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marabou <not### [at] available yet> wrote:
: where is the border to an advanced question.
I don't think there's a clear border. However, there are questions which
are clearly newbie and questions which are clearly advanced.
When it's not clear, just post where it better fits. :)
--
#macro N(D,I)#if(I<6)cylinder{M()#local D[I]=div(D[I],104);M().5,2pigment{
rgb M()}}N(D,(D[I]>99?I:I+1))#end#end#macro M()<mod(D[I],13)-6,mod(div(D[I
],13),8)-3,10>#end blob{N(array[6]{11117333955,
7382340,3358,3900569407,970,4254934330},0)}// - Warp -
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> "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. =)
- Slime
[ http://www.slimeland.com/ ]
[ http://www.slimeland.com/images/ ]
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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...
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My guess would be evaluating various points near a point on the surface to
determine various derivatives... but I'm not really sure...
- Slime
[ http://www.slimeland.com/ ]
[ http://www.slimeland.com/images/ ]
"Dave Dunn" <poi### [at] aolcom> wrote in message
news:3BDEBCBB.6F77D350@aol.com...
>
>
> 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...
>
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Slime wrote:
>
> My guess would be evaluating various points near a point on the surface to
> determine various derivatives... but I'm not really sure...
The easiest way is to just let an advanced user figure it out for you :)
--
Ken Tyler
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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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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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On Tue, 30 Oct 2001 10:35:04 -0500, Slime wrote:
> 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?
Nobody said it has to be a point on the surface, did they? I suppose it's
implied by the word "normal" but I thought I'd put the warning out there
anyway.
By the way, the gradient is a direction, so the phrase "zero gradient in
any direction" is meaningless.
--
#local R=<7084844682857967,0787982,826975826580>;#macro L(P)concat(#while(P)chr(
mod(P,100)),#local P=P/100;#end"")#end background{rgb 1}text{ttf L(R.x)L(R.y)0,0
translate<-.8,0,-1>}text{ttf L(R.x)L(R.z)0,0translate<-1.6,-.75,-1>}sphere{z/9e3
4/26/2001finish{reflection 1}}//ron.parker@povray.org My opinions, nobody else's
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> By the way, the gradient is a direction, so the phrase "zero gradient in
> any direction" is meaningless.
Oops, I meant "a derivative of zero in all directions."
- Slime
[ http://www.slimeland.com/ ]
[ http://www.slimeland.com/images/ ]
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