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How "should" an isosurface respond when there is an undefined region of
space?
I just ran something like
function{noise3d(x^0.5/constant , y/constant , z/constant}
. The result is symmetric about the x-axis!
Is this an algorithm mistake?
Did pov just uncover a great secret of mathematics: all this fuss over
the square root of negative numbers was a tempest in a teapot??
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From: david sharp
Subject: Re: Square roots of negative numbers in isosurfaces?
Date: 10 Jan 2000 10:55:10
Message: <387a00de@news.povray.org>
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Greg M. Johnson <gre### [at] my-dejanews com> wrote in message
news:3879E51F.77B9A241@my-dejanews.com...
> How "should" an isosurface respond when there is an undefined region of
> space?
>
> I just ran something like
> function{noise3d(x^0.5/constant , y/constant , z/constant}
> . The result is symmetric about the x-axis!
>
> Is this an algorithm mistake?
*I* wouldn't want to get an error every time I had an isosurface
do (-1)^.5, but I think this is a very debatable topic.
What would you like the program to do in this case?
The isosurface stuff converts x to absolute value of x
before trying to use the ^. This is just to avoid many floating
point errors. The isosurface code does the same conversion
before applying sqrt() or ln().
Personally I think its OK, (but perhaps the program should put out
a warning). If you look at isosurface scenes posted in these newsgroups,
you will find a lot of square roots and logs of negative numbers being done,
and a lot of this is probably being done completely oblivious to the
mathematical inconsistency.
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From: Ron Parker
Subject: Re: Square roots of negative numbers in isosurfaces?
Date: 10 Jan 2000 11:02:27
Message: <387a0293@news.povray.org>
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On Mon, 10 Jan 2000 10:55:52 -0500, david sharp wrote:
>The isosurface stuff converts x to absolute value of x
>before trying to use the ^. This is just to avoid many floating
>point errors. The isosurface code does the same conversion
>before applying sqrt() or ln().
Does it only do that for fractional exponents, or does it also
do it for odd integer exponents?
--
These are my opinions. I do NOT speak for the POV-Team.
The superpatch: http://www2.fwi.com/~parkerr/superpatch/
My other stuff: http://www2.fwi.com/~parkerr/traces.html
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From: david sharp
Subject: Re: Square roots of negative numbers in isosurfaces?
Date: 10 Jan 2000 11:45:33
Message: <387a0cad@news.povray.org>
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david sharp <dsh### [at] interportnet> wrote in message
news:387a0473@news.povray.org...
>
> Ron Parker <ron### [at] povrayorg> wrote in message
> news:387a0293@news.povray.org...
> > On Mon, 10 Jan 2000 10:55:52 -0500, david sharp wrote:
> > >The isosurface stuff converts x to absolute value of x
> > >before trying to use the ^. This is just to avoid many floating
> > >point errors. The isosurface code does the same conversion
> > >before applying sqrt() or ln().
> >
> > Does it only do that for fractional exponents, or does it also
> > do it for odd integer exponents?
>
> Always.
No, not always. (I should have actually checked before replying)
there is a ffloor test to distinguish integers from fractions.
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Are you sure?
function {noise3d(x ^0.5, y, z)}, I know, is symmetric about the x=0
plane.
function {noise3d(x^3.0, y, z)}, I will bet, behaves correctly, and has
a kind of symmetry like the curve y=x^3.
There is something "more wrong" here. If Ron were correct, then x^3
would also be symmetric about x=0.
david sharp wrote:
> david sharp <dsh### [at] interportnet> wrote in message
> news:387a0473@news.povray.org...
> >
> > Ron Parker <ron### [at] povrayorg> wrote in message
> > news:387a0293@news.povray.org...
> > > On Mon, 10 Jan 2000 10:55:52 -0500, david sharp wrote:
> > > >The isosurface stuff converts x to absolute value of x
> > > >before trying to use the ^. This is just to avoid many floating
> > > >point errors. The isosurface code does the same conversion
> > > >before applying sqrt() or ln().
> > >
> > > Does it only do that for fractional exponents, or does it also
> > > do it for odd integer exponents?
> >
> > Always.
>
> No, not always. (I should have actually checked before replying)
> there is a ffloor test to distinguish integers from fractions.
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From: david sharp
Subject: Re: Square roots of negative numbers in isosurfaces?
Date: 10 Jan 2000 23:17:20
Message: <387aaed0@news.povray.org>
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Greg M. Johnson wrote:
> Are you sure?
Sure about what?
