Slice
Cutting polygons in realtime!
Here's the problem setup: we have a set of arbitrary simple polygons (define simple: polygons do not intersect themselves but may be nonconvex) and mouse pointer coordinates. Both this set's positions and mouse positions are sampled in discrete time, so the mouse historical path is a polyline.
The core of the algorithm is just two steps, to differentiate two classes of interactions between the mouse and polygons.

Most of the time, the mouse will enter a polygon, spend some time moving inside, and leave. We can take this path it draws during this time and partition the parent polygon with it.

Occasionally, the mouse will enter and leave one or many polygons all in one timestep, in a kind of awesome swipe of carnage.
To clarify this is not a dichotomy, 1) and 2) can happen simultaneously, and of course this leads to more fun!
Details of the implementation can be found at lam.io/projects/slice.
Running
$ npm i
$ node_modules/.bin/webpack
Open public/index.html
. Enjoy!