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USA relief models

Download a free Elevation Dataset and machine a relief of your hometown

DeskProto user Jeffrey Switzer from Ovando (Montana, USA) taught us about a great application for DeskProto: machining geographic relief models. This application in itself is not new, the news is that the Digital Elevation Data (satellite-made measurements) is a free download for any part of the USA.

So any DeskProto user in the USA can create a relief model of his/her hometown,
completely free of charge !


As this is a long gallery page a few navigation shortcuts have been added:

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1. San Francisco model


Aerial view of the Golden Gate bridge
Detail view of the San Francisco relief
Left Golden Gate, real world; right Golden Gate, relief model.


This Gallery page will first show you the basics of this process, using a model of San Francisco. You will be amazed about the result! See the two pictures above: at the left an aerial view of the Golden Gate, and at the right the same view on the CNC machined relief model.
After that some tips will given, and a few more example reliefs will be shown.


Screenshot of the datagateway website
Contents of the ZIP archive
Left the NRCS geospatial data gateway, right the ZIP with elevation data files.


The elevation data that you need is provided by the United States Department of Agriculture, and is called the Geospatial Data Gateway. You can find it on datagateway.nrcs.usda.gov. On this website you will see a large button GET DATA (see the picture above).
Press that button and continue as follows:
Select State (for this project California)
Select County (for this project San Francisco)
Press button "Submit selected counties"
Check "National Elevation Dataset 10 Meter" (for our county 7 maps, 20.869 MB) and press Continue
As delivery method select FTP and press Continue
Fill in your name and address data and press Continue
Press "Place order" (no charge)
You will then receive an email with a link to the ZIP file to be downloaded.

In this ZIP file you will find four files for each of the maps, and some extra files with meta-data. Most important is the large TIFF file for each of the maps, containing the actual elevation data.


The original elevation data, one map
Same data with the sea colored blue
The elevation tiff file for SF, the bridge added in gold, right with the sea made blue.


Having a TIFF file sounds like good news, as TIFF is supported by almost any graphics program. That would be too easy though: this is not the normal TIFF format but something called GeoTIFF, and the graphics programs that we tried could not read it (although Wikipedia mentions that it should be compatible).
The solution was to download a GeoTIFF reader. We used a free program by GIS specialist Hexagon, called the Erdas ER Viewer, see www.hexagongeospatial.com. This program can read GeoTIFF files and export them as standard BMP files.

Above left you can see one of the datasets in ER Viewer: San Francisco. For your orientation we added a line in gold that indicates the Golden Gate Bridge. The hatched area on the right does not belong to the bitmap. As the sea is black (lowest point) it is almost impossible to see the coastline: for more clarity in the second picture the sea has been made blue.


Bitmap showing errors along the coastline
The same area in Google maps
Left errors in the sea's elevation, right the same area in Google Maps.


Two more issues need your attention before the data is ready to be used in DeskProto.

As you can see in the picture above, at sea level the elevation map may contain measurement errors. Such errors may be present everywhere on the map, though only on the flat sea area they will be clearly visible in the result. So these coastline errors need to be corrected.
This can be done by comparing with Google Maps and Google Earth. Any graphics program then can be used to fill all sea area with one color. That will be black, for the lowest Z-value (unless of course you live below sea level, like we do in Holland).


Screenshot of about 30 tiled tiff maps
Detail showing the two maps for San Francisco
Tiled view of the Bay area, and the two tiles used for this relief.


The second issue is important when you need to combine two or more different maps in order to cover the area that you want to machine. You cannot just stitch two BMP files with elevation data, as in each BMP file the height information will be on a different scale !!

This sounds rather awkward (in fact it is...) still it does make sense. A bitmap file can contain 256 grey values, so 256 Z-levels. In order to use the same scale for all maps these 256 Z-levels would need to be used for the complete Z-range that can be found in the USA. So from Death Valley (-282 feet = -86 m) to Mount McKinley (20,320 feet = 6,194 m): one step being 20,602/256 = 80.5 feet or 24.5 meters. As a result most maps would only contain very dark grey, and almost no information.
So each map comes with it's own scale, evenly dividing the 256 grey values between the min and max Z as present in that one map. Tiling a series of maps will this give a strange result: see the images above.

For combining tiles with varying Z scales to one bitmap file specialized software does exist, see below in section Combining tiles (mosaicing).


