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

This is shown in the screenshot attached

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This is shown in the screenshot attached

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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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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 !