Difference between "before" and "in front of"

Which one is correct?

The patterns swam before her eyes.

OR

The patterns swam in front of her eyes.

I know that "before" is mostly used when we talk about the time, but is it right to use "before" when we talk about space? I'm most interested in spoken usage.

Certainly. The ways in which prepositions are used in English - and probably in other languages - are numerous and often bewildering. I was about to add idiosyncratic, but there is probably a logical explanation behind even the most idiomatic usages, perhaps lost in time. Some grammarians have said that prepositions constitute a class of words both semantic and functional. Prepositional usages are sometimes graded:

central (locative, directional; temporal) (eg on the bed, to the park; before midnight)

semi-idiomatic (eg on the train, at a loss)

peripheral (eg on fire)

As you suggest, before has a locative sense, synonymous with the three-word (sometimes termed 'complex') preposition in front of. Using the word idiomatic in its other main sense now (in common use in the common register), in front of is the more idiomatic of the two choices - before sounds rather poetic, of a slightly refined register.

Both are correct and mean the same thing. Here before simply means in front of.

These are synonyms do represent two different ideas:

I stand in front of the court.

And

I stand before the court.

The first implies location and direction while the other implies "in the presence".

Similarly,

before my eyes

Implies presence while

In front of my eyes

Implies location. The former would mean that it happened and you were participant if only as an observer. The latter implies that there was something flitting around (think fly, blindfold, or glasses).

Should also note: you'd generally not say, "before" unless it is in the context of people (or animals). "Before the chair" implies time or direction along a route (there is also a sense of "after" in both cases).