Tom Melly wrote:
> 
> "Christoph Hormann" <chr### [at] gmxde> wrote in message
> news:3A6437A2.950441F9@gmx.de...
> >
> >
> > Saadat Saeed wrote:
> > >
> > > What exactly is an isosurface?????
> >
> 
> An isosurface is the result of using a function to define a surface. It
> essentially has two parts - the function and the threshold.
> 
> The simplest isosurface would be x^2, y^2, z^2 threshold 1.
> 
> This would produce a sphere, centered at <0,0,0> with a radius of 1 unit.
> Why? Well, take the point <0,1,0>. Using our function, we get 0^2 + 1^2 +
> 0^2 = 1, which would mean that the point <0,1,0> is on the surface of our
> isosurface. The same will be true of any vector consisting of 2 zero vals
> and one one val (and, needless to say, many other points - eg.
> <0,0.707,0.707>  or <0.577, 0.577, 0.577> (approx.;)).
> 
> So an isosurface is a shape defined by those points that, when passed to a
> function, return the threshold.
> 
> An iso-pigment is similiar, but, rather than concentrating on a specific
> threshold,  the product of any particular point has a texture assigned to it
> by matching the result of the function applied to that particular point to a
> texture map.
> 
> It should be noted that purists always use threshold 0 - the sphere function
> rewritten for threshold 0 would be (x^2, y^2, z^2) + 1

Ahem.  x^2 + y^2 + z^2 - 1.

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