5 ms·

This. I was hoping for some weird pictures of distorted maps.

by qznc 9y ago

microcolonel 9y ago
For what it's worth, I think it would be computationally quite hard. You would have to pick a set of points and maybe isomap them from three dimensions (x, y, and time) to two, then find a visually acceptable cage transformation using those points as anchors. You'd have to do this for each query.
- ctdonath 9y ago
  Alternative would be to keep the standard geographic map, but have clear points on all possible destinations X minutes away - ideally with a slider, watching the "X minutes" points slide around. Actually pretty easy, given each road segment knowing expected speed, and "X+1" just extending into untraveled areas.
  - jamessb 9y ago
    There are many interactive isochrone maps with sliders - one such example is [1]. Other isochrone maps listed here [2] may also have time sliders. [1]: http://property.mapumental.com http://property.mapumental.com [2]: https://wiki.openstreetmap.org/wiki/Isochrone#Examples https://wiki.openstreetmap.org/wiki/Isochrone#Examples
    - ctdonath 9y ago
      They're all public transit. I'm looking for general roads, re: "I'm here, where can I drive to in 35 minutes?"
      - lemonlyman516 9y ago
        Mapbox actually has this! Peter, the author, shared our github plugin to generate isochrones in your browser. https://blog.mapbox.com/add-isochrones-to-your-next-application-e9e84a62345f https://blog.mapbox.com/add-isochrones-to-your-next-applicat...
        ctdonath 9y ago
        The demo of that is staggeringly awesome. Thank you.
- qznc 9y ago
  The Isochrones [0] mentioned in the article include basically all the necessary information. I guess a capable GPU-shader programmer could easily render the distortion in real time. (Hint Hint Hacker News for a cool weekend project) [0] https://www.mapbox.com/bites/00156/#10/51.6840/-0.1480 https://www.mapbox.com/bites/00156/#10/51.6840/-0.1480
  - nemetroid 9y ago
    The problem isn't in getting the data for the transformation but to figure out which transformation to use. It's not possible to do in the general case, imagine e.g. an infinitely quick circle line. Where do you put the part of the map that's inside the circle?
    - qznc 9y ago
      Good point. An infinitely quick circle would reduce to a point. Morphing a 2D map in 3D, I would imagine the inside of the circle like a balloon with the circle as the opening. Reducing that to 2D seems impossible without breaking it somehow. I guess the problem is worth at least a paper, if not a dissertation. Maybe there is some esoteric math paper in topology which already solved that? Or has proven it impossible?
    - TFortunato 9y ago
      I think as far as figuring out the transformation to use on the a generic map I would: 0) ignore stuff like "infinitely quick" since that isn't realistic for what we are doing :-) 1) For the map I am displaying, pick a handful of points of interest to hse as controls, as well as my current location. 2) Use existing data we already have for stuff like direction routing to get travel times between all the pairs in our points of interest. 3) Draw a weighted graph, where each vertex is one of our points of interest and each edge is weighted by travel time. The initial position of each point should be it's geographic position, but we can then use an existing graph layout algorithm that uses an energy-based method (e.g. pretend the edges are springs) to deform the graph. This way each point will end up with its distance being proportional to travel time. 4) Using initial points as our input control points, and their location in the graph as output cobtrol points, use any number of image warping algorithms put there to calculate our warp / morph / deformation field. 5) Apply to initial map image. I don't know how well it would work in practice but seems like a reasonable first stab at it! :-) EDIT: Apologies for typo, fat fingers on mobile!
- nkoren 9y ago
  I suspect it would be relatively straightforward. Treat each datapoint as origin of a voronoi cell, in both realspace and travel-timespace. This would give you appropriate cage boundaries on both maps, and the transformation between them should be easy.
- dredmorbius 9y ago
  See Cartograms.
mxfh 9y ago
Here you go. The prior art you were looking for: http://www.spiekermann-wegener.com/mod/time/time_e.htm http://www.spiekermann-wegener.com/mod/time/time_e.htm
- microcolonel 9y ago
  It would be interesting to reproject a map by mutual travel time using isomap. I suspect error per point would be very high, but still interesting.
- leoc 9y ago
  Another one, for the London Underground: http://www.cityam.com/234508/this-alternative-tube-map-shows-you-the-travel-time-from-every-station-on-the-london-underground http://www.cityam.com/234508/this-alternative-tube-map-shows... The map itself https://petertrotman.com/special/london-underground-travel-time-map/map.html https://petertrotman.com/special/london-underground-travel-t... is having certificate issues atm.
  - deleted 9y ago
    [deleted]

This. I was hoping for some weird pictures of distorted maps.

by qznc 9y ago

This. I was hoping for some weird pictures of distorted maps.

