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"4the smallest size of inset image measured in template image pixels
"Mask"Automaticthe shape to eliminate from the template
"MaskScaling"1the magnification of the mask to eliminate from the template
"InsetScaling"0.98the magnification of the inset image to place in the output
"MaxIterations"6the 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 (2) 

Where the mask is Graphics, white areas are to be filled and black areas and Background are not. For example, fill a half Disk with disks:

In[1]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), Graphics[{White, Disk[{0, 0}, 1, {0, Pi}]}]]
Out[1]=

Where the mask is an Image, areas of white pixels are to be filled and black areas are not. For example, create an image of a car using disks:

In[2]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA7Pg/
JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\)]
Out[2]=

Scope (4) 

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

In[3]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/b51a1e9d-ba8c-4913-9f8a-25b1ab93ef5d"]
Out[3]=
In[4]:=
ResourceFunction["TessellateGraphics"][Graphics3D[Sphere[]], \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA7Pg/
JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\)]
Out[4]=

If the inset contents is an image without an alpha channel, the whole image will be used:

In[5]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/e0564e98-0055-413c-9300-a197e82433e2"]
Out[5]=

To use nonrectangular images, set the alpha channel to modify their shape:

In[6]:=
gr = SetAlphaChannel[\!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 120}, {120, 0}}, {0, 255},
ColorFunction->RGBColor],
BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{120, 120},
PlotRange->{{0, 120}, {0, 120}}]\), ColorNegate@Rasterize[Graphics[Disk[]], RasterSize -> {120, 120}]]
Out[6]=
In[7]:=
ResourceFunction["TessellateGraphics"][gr, Graphics[{White, Disk[{0, 0}, 1, {0, Pi}]}]]
Out[7]=

RemoveBackground can be useful preprocessing for an inset Image:

In[8]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/44c2c009-0a59-4061-8f39-4ac90e9f811c"]
Out[8]=

Options (3) 

TessellateGraphics attempts to generate an inset image 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. If the inset graphic contains transparent contents, this may cause inset graphics within the inset graphics:

In[9]:=
ResourceFunction["TessellateGraphics"][Graphics[Circle[]], \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "Mask" -> Graphics[Disk[]]]
Out[10]=

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[11]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "InsetScaling" -> 0.5]
Out[11]=

Increasing it will cause overlapping images:

In[12]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "InsetScaling" -> 1.05]
Out[12]=

TessellateGraphics recursively fills empty space with smaller inset images. 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[13]:=
ResourceFunction["TessellateGraphics"][\!\(\*
GraphicsBox[DiskBox[{0, 0}],
Axes->False,
PlotRangePadding->0]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
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JhWH8Q==
"], {{0, 407}, {1000, 0}}, {0, 1},
ColorFunction->GrayLevel],
BoxForm`ImageTag["Bit", ColorSpace -> Automatic, Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSizeRaw->{1000, 407},
PlotRange->{{0, 1000}, {0, 407}}]\), "MaxIterations" -> 10, "MinInsetSize" -> 2, "InsetScaling" -> 1]
Out[13]=

Possible Issues (2) 

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

In[14]:=
img = Graphics[Disk[{0, 0}], Axes -> False, PlotRangePadding -> 2];
ResourceFunction["TessellateGraphics"][img, Graphics[{White, Disk[{0, 0}, 1, {0, Pi}]}]]
Out[15]=

Use "InsetScaling" to partially compensate:

In[16]:=
ResourceFunction["TessellateGraphics"][img, Graphics[{White, Disk[{0, 0}, 1, {0, Pi}]}], "InsetScaling" -> 1.4]
Out[16]=

Publisher

Jon McLoone

Version History

  • 2.0.1 – 08 April 2022
  • 2.0.0 – 20 April 2020
  • 1.0.0 – 18 October 2019

Related Resources

License Information