Wolfram Research

Function Repository Resource:

TessellateGraphics

Source Notebook

Create an image by tessellating many copies of a source image into a template

Contributed by: Jon McLoone

ResourceFunction["TessellateGraphics"][graphic,mask]

creates an image using many copies of graphic placed using the binary image mask as a guide.

Details and Options

TesselateGraphics can take all the options of Graphics, as well as the following:
"MinInsetSize” 4 the smallest size of inset image measured in template image pixels
"Mask" Automatic the shape to eliminate from the template
"MaskScaling" 1 the magnification of the mask to eliminate from the template
"InsetScaling" 0.98 the magnification of the inset image to place in the output
"MaxIterations" 6 the number of times to search for remaining space to insert images
ResourceFunction["TessellateGraphics"] attempts to generate a mask automatically from the inset image. No further inset images will be placed in masked areas.
For images, the alpha channel is used to decide the mask. For Graphics and Graphics3D expressions, all primitives are used regardless of color.

Examples

Basic Examples

Create an image of a car using disks:

In[1]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\)]
Out[1]=

Scope

The inset contents can be a Wolfram Language Image, Graphics or Graphics3D:

In[2]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/834749cb-b86e-40f5-b35a-132ec6b51211"]
Out[2]=
In[3]:=
ResourceFunction["TessellateGraphics"][Graphics[Triangle[]], \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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Out[5]=

To prevent this, you can specify the option "Mask":

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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "Mask" -> \!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\)]
Out[6]=

By default, the inset image is 2% smaller than the mask, leaving space around each image. Decreasing the value of "InsetScaling" will leave more space:

In[7]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "InsetScaling" -> 0.5]
Out[7]=

Increasing it will cause overlapping images:

In[8]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "InsetScaling" -> 1.05]
Out[8]=

TessellateGraphics recursively fills empty space with smaller inset images. You can control the number of iterations with the "MaxIterations" option. The smallest graphic to be inset is controlled by the "MinInsetSize" option, given in pixel sizes from the template image:

In[9]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "MaxIterations" -> 10, "MinInsetSize" -> 2, "InsetScaling" -> 1]
Out[9]=

Possible Issues

If the inset image has PlotRangePadding, ImagePadding or a PlotRange, it may not fill its bounding box:

In[10]:=
ResourceFunction["TessellateGraphics"][
 Graphics3D[Ball[], Boxed -> False], \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\)]
Out[10]=

You can compensate using "InsetScaling":

In[11]:=
ResourceFunction["TessellateGraphics"][
 Graphics3D[Ball[], Boxed -> False], \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "InsetScaling" -> 1.25]
Out[11]=

Images should have transparent backgrounds, otherwise overlapping image backgrounds will obscure contents:

In[12]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/7a407250-b6d8-4f9f-b563-36a0100e70bc"]
Out[12]=

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