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Make a 3D Image from an Elevation Map

From an array of elevation values, create a 3D image of terrain.

code

ElevationMapToImage3D[emap_] := Block[{}, data = ImageData[emap]; data3D = Map[# Table[UnitStep[50 # - k], {k, 50}] &, data, {-1}]; transposedData = Reverse[Transpose[data3D, {2, 3, 1}], {1}]; Image3D[transposedData, ColorFunction -> "AlpineColorsOpacity"] ]

how it works

Here’s a simple 2D elevation map:

emap = \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJw0fAN8XNn/drU1t7a21tYIGk8wtm3bVuykaZOmSG1ra9vaWlvbbt/vnd// 3fO5k0manWTucx7dc24GCnVEaZNGjRqZWsIDUWBLNhoFDtIf8EmKwjx+ihz5 t+P/d9zN7Ju5JYOdrk5zp9alNE82zGyV+CK+FwxUPDX+dlxWHD1uRtyBGdkw Dsx4PeP8DDl8lMXdjhsRvzD+VjwlIZhgSihP2JMwJTGQeCNx8sxJSf8m/5c2 BvUrc2T295x67FHCIfIimolJ5Gh42/hbBRdEL6U3FMfV/fVtzWvsGvclr9M7 3t3c+cw21Wq23DbvM6+3iK0Bm8FOdFxzpDibOw32ntbXxq26Ok1z9VrFWald 5Ob52fPYa9i72KXsNPZk9lfWV1ZLeLaGncoZz6sRVknWyUuVfHWStkbfx/TC 0s3RzD3Om+1vG1wfKouszu1coCqaVTKrJL9oR35p9EfwTkAWGAn/NiUyJPdT 3oeCjsWHiz4U/JX3LPIz0N93yZvgq/HRAzfDE/I7Fm8sW1s5pNo9+1Dd6/oD 9S8WbJzHnNu4zlPTqrJj8Y78YZF2AY7ns6OntcEcMdmMDON5o9y42XDQYDPe Ne433TH1McUZFYYE/VFtkWayki65JKjl8bjz2Omsb8ybzCDTkXE4/b+0K6na FG9yt6T5iVMTQvEVgMYIGGfjZIBGn7jzgMGBGVHAov2M0XD0nfFrxr64NvES wGQqoPEtoUdij8T5ic8SDTNbJA1J8iV9Sp6TZkf1yWrINqGLcSpSe+oG+nfG N+Zk9jXOTP4hYVvpMAVeEzWKrd0cyz1cd6qjzLbO2tPayzIS3ofVtN9kMbex oCzrLVOtPWzPrRvMbwzLdFc1E9W7FS+lswCR63D2n8K4zj4Jw882ADZ+dguO 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You can see what that data looks like as a contour map using ListContourPlot:

ListContourPlot[ImageData[ImageReflect[emap]], Contours -> 50]

Here’s the same data in three dimensions:

ListPlot3D[ImageData[ImageReflect[emap, Top -> Bottom]], MeshFunctions -> {#3 &}, Mesh -> 50]

To turn the elevation map data into a 3D image, extract the 2D data array from the map image:

data = ImageData[emap];

Fill the column of voxels above each pixel with the pixel value to a height proportional to the value:

data3D = Map[# Table[UnitStep[50 # - k], {k, 50}] &, data, {-1}];

Rearrange the 3D data so that its x, y, and z axes correspond to the original elevation map:

transposedData = Reverse[Transpose[data3D, {2, 3, 1}], {1}];

Render the 3D image using geographic colors:

Image3D[transposedData, ColorFunction -> "AlpineColorsOpacity"]

Package those steps as a function that can be easily applied to other elevation maps:

ElevationMapToImage3D[emap_] := Block[{}, data = ImageData[emap]; data3D = Map[# Table[UnitStep[50 # - k], {k, 50}] &, data, {-1}]; transposedData = Reverse[Transpose[data3D, {2, 3, 1}], {1}]; Image3D[transposedData, ColorFunction -> "AlpineColorsOpacity"] ]

Test the function on elevation data from Denver, Colorado:

denverMap = Image[QuantityMagnitude[ GeoElevationData[ Entity["City", {"Denver", "Colorado", "UnitedStates"}]]]] // ImageAdjust

ElevationMapToImage3D[denverMap]

Scale the elevation map to reduce height exa