The bitmap file as used for the relief
The resulting bitmap file used to create the San Francisco relief (the sea made blue).
To download the real bitmap file:  Right-click this link  and Save As (7MB).


Easiest way to start is to just use one tile and convert that to a bitmap. For this San Francisco project we could use two tiles (picture above at the right) with almost the same Z scale (Z max 330 m resp 341 m). We stitched the two bitmaps together in a graphics program (an old Paintshop Pro). As the tiles have some overlap the exact position of the stitch needed to be set: we just visually selected what seemed the proper position. The result is not perfect (the stitching line is visible in our model) so a one-tile model is the best start.
The picture above shows the result: this BMP file is the input for DeskProto. Feel free to download and use this file for a quick start.

The next step is to determine the correct height for the relief.
The ZIP file that was downloaded from the Geospatial Data Gateway contains for each tile an XML file (extension .tif.aux.xml) with metadata, including the min and max height for that tile (in meters!).
For this San Francisco bitmap it said:

[HistMin] -8.5240421295166[/HistMin]
[HistMax]341.0674133300781[/HistMax]

so a Z-range of about 350 meters.

The east-west distance covered by this bitmap is about 19 km (ca 11 mile)
We machined the 1800 x 1300 pixel bitmap at a size of 200 x 145.5 mm (ca 8 x 5.7 inch).
The scale of this relief is thus 200:19,000,000 or 1:95,000 and the real height of 350 meters in the relief needs to be 350,000 / 95,000 = 3.7 mm (0.15").


DeskProto screenshot with toolpaths
Toolpaths in DeskProto, for Bonita Point and the Rodeo Lagoon.


In DeskProto the BMP file can be loaded in a bitmap operation: create one in the tree or use the Bitmap wizard to let DeskProto do this automatically. Browse the bitmap file, and in the bitmap settings set the correct dimensions: 200 mm (8") for X, -3.7 mm (0.15") for black and 0.0 mm for white. The sea then will be machined at -3.7 mm and the highest mountain top at 0.0
You are of course free to exaggerate the Z a bit in order to get a more distinct relief: we did in fact use -5 mm (0.2") for black (and thus for the total relief height).


DeskProto screenshot with a simulation
Simulation in DeskProto of the total relief


For our sample project we used three bitmap operations (all with the same bitmap and with the same bitmap settings, so easily made by copying the first operation):
1. First the roughing operation, with a ballnose cutter of 3 mm diameter (1/8")
2. Next for semi-finishing, with the same cutter but without roughing skin.
3. Third the finishing operation, with a 1 mm diameter ballnose (0.04").
A cautious setup, in order not to snap the very thin finishing cutter. All three operations were done with strategy parallel.


Roughing toolpaths on the machine
Finishing toolpaths on the machine
Roughing (ball D3) and finishing (ball D1 mm).


The relief model shown was machined in tooling board, as that is very easy to machine and makes even the smallest detail visible.
A model in a fine wood will nevertheless give an even better looking result.


The resulting relief model
The resulting relief model, scale 1 : 95,000. There is a big difference between the rough mountains north and the cultivated city area south.


The resulting model shows many details. Easily visible are the islands Alcatraz and Angel Island. Smaller details include the various harbors, Bonita point, Mount Sutro and the Twin Peaks, and the streets in the city (visible as contrast to the Golden Gate Park area).



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2. Tutorial Video


Creating a geographic relief model. The complete process is shown, including data download, for this San Francisco relief model   (14 min)


For all website visitors who rather watch a video than read a website text: this tutorial video will show you step-by-step how this relief model of San Francisco has been created.

Data download, data preparation, the use of DeskProto and the actual milling process are all completely shown.



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3. Other Countries


For digital elevation data of other parts of the world: visit srtm.csi.cgiar.org. The CGIAR - Consortium for Spatial Information offers the whole world for download, at a three arc second resolution, also in GeoTiff format. Three arc seconds is about 90 meters, so the USA data mentioned above (10 m) shows more detail.
This data is called the SRTM 90 m Digital Elevation Data, where SRTM stands for the Shuttle Radar Topography Mission: an 11-day mission flown by space shuttle Endeavour in February of 2000, see www2.jpl.nasa.gov/srtm.

This same data is also available from www.viewfinderpanoramas.org, however in a different format (.HGT files). The tool that we just mentioned to open GeoTiff files cannot convert these to the grey-scale images that we need, on Thingiverse you can find a HGT 2 STL converter (made by DWilbourn).



