Perhaps this can add to the discussion: Exploring Lunar Geography with GeoElevationData

Ah, yes. The difference turns out to be an update to Mathematica. In version 11.0.1, GeoElevationData[] produced the low-res images I posted above. Now that I have updated to 11.2, the same code results in the models that Marco, Vitaliy, and Emmanuel have posted. Problem solved, though I'm somewhat embarrassed that my laziness in updating Mathematica has wasted my time and yours.

I suppose it is not entirely a waste for me. I learned how to import outside data, in this case the elevation data from USGS, even though it turned out I didn't need to. I also learned a lot about elevation data. Of particular interest is the LiDAR data that Ian posted about. In some parts of Wales the resolution of the data set is 25 cm. At first that sounds like a mistake. How can elevation data points be spaced about the width of a soccer ball? But it is true. If you look at the relief images from the Wales LiDAR data, you can not only see individual buildings, but also the air-conditioner units on top of each building!

Again, thank you all.

Mark Greenberg

P.S. Here are the models I promised of the mountains in the United Kingdom. The first is Ben Nevis and the second is Ben Macdui:

GeoElevationData[] has a good amount of data for plotting 3d views of mountains and volcanoes.

Here is an example for the Popocatépetl volcano located at the center of México. Notice that the x and y axis units were transformed to meters by converting pairs of coordinates to geodesic distances using GeoDistance.

coords = Flatten[
   Table[{lat, lon}, {lat, 18.98, 
     19.07, .0006}, {lon, -98.68, -98.57, .0006}], 1];

elevations = 
  QuantityMagnitude@Normal@GeoElevationData[GeoPosition[coords]];

distances = 
  Map[{QuantityMagnitude@
      UnitConvert[GeoDistance [{18.98, -98.68}, {#[[1]], -98.68}], 
       "Meters"], 
     QuantityMagnitude@
      UnitConvert[GeoDistance [{18.98, -98.68}, {18.98, #[[2]]}], 
       "Meters"]} &, coords];

data = MapThread[Append, {distances, elevations}];

ListPlot3D[data, InterpolationOrder -> 3, Mesh -> None, 
 PlotStyle -> RGBColor["#bcdcdd"], ImageSize -> 1000]

Thanks, Vitaliy. I'm not sure that I'd consider Mt. Everest "typical," especially when giving an example of size, scale, and resolution.

Even so, when I run your code on my machine, I get much different results:

data = GeoElevationData[GeoDisk[Entity["Mountain", "MountEverest"],Quantity[3, "Miles"]]];
ListPlot3D[data, MeshFunctions -> {#3 &}, Mesh -> 20,ColorFunction -> "LightTerrain", Boxed -> False]

The results are even worse for smaller mountains like Mt. Fuji.

Why would you get different results? I'm using Wolfram 11.0.1 on Mac OS X 10.12.6. I'll try updating to the latest version of Wolfram to see whether that makes a difference.

If I could create models of all sized mountains the same quality that you were able to make of Mt. Everest, then I'd have no reason to use outside data sets.

I have made a model of Mt. Fuji using the GeoTIFF file format for data downloaded from a site whose data covers the entire earth, the GMTED2010 Viewer, also by the USGS. GeoTIFF is a .tif image file that has elevation data instead of color. It comes into Wolfram as an image, and then I used the following code to turn it into a model.

tDat = Import["/Path/Japan34.tif", {"GeoTIFF","Data"}][[4800 - 3550 ;; 4800 - 3450, 4450 ;; 4550]];
model = ListPlot3D[tDat, PlotStyle -> RGBColor["#bcdcdd"], PlotRange -> {0, 3800}, Mesh -> None, Boxed -> False, 
   Filling -> Bottom, FillingStyle -> {Brown, Opacity[1]},Axes -> {False, False, True}, BoxRatios -> {1, 1, .2},ImageSize -> 480];

The data has a resolution of 7.5 arc seconds, about 225 meters. This is low res for a mountain, so the model doesn't look as good as I'd like:

Cropping the data further makes the mountain look like a nondescript bump. I need a resolution of about 1 arc second for a good looking model.

