The actual national qualification system is more complicated than what I posted (a diver has to finish top16 in 2016 world cup and finish top12 in an imaginary list of world cup semifinalists, which excludes divers from nations winning quotas at 2015 world championships and asian cup)
2012 qualification rule was more severe(a diver had to finish top 3 in a list of 2012 world cup semifinalists, which excluded already-qualified divers, so Sakai was placed fourth in the list)
Sorry for my confusing post