For what it's worth, I think it would be computationally quite hard. You would have to pick a set of points and maybe isomap them from three dimensions (x, y, and time) to two, then find a visually acceptable cage transformation using those points as anchors. You'd have to do this for each query.

ctdonath 9y ago
Alternative would be to keep the standard geographic map, but have clear points on all possible destinations X minutes away - ideally with a slider, watching the "X minutes" points slide around. Actually pretty easy, given each road segment knowing expected speed, and "X+1" just extending into untraveled areas.
- jamessb 9y ago
  There are many interactive isochrone maps with sliders - one such example is [1]. Other isochrone maps listed here [2] may also have time sliders. [1]: http://property.mapumental.com http://property.mapumental.com [2]: https://wiki.openstreetmap.org/wiki/Isochrone#Examples https://wiki.openstreetmap.org/wiki/Isochrone#Examples
  - ctdonath 9y ago
    They're all public transit. I'm looking for general roads, re: "I'm here, where can I drive to in 35 minutes?"
    - lemonlyman516 9y ago
      Mapbox actually has this! Peter, the author, shared our github plugin to generate isochrones in your browser. https://blog.mapbox.com/add-isochrones-to-your-next-application-e9e84a62345f https://blog.mapbox.com/add-isochrones-to-your-next-applicat...
      - ctdonath 9y ago
        The demo of that is staggeringly awesome. Thank you.
qznc 9y ago
The Isochrones [0] mentioned in the article include basically all the necessary information. I guess a capable GPU-shader programmer could easily render the distortion in real time. (Hint Hint Hacker News for a cool weekend project) [0] https://www.mapbox.com/bites/00156/#10/51.6840/-0.1480 https://www.mapbox.com/bites/00156/#10/51.6840/-0.1480
- nemetroid 9y ago
  The problem isn't in getting the data for the transformation but to figure out which transformation to use. It's not possible to do in the general case, imagine e.g. an infinitely quick circle line. Where do you put the part of the map that's inside the circle?
  - qznc 9y ago
    Good point. An infinitely quick circle would reduce to a point. Morphing a 2D map in 3D, I would imagine the inside of the circle like a balloon with the circle as the opening. Reducing that to 2D seems impossible without breaking it somehow. I guess the problem is worth at least a paper, if not a dissertation. Maybe there is some esoteric math paper in topology which already solved that? Or has proven it impossible?
  - TFortunato 9y ago
    I think as far as figuring out the transformation to use on the a generic map I would: 0) ignore stuff like "infinitely quick" since that isn't realistic for what we are doing :-) 1) For the map I am displaying, pick a handful of points of interest to hse as controls, as well as my current location. 2) Use existing data we already have for stuff like direction routing to get travel times between all the pairs in our points of interest. 3) Draw a weighted graph, where each vertex is one of our points of interest and each edge is weighted by travel time. The initial position of each point should be it's geographic position, but we can then use an existing graph layout algorithm that uses an energy-based method (e.g. pretend the edges are springs) to deform the graph. This way each point will end up with its distance being proportional to travel time. 4) Using initial points as our input control points, and their location in the graph as output cobtrol points, use any number of image warping algorithms put there to calculate our warp / morph / deformation field. 5) Apply to initial map image. I don't know how well it would work in practice but seems like a reasonable first stab at it! :-) EDIT: Apologies for typo, fat fingers on mobile!
nkoren 9y ago
I suspect it would be relatively straightforward. Treat each datapoint as origin of a voronoi cell, in both realspace and travel-timespace. This would give you appropriate cage boundaries on both maps, and the transformation between them should be easy.
dredmorbius 9y ago
See Cartograms.

mxfh 9y ago

Here you go. The prior art you were looking for: http://www.spiekermann-wegener.com/mod/time/time_e.htm http://www.spiekermann-wegener.com/mod/time/time_e.htm

microcolonel 9y ago
It would be interesting to reproject a map by mutual travel time using isomap. I suspect error per point would be very high, but still interesting.
leoc 9y ago
Another one, for the London Underground: http://www.cityam.com/234508/this-alternative-tube-map-shows-you-the-travel-time-from-every-station-on-the-london-underground http://www.cityam.com/234508/this-alternative-tube-map-shows... The map itself https://petertrotman.com/special/london-underground-travel-time-map/map.html https://petertrotman.com/special/london-underground-travel-t... is having certificate issues atm.
- deleted 9y ago
  [deleted]