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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 = \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 201}, {201, 0}}, {0,
65535},
ColorFunction->GrayLevel],
BoxForm`ImageTag[
"Bit16", ColorSpace -> "Grayscale", Interleaving -> None],
Selectable->False],
BaseStyle->"ImageGraphics",
ImageSizeRaw->{201, 201},
PlotRange->{{0, 201}, {0, 201}}]\);
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 exageration
ElevationMapToImage3D[ImageMultiply[denverMap, .5]]