Pspsps is essential. It draws the cat's attention to you. Then you extend a hand and look at how the cat's reacting to it. You can tell with great accuracy how interested the cat is in being pet by you, just by watching that. Works great for me. And believe me, as a resident of İstanbul for more than two decades, I have considerable experience with stray cats. I have honed my stray cat petting skills by going out of my way to interact with most of the cats I see on the streets, which is of course a rather large number of cats because İstanbul.