The biggest modern movie co-production between a U.S. studio and China had access to spectacular locations under censors' watchful eye. For years, Sony Pictures considered—and then decided against—updating "The Karate Kid," its beloved 1984 family film about a browbeaten kid (Ralph Macchio) with a single mom and the enigmatic martial arts coach (Noriyuki "Pat" Morita) who teaches the boy how to believe in himself, catch a fly with chopsticks and kick some bully butt along the way.