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What does Explicit Form, Implicit Form and Parametric Form mean in Virtual Reality Modeling (screenshot attached)

What does Explicit Form, Implicit Form and Parametric Form mean in Virtual Reality Modeling?
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whatisittellme

in the following link : http://arxiv.org/html/cs.GR/0512098

see equations (1) through (6). They pretty much explain what explicit, implicit and parametric forms mean in general (and in modeling too).
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I cant really understand that text... I am a noobie to the subject :(

I dont understand that formula (1)?
it also doesnt explain what parametric form is.. it just says it easier to use to represent an object in 3D space rather than implicit form whatever that is :)
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thats perfect..
exactly the help I was looking for
thanks a million