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4. Preventing Moiré patterns


Two line grids of different mesh size
A moiré pattern is an interference pattern that will be visible when (for instance) two grids of slightly different cell sizes are overlaid. This picture clearly shows what happens.


In bitmap projects two different grids are used:
1. the bitmap itself is a grid: the size of one pixel is set by the bitmap's DPI (Dots Per Inch).
2. the toolpaths are calculated over the Z-grid: one grid-cell for each cutter position, the cell-size set by the Operation's Precision.
These two grids will typically have different cell-sizes, which will cause interference: a Moiré pattern.
The picture above shows what happens: a pattern will become visible.


Toolpaths showing Moiré
Toolpaths without any Moiré
Left the moiré effect is clearly visible in the toolpaths, right the same area, no moiré.


In DeskProto this Moiré pattern will be visible in the Z-values of the toolpaths. Like in the left picture: on this continuous slope, after every 8 paths there will be two toolpaths at the same Z height. In the resulting model a series of small ridges (ripples) will be clearly visible (in this example every 8 paths): see the photo below.


Moiré lines over the machined model
Part of the Bitmap settings dialog
Left a moiré effect visible in the relief model, right the Bitmap settings.


In order to prevent such Moiré pattern, in DeskProto two extra options were added for setting the X en Y dimensions of the relief model (in the Bitmap settings): options to set the dimensions based on the precision settings. See the illustration above.
The option "Calculate from precision on scale 1:1" will give one pixel the size as set in the precision (so one toolpath for each row of pixels). The two grids then have an identical cell-size: no Moiré pattern.
The option "Calculate from precision on (path distance:pixel)" will make sure that one pixel will exactly fit a number of Z-grid cells (or the other way round), which will also prevent a Moiré pattern.
For more information also see the Help information for this dialog page.

Setting the dimensions this way is less convenient, as not all dimensions are possible. Also the dimensions will change when you later change the precision. So take care when you use both roughing and finishing operations. Still it is worthwhile, as a Moiré pattern over your relief model is not a pretty sight!



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5. Combining tiles (mosaicing)


As explained above, each tile in the downloaded data applies a different scale for converting the grey values to Z-heights. In most cases this makes it impossible to combine several tiles to one relief (the San Francisco relief being an exception as these two tiles use almost the same scale).

For combining tiles special software is needed, meant for maps and geographic information: GIS software (Geographic Information System). This combining of tiles is called mosaicing, the result being one large bitmap with one height scale.

A widely used GIS program is ArcGIS, by ESRI, Inc. The website offers a free trial version for ArcGIS, which is a perfect tool for mosaicing. Jeffrey Switzer has written a short tutorial on mosaicing in ArcGIS: MosaicingElevationData-ArcGIS.pdf. For unexperienced users ArcGIS will be rather overwhelming, following the steps in this tutorial makes the process easy.



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6. Adding extra information to the relief


As the basis of the DeskProto relief is a simple bitmap, it is easy to add extra information by editing the bitmap. Open the bitmap in any Paint-like program (MS Paint, PaintShop, PhotoShop, GIMP,...) and for instance draw an arrow that points to your house. The arrow, being an area in one color, will be clearly visible in the relief as a flat area. This way you can also add text, or any other information.
More sophisticated is adding information on top of the existing relief, by adding layers. In this example: add the arrow by making all pixels within the arrow's area a few grey steps lighter. The arrow then will be "draped" over the relief.

The following example is a relief where we added all major roads on top of the model, as a 0.1 mm elevation. These roads were downloaded from the same Geospatial Data Gateway, converted to DXF in ArcGIS, then to a high-res bitmap, and next added to the relief bitmap. This is a rather complicated process, so be prepared for some complexity when you start reading this section !


Google maps screenshot of Silicon Valley
ArcGIS screenshot (grey values) of Silicon Valley
Silicon Valley in Google Maps (l) and in ArcGIS (r).


The model is for the Bay area: showing Silicon Valley in 3D. As the resulting relief will show: indeed it is a valley. The bitmap data was generated for us by Jeffrey Switzer, who collected all tiles that were needed and mosaiced them (see above) in ArcGis. The result was a bitmap file of 8775 x 8573 pixels, file size 73.5 MB.
The grey scale image shown above is converted for better visibility, using a process called "histogram equalization". Do not use such picture for machining as the relief will be incorrect.


