"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

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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.

-- 
Francois Labreque | Unfortunately, there's no such thing as a snooze
    flabreque     | button on a cat who wants breakfast.
        @         |      - Unattributed quote from rec.humor.funny
   videotron.ca

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Tom Melly wrote:

> The simplest isosurface would be x^2, y^2, z^2 threshold 1.

In fact the simplest isosurface would be y (or x, or z) threshold 0...
The plane isosurface is one of the most useful too, since it's the basic
substrate for adding other functions (noise, ridge multifractals etc.).

G.

--

**********************
http://www.oyonale.com
**********************
Graphic experiments
Pov-ray gallery

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"Francois Labreque" <fla### [at] videotronca> wrote in message
news:3A643F0A.F7E9F4A4@videotron.ca...

> > 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.
>

Oops... (and shouldn't that be "Eh")

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"Gilles Tran" <tra### [at] inapginrafr> wrote in message
news:3A644E20.AE2D2EF6@inapg.inra.fr...
>
> In fact the simplest isosurface would be y (or x, or z) threshold 0...
> The plane isosurface is one of the most useful too, since it's the basic
> substrate for adding other functions (noise, ridge multifractals etc.).
>

Very true - I should have said "... simplest isosurface using 3
dimensions" - and even that's a matter of opinion. After all (x,y,z) is even
simpler, but a bit boring.

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Tom Melly wrote:

> "Gilles Tran" <tra### [at] inapginrafr> wrote in message
> news:3A644E20.AE2D2EF6@inapg.inra.fr...
> >
> > In fact the simplest isosurface would be y (or x, or z) threshold 0...
> > The plane isosurface is one of the most useful too, since it's the basic
> > substrate for adding other functions (noise, ridge multifractals etc.).
> >
>
> Very true - I should have said "... simplest isosurface using 3
> dimensions" - and even that's a matter of opinion. After all (x,y,z) is even
> simpler, but a bit boring.

How about f(x,y,z) = n
But we should narrow that to "...having a defined surface" ;)

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

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