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

Posted on 2009-05-18
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What does Explicit Form, Implicit Form and Parametric Form mean in Virtual Reality Modeling?
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Question by:jtiernan2008
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by:whatisittellme
ID: 24415167
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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by:jtiernan2008
ID: 24415252
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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whatisittellme earned 2000 total points
ID: 24415382
ok, lemme try explaining :)

lets use circle equation: x^2 + y^2 = 1 for explaining each of the forms

explicit form:
eg: y = f(x) ; means that one variable is expressed as a function of other variables explicitly.
** for circle ** : x = sqrt(1-y^2)  this is explicit form .... where sqrt = square root.

implicit form:
eg: f(x,y)=0; an equation containing both the variables is used. one variable is NOT explicitly mentioned in interms of the other.
** for circle ** : x^2 + y^2 = 1 is implicit form. the relationship between x and y is not mentioned explicit. it is mentioned implicitly.

parametric form:
x = f(t);  y = g(t); a different value called parameter is chosen such that both the vaiables x ans y can be expressed using the parameter.
for circle example the parametric equations would be : x = r*cos(t) ; y = r*sin(t)
note that the relation x^2 + y^2 =1 still holds true. it is just a different form of representation.

hope that helps you understand difference between three forms of representation !
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by:jtiernan2008
ID: 31582715
thats perfect..
exactly the help I was looking for
thanks a million
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