New ideas for three dimensional structure of geographical time-space

We want to introduce new ways to draw the three dimensional structure of geographical time-space. Currently we have lines for high speed air links and cones for terrestrial transport modes, road and high-speed rail. Cities served by road only have a unique slope given by the ratio produced by comparing with the fastest speed, of long range flights.

In the current state of the code, cities served by even a unique high-speed rail link generate a cone with a different slope, given the different ratio with the fastest speed. This approach may easily be critiqued since it applies high speed rail speed to the whole area surrounding the city, id est, its cone.

For this reason we want to introduce new principles for generating the terrestrial time-space surface. High-speed lines between two cities A and B will be draw and used as the basis for a surface located between the cones A and B. In a first model the line will be drawn with two broken lines. This choice is coherent with the way cones are drawn, with broken segments for terrestrial path between cities, along the cones.

Sketch of the principle of drawing cones and edges with broken lines
Sketch of the principle of drawing cones and edges with broken lines

A variation of this model considers the high-speed line as a smooth curve instead of a broken line. This choice is coherent with the way aerial edges are currently drawn — as curved Bezier lines — a choice justified by the lack of geographical meaning of the broken segment despite a strong visual presence, as can be seen here.

Sketch of the principle of drawing cones and edges with smooth lines
Sketch of the principle of drawing cones and edges with smooth lines

While previously the terrestrial surface was an assemblage of cones, the new surface is generated from a more complex three dimensional geometry with cones and and complex shapes. Slope keeps its time-space meaning and several terrestrial speeds can be represented with a basis of cones.

We will see what the final visual result will be in hopefully a few days, thanks to Farouk. Thanks also to Jules for the drawing.


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