For those not familiar with crescent-stepping (as I was not, my own martial art being taekwondo rather than karate), the videos in http://dandjurdjevic.blogspot.com/2010/12/crescent-stepping.html seem to be representative.

(On a side note, academic prose is terrible at describing bodily movements. I've read it twice or thrice now and still have no idea what movements exactly the abstract is talking about besides 'longer stride length, faster walk'.)