Separating Axis Theorem

The SAT states that two convex objects do not overlap if there exists a line (called an axis) onto which the two objects' projections do not overlap.

Disclaimer: obviously this is only a quick prototype/poc just for the fun of it.

SAT steps in general

Define or generate the vertex vectors of the tested polygons;
Calculate the edge vectors of the polygons, based on the vertices;
Calculate the normal vectors of the polygons (the vectors perpendicular to the edges);
Project the vertices of the polygons onto the normal vectors;
Select the min and max projection values of the tested polygons;
Compare the min and max projection values of the polygons to check if these overlap;
If the all projections on all normal vectors overlap, a separating axis can not be drawn between the polygons, and the objects collide;
Optionally calculate the MTV (minimum translation vector) to be able to compensate for the overlap.

Bail out as soon as one of the projections doesn't overlap (the Array.prototype.every function used here already takes care of that);
Regular polygons with an even amount of vertices only need half of their projections checked;
Use a quick precheck on the bounding box of each polygon to filter out cases that could not possibly overlap;
Concave polygons could potentially be tested by splitting these up into convex polygons first.