I read about Simple Stupid Funnel Algorithm at http://digestingduck.blogspot.com/2010/03/simple-stupid-funnel-algorithm.html
That article made sense to me. You maintain one line to the left wall and one line to the right wall. When they cross in updating then you know part of the shortest path has been found.
I was reading the thesis of Douglas Jon Demyen https://skatgame.net/mburo/ps/thesis_demyen_2006.pdf
On pages 52 to 57 he describes a funnel filter algorithm using a deque. Is there anyone who understands the pseudo code he gives. The notation he uses is left unexplained. I don't understand how the code he gives works.