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.

Sketch of the model

Sketch of the time-space model with a conic time space surface limited by the shoreline of an island
Sketch of the time-space model with a conic time space surface limited by the shoreline of an island (L’Hostis 2016 CC-BY)

This is how it will look like when the model will be complete. Time-space is represented by cones. As explained here, the slope of the cone allows to produce longer itineraries proportionally to the maximum available speed on the space considered.

Then two issues must be resolved, one theoretical, and the other more linked to graphic and cartographic choices. Firstly this is a terrestrial time-space, and the surface should not extend in the maritime domain, where different transport conditions occur. Secondly, these representations have a major issue to overcome: the readability of the representation in reference to the conventions of classical maps. This second arguments implies to render shorelines and continents shapes in order to make the representation more easy to read.

For these two reasons the basic cone structure will be cut along shorelines, as in this example of an island carrying a city. It remain to be decided, judging again by the criterion of legibility, if the final structure will be a volume or a surface.

Shriveling untill resembling a chestnut

Concorde time shriveled world
Shriveling time-space relief representation of the world at the time of Concorde 1977-2003 CC-BY A L’Hostis

“And yet it moves”, said Galileo. “And yet this is the earth as we experience it” could we now say, looking at this image.

Produced by a JavaScript code based on the library three.js, with decisive help from Farouk Abdou, this is the first accurately parametrized representation of the global time space, at the time of Concorde (1977-2003), when the maximum available transport speed, that indicates the standard for maximum speed, was 1500 km/h. The principle of construction of the image is detailed here.

This has been, so far, the most intense shriveling movement in transport history, when the maximum available speed raised from 700 km/h with jets to the supersonic speed of Concorde.

Considering, in a simplified model, terrestrial speed of 100 km/h, say on a motorway or by train, the slope of cones takes this geometry. During this Concorde period, terrestrial speed was 15 times slower than the maximum available  speed.

This image is very close to the idea of the chestnut that I announced in 2007. High quality image download link.

The shriveling map construction principle

Unlike all previous time-space relief representations (1997, 2009) where the surface is based on the edges of a graph,  in the representations developed in 2016, we introduce conic shapes to represent time-space. The cone is the basic structure of this representation. Cones are characterized by a slope that follows the ratio between the speed of basic terrestrial networks, i.e. the road system, and the maximum available speed, which is attained, on the period we consider, through the air transport system.

Cones for time-space representation
Cones and edges in three dimensions as a basic structure for time-space representation CC-BY L’Hostis

On the figure we have two cities joined by a fast non-stop transport system, and also by a slower terrestrial transport mode. The fast transport link is represented through a red straight line, while the cones represent the surface on which slower terrestrial transport mode are drawn.  Assuming that travel speed are similar in all the geographic space considered, the slope of the cones centered on the two cities is a coherent representation of time-space. The two cones intersect midway between the two cities. The slope of the cones implies that the length of  the straight red line, and of the line drawn on the cone and joining the two cities, are proportional to the respective transport time. This forms a time space representation with different transport speed, and a time-space scale can be added, as in the USA map (p. 8).


The first image of a shriveling world

Shriveled world unparametrized
The first unparametrized image of the shriveled world. CC-BY A L’Hostis 2016

Using the library Cesium, and with great help from Thomas Leysens and Farouk Abdou, this is the first image (in higher quality here) out of this new project, producing a representation of global time space.

Very excited when I first saw it on my computer screen. This is the first time this image, which I had in mind for years, finally materializes.

Unfortunately it has proven very difficult, for me at least, to control cones geometry. In addition in Cesium it is not possible to draw geometries under the surface of the globe. the problem is that, conceptually, the time-space relief map model, everything occurs under the surface.

An exchange with Cesium developers has indicated an alternative choice: the library three.js, which has less limitations for our purpose.

A shriveling world

Time space relief cartography was invented in 1993 to map the time-space contraction assuming the coexistence of fast and slow transport modes. Initially applied locally to terrestrial modes (1993 p. 41), the principle has been applied to urban spaces (1997 p. 209 and 235) continental scales (1994 p. 253) and to the air mode (2009). The next major step, an ongoing work, is to create a cartographic representation of the earth, the global time-space.

The first time-space relief cartography, analog photography of cathodic screen

In 1994 in the CESA, spatial planning center of Tours University, the first time-space cartography took the form of an analog photo of a cathodic screen of European time-space, as shown on the image. The image was produced by Alain L’Hostis, by means of the computer program MapNod, from the indications of Philippe Mathis.

Time-space relief cartographic representation of Europe
The first time-space relief cartography, analog photo of cathodic screen, Europe CC-BY A L’Hostis

At that time the model is not finished as illustrated by the incomplete bottom of facets. A triangle is missing but all the networks are visible, since they form the structure on which the relief is drawn.  Relief comes as a surface along the deformed road network. Three terrestrial transport modes are represented here: classic road, motorway (mode 6) and  high-speed rail (mode 3).

By lack of available color printer in the CESA laboratory, analog photo of computer screen was one of the few possible options to realize this cartography. Later we used print-screen software to produce bitmap images, and even later developed the software MapNod to produce direct vectorial images in the WMF format.