Euclidean geometry in JS.

After seeing the incredible geometric designs throughout the Alhambra in Granada, I wanted to try to explore some of the underlying symmetry and geometry. I could have jumped straight to the tessellations, but it felt like a deeper way to get into it would be to build up from basic constructions, and so, over the course of a few train rides, I started with this little library–EuclidJS–for building and rendering plane geometry scenes. Code on Github.

Building the scene can be done programmatically with a simple API, or by describing the it with a (sort of) friendly grammar that Euclid can parse. The diagram above comes from the text below (which you can edit, at your own risk!).

[main-figure]
Let a = (150, 100).
Let b = (350, 300).
Let c = (300, 400).
Draw a segment joining a and b.
Draw a segment with endpoints b and c.
Draw a segment from a to c.

[guides]
Let k be a circle through b centered at a.
Let l be a circle containing a with center b.
Let m be the circle centered at b through c.
Let n be the circle centered at c containing b.
d = the intersection of k and l
e = the intersection of k and l that is not d
f = the intersection of m and n
g = the intersection of m and n that is not f

[result]
Let O be the intersection of line d-e and line f-g
Draw the circle centered at O containing a.

Next up:

I’d still like to make the grammar more flexible (and thus concise), with, e.g., things like “Let d and e be the points where circles a and b intersect”, or even “Let v be the line determined by the points where circles a and b intersect”.
A tessellation builder using this that will, hopefully, be simultaneously simple to use and true to the underlying geometry.
A geometry proof parser that attempts to generate diagrams based on the text in a proof. (This is very ambitious, but would be very cool.)