javascript - How would I implement the shoelace theorem to find the areas of multiple convex polygons created from intersecting lines? -

i creating piece of javascript code it's necessary identify every polygon created number of randomly generated intersecting lines. following screenshot give better explanation of i'm talking about:

now, need calculate area of each polygon , return largest area. approach i'm taking identify every intersection (denoted red dots) , treat them vertex of whichever polygon(s) belong to. if can somehow identify polygon(s) each vertex/intersection belongs to, arrange vertices of each polygon in clockwise direction simple apply shoelace theorem find area of each polygon.

however, i'm afraid i'm lost , have tried various (failed) methods achieve this. best way compile list of clockwise-arranged vertices each polygon? i'm working on acquiring segments associated every given intersection, , think step in right direction don't know go there. require vector work?

i can think of 1 possibility. here i've labeled each of vertices.

http://i.imm.io/1h5ts.png

i'm assuming if know lines involved , intersections, can find line segments intersect @ particular point. lets start particular point, k, , directed segment, ik. have 4 directed segments lead end of that, ki, kj, kl, , km. interested in 2 closest to, not on, line ki. let's focus on km, although can same thing kj.

(note if there more 2 lines intersecting @ point, can still find 2 closest line, 1 forming positive angle initial segment, other negative one.)

we notice ikm positive angle, , examine segments containing m, choosing 1 smallest positive angle km, in case mf, again @ f (although there 2 choices here) fg, , gh, , hi, completes 1 polygon, hexagon ikmfgh.

going our original segment of ik, @ our other smallest angle, ikj, , similar process find triangle ikj. have found polygons containing ik.

then of course again, each other segment. need remove duplicates, or smarter not continuing analyze path when can see duplicate. (each angle in @ 1 polygon, if see angle recorded, can skip it.)

this not work if polygons weren't convex, if made lines cut through rectangle, i'm pretty sure convex.

i haven't tried code this, i'm pretty sure work.