How can I determine all the codepoints that do not have glyphs in a font using FreeType?

Question

This question is closely related to

http://stackoverflow.com/questions/103725/is-there-a-way-to-programatically-determine-if-a-font-file-has-a-specific-unicode

However, I am looking for a solution that does not use the Windows API. Freetype in particular looks promising, and I was wondering if anyone familiar with it could provide pointers.

Basically, I'd like to, given a font, calculate a mapping from character map to a sequence of codepoints without glyphs for that character map.