It's super nit-picky of me to point out: the double and add visualization is a meme among professional elliptic curve guys. You are in fact drawing a hyperbola

It's super nit-picky of me to point out: the double and add visualization is a meme among professional elliptic curve guys. You are in fact drawing a hyperbola between points on an (almost) circular plane. However, you won't find this published anywhere idk why. It's just one of those things you get from spending 3 years in office hours with the 73 year old math professor who's worked on elliptic curves since they became mainstream in the 1980's.