Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 ImageRadialDivide

Source Notebook

Divide an image into a list of colored polygons centered around the origin

Contributed by: Erik Mahieu

ResourceFunction["ImageRadialDivide"][img]

divides the image img into polygons centered around the origin.

Details and Options

An image of width w is divided into w/2 rings of w polygons each, resulting in w2/2 colored polygons.
Both face and edge colors are taken to be the color of the pixel closest to the centroid of the polygon in the image.
The result is a disk-shaped image where pixels outside of the disk region are discarded.
ResourceFunction["ImageRadialDivide"] is very important for transformations of an image that operate inhomogeneously, that is, differently on different parts of the image. This is the case with anamorphic transformations where the deformation of the original is dependent on the locations of each pixel.

Examples

Basic Examples (1) 

Radially divide an image into a list of colored polygons:

In[1]:=
Graphics[ResourceFunction["ImageRadialDivide"][mandrill]]
Out[1]=

Scope (2) 

The output of the function is a list of colored polygons:

In[2]:=
ird = ResourceFunction["ImageRadialDivide"][mandrill];
In[3]:=
Short[isd, 2]
Out[3]=
In[4]:=
Dimensions[ird]
Out[4]=

The function operates best on circular images such as logos and the like:

In[5]:=
wolf = ImageResize[\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJztXQeUFFXWVnKaDpPzDAxRFBiQDAMIEgRJgyxIEBQZyRkcEQQlOT+ISgYR WSQHEYYkYde0gKgIrLC7YgBUQDAjZt//vjo2W139XoWuV13ds/Wd83mOQ3d1 vVe33rv3vhsq3j+q++BiN91007gy9D/dB05qNXbswPxcD/2fe0aOG5I38sFB HUaOfzDvwbGN7i9O/1jwJ0tQEgcOHDhw4MCBAwcOHDhw4MCBAwcOKD777DOy d+9esmDBAjJu3DiSm5tLGjduTKpVq0ZiY2NJ6dKlCdxJcpYqVYrExMSQKlWq kEaNGpGuXbuSUaNGkfnz55PCwkJy7tw5u4flwAR++OEHsm/fPvLYY4+Rtm3b Eq/XGyADouhyuUirVq1Ifn4+2bVrF/n222/tHr4DFZw9e5YUFBRIzwzrgFVy ocXixYuT5s2bk8cff5ycPHnS7mlxQHHhwgUyY8YMUrt2bdvkQovY16ZMmSLJ sYPQ4ffffyfbtm0j7du3J8WKFbNdDoywZcuWZO3ateTnn3+2exqLLL7//ntJ f6xYsaLtz9ssk5OTyaxZs8jXX39t97QWGUA+Zs+eLdkdZp9PubJlSfXUdNIy M4v0SMskQxNTyJSYOLLA4yGr3RVIoas02S3jX+nfFtJ/mxYTS4YlJJN76Hda 0e/WTMsg5cuVM30/brdb0rUdeQkev/76K1m8eLFkswb7HLKSU0iH9EwyPjaB 7HCVIR94byYfem8Sxr2uUiSfylknKj+Qv5tvvjloeYEO/tNPP9k97RGF/fv3 k1tuucXwfMMH0iSzEhkTl0j+7iouVCb08LC7BJlE5aY5vYdg1hvsqS+99JLd 0x/2+OKLL0jfvn0NzS3e4bp0zZgYG09OeIppPssJ9DmudEVZLjNnKB/zxpCG 