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https://github.com/fogleman/Tiling

Tilings of regular polygons.
https://github.com/fogleman/Tiling

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Tilings of regular polygons.

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README 

        
## Tiling



Quickly construct tilings of regular polygons and their dual tilings using a

simple API.



Scroll down for a tutorial. Here are some examples.



![Sample](http://i.imgur.com/gyoQnuG.gif)



### Links



http://en.wikipedia.org/wiki/Tiling_by_regular_polygons



http://en.wikipedia.org/wiki/List_of_uniform_tilings



### Motivation



1. Write polygon tiling code.

2. ???

3. Profit!



### Wallpaper



* [16x9 Wallpaper](http://i.imgur.com/oerkmDS.png)

* [16x10 Wallpaper](http://i.imgur.com/H28k39a.png)



### How To



[pycairo](http://cairographics.org/pycairo/) is used for rendering.

Installation on OS X is easy using Homebrew.



    brew install py2cairo



Before creating a new pattern, set these flags to zoom in and label the

polygons and their edges.



    SCALE = 128

    SHOW_LABELS = True



The first step is to create a Model that will hold our polygons.



    model = Model()



Next, we will place our first polygon at the origin. We need only specify its

number of sides. Let's add a hexagon.



    model.append(Shape(6))



At this point we can run the following code to render the model.



    surface = model.render()

    surface.write_to_png('output.png')



![Image](http://i.imgur.com/OjV0HTb.png)



Now, let's add squares adjacent to all of the hexagon's edges.



    a = model.add(0, range(6), 4)



The first parameter, `0`, specifies which shape(s) we're attaching to. Here,

we're only attaching to one shape (the hexagon) and it was the first one

created, so it's referred to by zero.



The second parameter, `range(6)`, specifies the edges we're attaching to. In this

case we want to attach to all six sides of the hexagon. You can see the edges

labeled in the output image.



The third parameter, `4`, specifies the number of sides for the new shapes. In

this case, squares.



The return value of `add` tracks the indexes of the newly created squares

so we can refer to them later.



![Image](http://i.imgur.com/D0zqHkA.png)



Next comes the cool part. We can attach triangles to all of the squares we just

created in one fell swoop by using the previous return value. Here, we are

adding triangles to edge number 1 of each of those squares.



    b = model.add(a, 1, 3)



![Image](http://i.imgur.com/lfyfaC0.png)



Now we'll add more hexagons which will represent the repeating positions of

our template.



    c = model.add(a, 2, 6)



![Image](http://i.imgur.com/2HgeMRd.png)



Now that we have positions for repeating the pattern, we can use the

repeat function to automatically fill in the rest of the surface

with our pattern.



    model.repeat(c)



![Image](http://i.imgur.com/JC2MSwH.png)



Here's all the code needed for this pattern:



    from tile import Model, Shape

    

    BLUE = 0x477984

    ORANGE = 0xEEAA4D

    RED = 0xC03C44

    

    model = Model()

    model.append(Shape(6, fill=RED))

    a = model.add(0, range(6), 4, fill=ORANGE)

    b = model.add(a, 1, 3, fill=BLUE)

    c = model.add(a, 2, 6, fill=RED)

    model.repeat(c)

    surface = model.render()

    surface.write_to_png('output.png')



Once finished, you can turn off the helper labels and adjust the scale as

desired.



![Image](http://i.imgur.com/cOrQsXW.png)



Dual tilings can be created with `model.render(dual=True)`. This setting

renders polygons such that the vertices of the original tiling correspond to

the faces of the dual tiling and vice-versa.



Here is the dual of the above pattern.



![Image](http://i.imgur.com/BnIdKV2.png)