Ah, it's much as I suspected. That's pretty cool.

Notice that this
> does not work properly for functions with zero gradients; you should
detect
> that and deal with it appropriately.


How would it be possible to have a point on the surface of the object with
zero gradient in any direction? Unless the function were something like
function (x,y,z) {0}... where every point of the function is part of the
surface, which would be sort of a strange case...

--
- Slime
[ http://www.slimeland.com/ ]
[ http://www.slimeland.com/images/ ]
"Ron Parker" <ron### [at] povrayorg> wrote in message
news:slr### [at] fwicom...
> On Tue, 30 Oct 2001 09:44:11 -0500, Dave Dunn wrote:
> >
> >
> > Slime wrote:
> >
> >> >   "How do I calculate the normal vector of an isosurface function at
a
> >> > certain point <x,y,z>?", for example.
> >>
> >> Now *there's* a question that's been plaguing me for a while. I'll ask
it
> >> later. =)
> >
> > I'll be watching for the answer to that one myself, as it is holding up
> > isosurface support for POVGUI. I suspect it involves using trace...
>
> Well, if you know how to take the derivative of the function, you just use
> the gradient vector, which is < df/dx, df/dy, df/dz > where "d" is really
> the lowercase delta we use to indicate partial derivatives.
>
> Since we're talking about arbitrary functions here, you can approximate
the
> gradient by using this:
>
> #declare d = 1e-5; //(some small number; POV uses the accuracy value)
> #declare Gradient=vnormalize(<F(X+d,Y,Z),F(X,Y+d,Z),F(X,Y,Z+d)>-F(X,Y,Z));
>
> This is what POV does.  As the comment says, we use the value you
specified
> for the accuracy of the isosurface to do the computation.  Notice that
this
> does not work properly for functions with zero gradients; you should
detect
> that and deal with it appropriately.
>
> --
> #macro R(L P)sphere{L __}cylinder{L P __}#end#macro P(_1)union{R(z+_
z)R(-z _-z)
> R(_-z*3_+z)torus{1__ clipped_by{plane{_ 0}}}translate z+_1}#end#macro
S(_)9-(_1-
> _)*(_1-_)#end#macro Z(_1 _
__)union{P(_)P(-_)R(y-z-1_)translate.1*_1-y*8pigment{
> rgb<S(7)S(5)S(3)>}}#if(_1)Z(_1-__,_,__)#end#end Z(10x*-2,.2)camera{rotate
x*90}

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