[eat_veggies]

The algorithm of going straight until you hit a wall, and then turning a (constant) angle has some really cool properties -- some angles/starting positions will eventually let you cover the entire floor, while others will produce beautiful repeating patterns [1].

One key insight for visualizing "hitting a wall and then turning" is that you can pretend that the walls in your room are covered with mirrors that you can walk through. Hitting the wall and bouncing at an angle is equivalent to approaching the mirror at your angle, and then continuing straight through it into the mirrored side. You can verify this in your bathroom mirror by bouncing your finger off it, vs. pretending it goes straight through: in both cases, which side of the bathroom does it bounce toward?

After a finite distance of continuing straight through mirror-walls, do you end up in your original location? I.e. can you see the back of your head in the room of mirrors? If so, then you're on a periodic path, and you're not going to cover the entire floor.

[1] https://arxiv.org/pdf/1810.11310.pdf

[chris_st]

Interesting! I wonder if it matters for this case... the walls of the room aren't going to be exactly parallel (or may be a trapezoid, pentagon, or worse), the robot's wheels are going to slip somewhat on each turn so the angle turned won't always be the same, etc. Stupid real world :-)