ArcGIS screenshot of the roads as lines
DeskProto screenshot (detail) with toolpaths
Left all major roads, and right toolpaths that show the roads (also SF Int airport is visible here).


The file with the roads was also created by Jeffrey using ArcGIS. Data source is the same Geospatial Data Gateway that was used for the Elevation data, now select the Transportation layer to download (primary roads only). As format select ESRI Shape, as projection select UTM Zone 10 NAD83 (important: otherwise elevation data and roads will not match). The data will arrive as .SHP file (ESRI Shape file): you will need ArcGIS to process these files and match them to the elevation data.
Exporting from ArcGIS as DXF is easy: right click the shapefile in ArcGIS and next select Data >> Export data >> Export to CAD.

For this project Jeffrey exported the roads in a DXF file, and we converted that to a bitmap of the same size as the elevation data (using the Print command in Rhino). This bitmap next has been reduced to 256 grey values, the road pixels having grey 2 on a background of grey 0 (when viewing this file you will see only black). In GIMP we could then open the elevation bitmap and the roads bitmap as two layers of the same image. For each layer the layer mode was set to Addition and then both layers were merged: increasing the grey value of the relief with 2 for each road pixel. The result is clearly visible in the DeskProto relief: see the toolpaths shown above.


Photo of the roughing process on the machine
Photo of the finishing process on the machine
Left roughing (the second layer), right finishing.


Machining was done in a slab of Oak, size 410 x 335 x 16 mm. The relief is 325 x 300 mm, the relief height is 9 mm (we exaggerated a bit: on scale it should have been 6 mm, for 1200 m in the real world). As the machine's working area is 300 for Y, the bitmap was rotated 90 degrees to fit it into the machine. Three operations:
Roughing. Ballnose cutter diameter 6 mm (1/8"), skin 0.5 mm, path distance 1.4 mm.
NC file 1.5 MB, machining time 2 hours.
Semi-finish. Ballnose cutter diameter 3 mm (1/16"), path distance 0.6 mm.
NC file 11 MB, machining time 2.5 hours.
Finishing. Ballnose cutter diameter 1 mm (0.04"), path distance 0.1 mm.
NC file 166.5 MB, machining time 17 hours.
And after that a 2D Operation was used to engrave the text in the frame of the relief.


Photo of the complete Bay Area relief model
The resulting Silicon Valley relief model, machined in oak and treated with a clear wood oil. Click for a high-res image (2250x1800) with more detail.


After the finishing operation the model was treated with wood oil: see the resulting model in the picture above. A great model ! Though the next time we will not be using oak for a relief model: the colors in the wood (its grain) conceal small relief details, and the surface quality after machining is not perfect.


Detail photo of the left side of the relief model
Detail picture that shows the coastline and the roads. You can see San Francisco, its airport, the major bridges, Half Moon Bay, and much more. Click for a high-res image (2500x2000).


When machined on a true scale, the coastline will not be clearly visible. In many places the coastline will be just one step: from grey value 0 to grey value 1. The image contains 256 grey values, to one step equals in real life 1200/256 = 4.7 m, and in the model 9/256 = 0.035 mm: almost invisible.
To make the coastline clearly visible we made the difference 8 steps (ca 0.3 mm). This was done by making the complete bitmap image a bit lighter and then filling the sea with pure black. This must have damaged the peak of the highest mountain, however we could not see this in the result.

A geographic relief model in 3D is much more instructive than just a flat map. This model for instance makes perfectly clear that Silicon Valley is indeed a valley.



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7. Other example models


Some more examples of geographic relief models that were made using DeskProto:


Relief model in wood of Napa Valley
A nice round relief model in wood by Jeffrey Switzer, showing Napa Valley in California.


The model shown above was made by Jeffrey Switzer. Jeff tells:
"DeskProto worked great for this application. I use a 48"x48" HobbyPlaz2000 from GearHeadCNC out of Virginia. It was originally built for a plasma cutter, but I fitted it with a router. I am very happy with DeskProto and intend to buy a license, I attached a photo of the trial piece I cut. It is a 15" round depiction of Napa Valley in California."

Feel free to email us a picture of the relief model that you created !



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8. Yet to come


More information will follow:
- some more results in wood, by DeskProto users ?

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