> function {noise3d(x ^0.5, y, z)}, I know, is symmetric about the x=0
> plane.
Because x^.5 actually does (abs( x))^.5
(calling the C function pow(abs(x),.5) )
> function {noise3d(x^3.0, y, z)}, I will bet, behaves correctly, and has
> a kind of symmetry like the curve y=x^3.
Because x^3.0 actually does x*x*x
> There is something "more wrong" here. If Ron were correct, then x^3
> would also be symmetric about x=0.
Ron didn't claim x^3 was (abs(x))^3. I prematurely did claim that, and
I was horribly, sorrowfully, and disgustingly mistaken.
> david sharp wrote:
>
> > david sharp <dsh### [at] interportnet> wrote in message
> > news:387a0473@news.povray.org...
> > >
> > > Ron Parker <ron### [at] povrayorg> wrote in message
> > > news:387a0293@news.povray.org...
> > > > On Mon, 10 Jan 2000 10:55:52 -0500, david sharp wrote:
> > > > >The isosurface stuff converts x to absolute value of x
> > > > >before trying to use the ^. This is just to avoid many floating
> > > > >point errors. The isosurface code does the same conversion
> > > > >before applying sqrt() or ln().
> > > >
> > > > Does it only do that for fractional exponents, or does it also
> > > > do it for odd integer exponents?
> > >
> > > Always.
> >
> > No, not always. (I should have actually checked before replying)
> > there is a ffloor test to distinguish integers from fractions.
>
>
>
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Actually, I think that this is what povray does:
if I say, noise3d (x^a , y,z)
it processes noise3d (sign(x)*pow(abs(x),a), y,z)
I will try to prove this tonight.
[I thought someone had asked what SHOULD it do--was that note deleted?] If
povray processes the formula above as I described, there's no problem--it was
just a mystery to be solved . . .
david sharp wrote:
> > function {noise3d(x^3.0, y, z)}, I will bet, behaves correctly, and has
> > a kind of symmetry like the curve y=x^3.
>
> Because x^3.0 actually does x*x*x
>
> > There is something "more wrong" here. If Ron were correct, then x^3
> > would also be symmetric about x=0.
>
> Ron didn't claim x^3 was (abs(x))^3. I prematurely did claim that, and
> I was horribly, sorrowfully, and disgustingly mistaken.
>
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From: Ron Parker
Subject: Re: Square roots of negative numbers in isosurfaces?
Date: 11 Jan 2000 15:38:34
Message: <387b94ca@news.povray.org>
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On Tue, 11 Jan 2000 15:23:26 -0500, Greg M. Johnson wrote:
>Actually, I think that this is what povray does:
>
>if I say, noise3d (x^a , y,z)
>it processes noise3d (sign(x)*pow(abs(x),a), y,z)
>
>I will try to prove this tonight.
>[I thought someone had asked what SHOULD it do--was that note deleted?] If
>povray processes the formula above as I described, there's no problem--it was
>just a mystery to be solved . . .
Well, there's that little problem of x^2+y^2+z^2-1 (threshold 0) not being a
sphere anymore, but other than that...
--
These are my opinions. I do NOT speak for the POV-Team.
The superpatch: http://www2.fwi.com/~parkerr/superpatch/
My other stuff: http://www2.fwi.com/~parkerr/traces.html
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Okay, how about:
x^a = sign(x)^int(a) * pow(abs(x), a) ?
Povray is doing SOMETHING, as it gives me a picture in a mathematically undefined
region of space! It was driving me crazy to figure out what it was doing . . .
Ron Parker wrote:
> Well, there's that little problem of x^2+y^2+z^2-1 (threshold 0) not being a
> sphere anymore, but other than that...
>
> --
> These are my opinions. I do NOT speak for the POV-Team.
> The superpatch: http://www2.fwi.com/~parkerr/superpatch/
> My other stuff: http://www2.fwi.com/~parkerr/traces.html
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What I think POV *should* do is not include these areas in the graph. Say I
want to graph a hemisphere on my TI-89, I do x^2+y^2+z^2=1, z^2=-x^2-y^2+1,
z=sqrt(1-x^2-y^2), and graph it and it gives me my hemisphere, and the area
*outside* the hemisphere is ignored (not rendered) because it is sqrt(neg).
Because if people want it to work the other way they can always just make
it sqrt(abs(x)) instead of sqrt(x).
--
Homepage: http://www.faricy.net/~davidf/
___ ______________________________
| \ |_ <dav### [at] faricynet>
|_/avid |ontaine <ICQ 55354965>
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