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Is there any Roman typeface that had been influenced by the style of the Asian typeface?
Well, there are display faces, like those pseudo Chinese brush stroke fonts so dearly loved by Chinese restaurants. Some characters in display fonts remind me of some of the Indian scripts, although I think they may also be based on 60s LSD imagery.
(Note: A discussion like this, that does not deal with Type Education, is best posted in the General Interest or Design forums, which get way more traffic. Maybe one of our sysops will move it.)