maps are used to compute a bundling of the trail set along paths in the secondary graph [TP15] or road networks are used to estimate optimal parameters and adapt the kernel density estimation of KDEEB [ZSJT19]. One advantage of the approach in Zeng et al [ZSJT19] is to morph [LLC*20] between a faithful representation of trails according to the road network and a visually simplified representation.…”