[lucideer]

I've also seen this, but in addition—and also contrary to what the article says about curving being polite—from anecdotal examples in a lot of dogs, I'd equate curving with recognition/familiarity.

If I meet a dog I know well on the street after a long absence, the dog will beeline (not immediately recognising me, but just liking to engage with humans in general), and then after being stopped in their tracks upon recognising me, immediately begin curving.