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I want to write a program with 'geometry automata'. I'd like it to be a companion to a book on artistic designs. There will be different units, like the 'four petal unit' and 'six petal unit' shown below, and users and choose rulesets to draw unique patterns onto the units:

enter image description here

I don't know what the best data structure to use for this project is. I also don't know if similar things have been done and if so, using what packages or languages. I'm willing to learn anything.

All I know right now is 2D arrays to represent a grid of units. I'm also having trouble mathematically partitioning the 'subunits'. I can see myself just overlapping a bunch of unit circle formulas and shrinking the x/y domains (cartesian system). I can also see myself representing the curve from one unit to another (radians).

Any help would be appreciated.

Thanks!!

Flying Spaghetti
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2 Answers2

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I can't guarantee that this is the most efficient solution, but it is a solution so should get you started.

It seems that a graph (vertices with edges) is a natural way to encode this grid. Each node has 4 or 6 neighbours (the number of neighbours matches the number of petals). Each node has 8 or 12 edges, two for each neighbour.

Each vertex has an (x,y) co-ordinate, for example the first row in in the left image, starting from the left is at location (1,0), the next node to its right is (3,0). The first node on the second row is (0,1). This can let you make sure they get plotted correctly, but otherwise the co-ordinate doesn't have much to do with it.

The trouble comes from having two different edges to each neighbour, each aligned with a different circle. You could identify them with the centres of their circles, or you could just call one "upper" and the other "lower".

This structure lets you follow edges easily, and can be stored sparsely if necessary in a hash set (keyed by co-ordinate), or linked list.

Welbog
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Data structure:

The vertices can naturally be stored as a 2-dimensional array (row, column), with the special characteristic that every second column has a horizontal offset.

Each vertex has a set of possible connections to those vertices to its right (upper-right, right, or lower right). The set of possible connections depends on the grid. Whether a connection should be displayed as a thin or a thick line can be represented as a single bit, so all possible connections for the vertex could be packed into a single byte (more compact than a boolean array). For your 4-petal variant, only 4 bits need storing; for the 6-petal variant you need to store 6 bits.

That means your data structure should be a 2-dimensional array of bytes.

Package:

Anything you like that allows drawing and mouse/touch interaction. Drawing the connections is pretty straightforward; you could either draw arcs with SVG or you could even use a set of PNG sprites for different connection bit-patterns (the sprites having partial transparency so as not to obscure other connections).

Ben Whitmore
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