My purpose for making these models is to show off the shapes of the mountains, so I do not have a need to overlay imagery onto the surface, though this would be a logical next step for a realistic model.

Next I'll see if I can make the LiDar data work for me that Ian mentioned.

I'll make sure to make a model of a mountain or two from the UK once a solution is found. I was unable to open the first link in your post. The second one for Wales allows viewing and printing of maps, but as far as I can tell the data is not available for download. They use Lidar data, and I've seen that format on other sites too. The formats that Wolfram can handle (from the docs) are ArcGRID, USGSDEM, GTOPO30, CDED, SDTSDEM, and SurferGrid. Also, GeoTIFF, which I'm experimenting with right now. GeoTIFF is tricky, but if I can master it, it covers the whole earth (except the South Pole).

Thanks for the help, Ian.

Mark,

A few years ago some interns of mine did an elevation project using Google's JavaScript API. Google has elevation data for the entire planet. Coincidentally, Google's example starts with a 3D relief of Denali! You can drag their example map around the globe and zoom in. The documentation is here with an example You can also get elevation data along a path. For your use it seems like it would be free -- they charge a fee for usage on a public website once you exceed a certain volume of map calls.

Mathematica should be able to make the API calls directly (although I have not tried this). If you get it to work it would be great to post the code (minus your API key!)

From what little I know about the API you get the best resolution from querying individual points but that will result in many API calls. You probably want to send straight line paths to the API and get the elevation along the path. In fact you can probably make a back and forth path and get the entire x-y-z map with one API call.

I hope this helps. I'd be curious if you are successful with this.

Regards

Neil

Mark,

In hindsight I would not be surprised if Wolfram got their GeoElevationData[] data from Google API calls! If this is the case than you would be no better of going to Google. Maybe someone at Wolfram can comment on this.

One other option -- If you found file formats that are available for the areas you want in the resolution you want but Wolfram does not support the file format, post the file types here -- maybe someone knows of some library or Source code to read the file and you can call the decoder from MMA.

Regards

Hi, Marco. The data set comes from the United States Geological Survey's "National Map." It's free and anyone can access it. They have an interactive viewer here. Zoom in to the part of the United States you are interested in and then select "Elevation Products (3DEP)." In the search filters, select "1 arc-second DEM," which gives data spaced about 30 meters apart. They offer higher resolution data, but the files are too large. Also select "ArcGrid" as the file format because Wolfram can read those types of files. Then click "Find Products" and it will tell you which data set contains the area you have selected in the map.

Then I use the following code to see a relief image of the terrain:

img = Import[ "/Path/n64w151.zip", {"ARCGrid", "ReliefImage"}, ImageSize -> 480]

Here is such a map. Unfortunately, on this one the mountain I was trying to make a model of, Denali, is right on the edge of the map in the lower left corner.

The data covers one degree longitude by one degree latitude, so the mountains are small features in the image. I find the mountain I am interested in by comparing this image to Google Maps. I use the following code to crop the image until I have framed the mountain just the way I want.

ImageTake[img, {750, 1050}, {1500, 1800}]

Then I use the following code to extract the data and make the model (3612 is the pixel with and height of the data):

smData=data[[3612-1050;;3612-750,1500;;1800]];
Export["/Path/Denali.dat", smData];
model = 
 ListPlot3D[smData, PlotStyle -> RGBColor["#bcdcdd"], Mesh -> None, 
  Boxed -> False, Filling -> Bottom, 
  FillingStyle -> {Brown, Opacity[1]}, Axes -> {False, False, True}, 
  ImageSize -> 480]

The data is arranged in a very similar way to Wolfram's ImageData[], except that instead of colors, each pixel location contains an elevation number in meters. ListPlot3D[] takes the data directly.

That's how I make a model of a mountain. However, the ArcGRID file format seems to be limited to geography in the United States. Wolfram imports a variety of elevation file formats, and there are dozens of data sets out there for the rest of the world, but I have yet to find a data set for non-US terrain that I can import into Wolfram. Here is a link to what appears to be the most comprehensive site on the subject. I did search other sites, but I'm not an expert in the field, so I probably overlooked the answer while I was searching.

Hope this helps.