There is an algorithm for triangulating a polygon in linear time due to Chazelle (1991), but, AFAIK, there aren't any standard implementations of his algorithm in general mathematical software libraries.
Does anyone know of such an implementation?
See this answer to the question Powerful algorithms too complex to implement:
According to Skiena (author of The Algorithm Design Manual), "[the] algorithm is quite hopeless to implement."
I've looked for an implementation before, but couldn't find one. I think it's safe to assume no-one has implemented it due to its complexity, and I think it also has quite a large constant factor so wouldn't do well against O(n lg n) algorithms that have smaller constant factors.