3.4.1. Algorithm for Advanced Weather Visualization

The mentioned polygons are simple, closed, and defined by the ordered set of its vertices consecutively linked by line segments without intersections that bound a connected interior area. Polygons with self-intersections, as well as polygons with holes, were not considered since they are not suitable for the representation of areas that aircraft should not fly through.

The main goal of the intended visualization is to perform a realistic interpolation of the transformation of a polygons' set at the current time *t* into a set of forecasted polygons at the time moment *t* + Δ*t* over the time period Δ*t*. The interpolation should have small time steps of less than five seconds in order to avoid gaps between consecutive visualization pictures and to follow the update rhythm of aircraft radar data.

Since convective cells move and can appear, disappear, merge together, or split into small parts over time, it is necessary and sufficient to develop approaches for performing the following main interpolations:


The formulated task belongs to the class of 2D polygon morphing problems. This class is well studied, especially for complex shapes, because of their wide applicability in computer graphics and animation. Therefore, these solutions imply significant computational effort or are instead developed for some initial objects with properties irrelevant for the visualization of weather. A detailed overview of the related literature is out of the scope of this paper. An overview on the existing methods is given in [37]. Here, we refer to works related to polygon morphing.

Approaches for polygon morphing consist of two main steps: the mapping of polygons by some characteristic or feature points and the specification of methods of interpolation or curves. The last step is more complicated because retaining some of the characteristic features of the considered objects during interpolation is often desirable. One of the main goals in defining interpolation methods is avoiding the local self-intersection of polygon boundaries.

There are many heuristics presented in the literature. Guaranteed intersection-free polygon morphing, described in [38], relies on an analytical basis. However, the approach uses a significant number of interior points and exterior Steiner vertices that increase its complexity. The morphing of simple polygons with the same number of edges that are correspondingly parallel is explored in [39]. Usually, morphing algorithms require user assistance to relate the morphing objects. Malkova introduced intuitive polygon morphing; however, the source and destination polygons must spatially overlap [40]. Moreira dealt

with the application of 2D polygonal morphing techniques to create spatiotemporal data representations of moving objects continuously over time [41]. The movement of icebergs in the Antarctic seas was used as a case study and the data sources were sequences of satellite images capturing the position and shape of the icebergs on different dates. The authors applied a perception-based approach in [42], in which the so-called feature points of the morphing objects were determined. The main challenges were the determination of feature points and correspondences between feature points. Since this work investigated the visualization of moving gaseous objects, rotations and similarities had an insignificant role compared to the solid objects in [41].

Considering relatively small time-steps between consequent sets of convective cells compared to their movement speed and transformation, linear interpolation appears to be the best choice for the defined approximation requirements.