9N5gKxsZU+fOncn58+ftfhxhiU2bNpHo6Gj9a3VUFOmWmkH2UD1C77O7LyFF +m5Xuk+Ecp35m6sE6ZWSTmI8+v19UXR8zz33nN2PJWwA/2X//v11z1+cN5oM pjrlSY8xXaNHYsqNa6TGJ4R8TwL/5S1GRtI9MSU+Xvd4u3TpQq5cuWL3Y7IV 8FdWrlxZ13xFuz3kASof/zQoH2Bf+j3l9da5ytkiK+B/qD49murWiTH6dPSU lBRy+PBhux+XLXjxxRdJOR26XsmSJUlXumYfcwenl46gz4N1XewDdsmJj5D5 XkmppGyZMrrmYeHChXY/tpDhjz/+II8++qiu96hWWgbZ6g7+vS+g+kCJEiWY 165MbWa75cTHvdRmb0DHqmdOhg4dSn777Te7H6OlgL+6d+/emnMBf9jwuARy 1oS/YxfVb6Hrqv0OfCp2y4icD3tjNe8Z7Nixo3QmXhSBceFMRmsOqqekkZfd ZU3NN2zSavQ6AWsI1YVq1qx54//7JaeZfraH3dq2uBEeoPKdrWNtQTzMN998 Y/djFQqMB2dgmu8J1RlgE5id6870Oqx38JdffpHOEH1/q5piTk6mRceQRukZ wtcV+I17UvtMy79bt25dyedUFIB1REtG4EedEB0rZI7nu90B1+/evbt0zgx8 9dVXQvYeyAh0H7OypsYZ3mhSoXx51bnLzs6O+HUF+ki7du1Ux+ml9u4S+mxF zOv71H5IS0j0uz5iG30y4kNmZqapvccnI/h+LH2WVskJuJ7a70mxcapz2LBh w4jVV2DXaOmsqQkJZIdJXUTO3GR/nQT+3evXrwfc26JFi258Jsug3SOXERA+ eSvlBPybqySplBToA5IT72Mk2kGTJ09WHVdGYhJ5RaC9Ab+Z0gY+deoU895w diL/nF7bWykjPuo5VzJLnDFWZ+jmcj700EMhfsrmAB+aloy8HqTfjMfaChth 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<|"InstanceID" -> "xmp.iid:724B5939489A11E6B11CEF5EF1A2CCEF", "DocumentID" -> "xmp.did:724B593A489A11E6B11CEF5EF1A2CCEF"|>|>, "DocumentID" -> "xmp.did:724B593C489A11E6B11CEF5EF1A2CCEF", "InstanceID" -> "xmp.iid:724B593B489A11E6B11CEF5EF1A2CCEF"|>, "RightsManagementSchema" -> <|"DerivedFrom" -> <|"DerivedFrom" -> <|"InstanceID" -> "xmp.iid:724B5939489A11E6B11CEF5EF1A2CCEF", "DocumentID" -> "xmp.did:724B593A489A11E6B11CEF5EF1A2CCEF"|>|>|>, "PagedTextSchema" -> <|"DerivedFrom" -> <|"DerivedFrom" -> <|"InstanceID" -> "xmp.iid:724B5939489A11E6B11CEF5EF1A2CCEF", "DocumentID" -> "xmp.did:724B593A489A11E6B11CEF5EF1A2CCEF"|>|>|>|>|>], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSizeRaw->{138., 138.}, PlotRange->{{0, 138.}, {0, 138.}}]\), 50];
In[6]:=
Graphics[ResourceFunction["ImageRadialDivide"][wolf]]
Out[6]=

Neat Examples (1) 

Here is an example of a conical mirror anamorphic function operating on the vertices of an image that was divided into squares:

In[7]:=
ana[{yi_, zi_}, \[Phi]_] := Re /@ {yi (3 - 2 yi^2 + 2 Sqrt[1 - yi^2] zi Cot[\[Phi]]), 2 (1 - yi^2)^(3/2) + (zi - 2 yi^2 zi) Cot[\[Phi]]}
In[8]:=
Graphics[MapAt[ana[#, 50 \[Degree]] &, ResourceFunction["ImageRadialDivide"][mandrill], {All, -1, -1, All}]]
Out[8]=

Publisher

Erik Mahieu

Version History

  • 1.0.0 – 09 November 2020

Related Resources

License Information