Last month, a TV program "Chico Will Scold You" of Japan public broadcasting picked up the Tokyo subway. The TV show introduced the 3 D model of Tokyo subway, "Tokyo Arteria" which created by Takatsugu KURIYAMA.

I was influenced by the beauty, so I tried to make something similar with Mathematica. Because I create it using Mathematica's Tube function, I named it "Tokyo Tube".

There are 13 subways in Tokyo. I gathered the information of latitude, longitude and depth (from the ground) of all stations (287 stations) from web and book.

I will explain on the Hanzomon line as an example. The figure on the left shows connecting stations by the shortest straight line. However, the actual route is a more complicated. The figure on the right is the result of Google Map route search.

The TV program explained why Tokyo's subway is so complicated. The answer is there is the law that if you buy land, you will have the right of both the ground and the underground. So it is necessary to pay the land fee to all of them to get through a subway. In order to avoid this, a subway runs under the roads owned by the state or municipality because their underground can be used free of charge for public interest purposes. In addition, the roads in Tokyo are not straight because the roads are made by filling roads and waterways that were made in a radial shape based on the Edo Castle during the Edo period.

• From the result of Google Map route search, I search the route position using PixelValuePositions function.

• I sort the points by y - axis, latitude. So the first point is the starting station, the Shibuya Station and the last point is the terminal station, Oshiage Station. However, just connecting the sorted points does not follow the route (left figure). So, I use FindShortestTour function to rearrange according to the route, and select about 100 points from them for the Graphics3D (right figure).

  p2 = Sort[p, #1[[2]] < #2[[2]] &]; 
  s = FindShortestTour[p2, 1, Length[p2]];
  p3 = Append[
     Take [p2[[Last[s]]], {1, m = Length@Last[s], Round[m/100]}], 
     p2[[-1]]];
  {ListLinePlot[p2], ListLinePlot[p3]}
  

These points are converted into 3 D display based on the information of latitude, longitude and depth of all stations above. The actual map obtained by GeoGraphics function is pasted on the top surface.

The following is the result of carrying out this work for 13 lines.

The figure below shows the Ginza Line, the oldest in business, and the Oedo Line, the newest. The subway created later is deeper. And the Roppongi Station on the Oedo Line is at the deepest position 42.3 meters underground.

In addition, the Fukutoshin Line, which is the most recently full-opened, was created between the Marunouchi Line and the Shinjuku Line. The distance between the lines is about 11 cm at the shortest distance.

Now, the law that it can be used free of charge at a place deeper than 40 meters if it is the public interest purpose was made. The Linear Chuo Shinkansen, which digs underground straight in the urban area, will aim to open in 2027.

I have attached a notebook of Graphics3D "Tokyo Tube", so please rotate it.

Attachments:

Tokyo tube .nb