Jesper Cook and Gary Katz have produced a fine remake of Jesper's JLC article on tricky miters, or "hunting miters" as they are formally called, that deserves lots of attention. This is a great in-depth piece on THISisCarpentry that adds a lot of context, insight, and references that trim-carpentry addicts of all stripes will relish.
Like a lot of carpenters, I’ve cut countless miters in arched door and window casings. But like every other carpenter, I’ve also noticed that the details in the molding profiles never seem to mate-up perfectly. Even when the short points and long points meet, and the joint is air-tight! Like those carpenters, I’ve also put in my share of time when it comes to carving and sanding those profiles to make the transitions look acceptable.
However, when the molding transitions from straight to curved at a more acute angle, typically on chair rail or panel molding…forget about it! No amount of sanding and carving will solve the problem adequately, at least not on the high-end jobs where I work. A hunting miter is a better choice.