"Mr" <nomail@nomail> wrote:
> Sorry for what may sound like a very basic question : Apart from their names I'm
> not sure to fully grasp the distinction between an isosurface and a
> parametric... Could you clarify the difference? the paradigms for when to best
> use one over the other? is it that one is a surface and the other a volume?

I would say that primarily, from an implementation perspective, the difference
is that an isosurface evaluates an implicit function - an ordinary function with
terms in x, y, and z - and it's a surface where that equation equals the
threshold value.

A parametric evaluates the x, y, and z coordinates as functions of the
parameters u and v, and is a surface as well.

They are both slow, or can be, depending on the settings, and the complexity of
the equations.

So generally, it's a matter of how you conceive of the math(s) involved, and/or
whether or not it's even possible to (efficiently) express the desired shape in
either implicit or parametric form.

A good exercise would be to make a sphere object, using small sphere{}
primitives to "plot" the points on its surface.
Do it "the isosurface way" using r=sqrt(pow(x,2)+pow(y,2)+pow(z,2)),

and "the parametric way" using
x = cos (u) * sin (v)
y = sin (u) * sin (v)
z = cos (v)

Where u goes from 0 to tau, and v goes from 0 to pi

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