Setting the height or the radius of cones?

The Sahara as one of the largest terrestrial area devoid of cities, an issue for time-space global cartography
The Sahara desert as one of the largest terrestrial area devoid of cities, an issue for time-space global cartography (L’Hostis 2016 CC-BY)

In the testing of the model, the issue of the height  of cones came quite quickly to the fore. As, by construction according to the principle of the model, cones are entirely drawn under the surface of the earth, cones  where initially envisaged as having the height of the earth radius. Nevertheless, this choice rapidly became problematic.

The limit case is when the maximum speed equals the terrestrial speed. In this situation the principle of the model implies that the slope of cones is null. The cone turns into a disk. In this situation, if the height is fixed, the radius tends to an infinite value and this creates visual artifacts.

To deal with this issue, the way forward consists in fixing not the height of the cone but rather its radius. In consequence the next step is to set the default radius of cones. This radius should be set at the half of the longest terrestrial area devoid of cities. The Sahara desert is a candidate for this situation. On QGIS it was possible to measure 2600 kilometers between El Djefa in Algeria and Niamey in Niger. the proposed default radius of cones will then be set at 1500 kilometers.

To deal with eventual issues in the radius of cones, a new column of data is added. It may prove relevant to set a smaller value for the default radius, and to set the cities close to Sahara to 1500 kilometers radius. But this will be a next step, to be adjusted when the first images will come out.