 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
In a book I'm reading, there is a nice 3d shape which the book says is the
result of the equation:
x^3 + y^3 = 1
However, it comments "x and y are regarded as complex variables".
What does a complex variable mean in this context and what would be the
iso-surface function for the above?
Many thanks in anticipation...
--
"To stop children being afraid of the dark, try to fill their daylight hours
with as much terror as possible"
www.tomandlu.co.uk
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Tom Melly wrote:
>
> In a book I'm reading, there is a nice 3d shape which the book says is the
> result of the equation:
>
> x^3 + y^3 = 1
>
> However, it comments "x and y are regarded as complex variables".
>
> What does a complex variable mean in this context
A complex variable is a variable that holds a a number that has the form
"a + bi", where i is an imaginary number defined as sqrt(-1).
> and what would be the
> iso-surface function for the above?
I could be wrong, but I don't think isos work with complex numbers and
since both x and y are two-dimensional values, it makes the function
describe a 4D shape, which I know isos don't understand.
--
Francois Labreque | The surest sign of the existence of extra-
flabreque | terrestrial intelligence is that they never
@ | bothered to come down here and visit us!
videotron.ca | - Calvin
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Cubic julia fractal?
--
David Fontaine <dav### [at] faricy net> ICQ 55354965
My raytracing gallery: http://davidf.faricy.net/
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Tom Melly wrote:
>
> In a book I'm reading, there is a nice 3d shape which the book says is the
> result of the equation:
>
> x^3 + y^3 = 1
>
> However, it comments "x and y are regarded as complex variables".
>
> What does a complex variable mean in this context and what would be the
> iso-surface function for the above?
>
> Many thanks in anticipation...
There is too little information to give you an answer. What I see is a
complex function which depends on four real variables with a real
constraint. I can't imagine how this could be used in a iso-surface. Is
there any other information in your book about how the shape was constructed?
If not, you could contact the author(s) and ask.
Regards, Alberto.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Thinking a little bit further, you can consider that you have a complex
restriction. In this case, your question has many answers. One solution is
x^3 - 3*x*y^2 - sqrt(3)*z^2*sqrt((-3*x^2*y + y^3 + z^3)/z) +
((-3*x^2*y + y^3 + z^3)/z)^(3/2)/(3*sqrt(3)) = 1
Alberto.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
> I don't think isos work with complex numbers
So you can't do iso-mandelbrots?
Nekar
--
#version unofficial MegaPov 0.7;#local Q=seed(7);#local S=<-2,2,5>;#local
E=<2
,-2,5>;#local B=S;#while(vlength(B-E)>.1)#local
B=(B+(<rand(Q),rand(Q),rand(Q)
>/20));#local B=B-(2*(B-S))*((vlength(B-E)>vlength(S-E)));#local
S=B;glow{//NX
location S size.1 radius.07}glow{location S size.1 radius.07 rotate
z*90}#end
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Nekar Xenos" <j-p### [at] citywalkcoza> wrote in message
news:3af65116@news.povray.org...
>
> > I don't think isos work with complex numbers
>
> So you can't do iso-mandelbrots?
>
Well, you can't have iterations in an iso. I've wondered if, provided you
were willing to accept a fairly low number of iterations, it would still be
possible by nesting the iterations (which would no longer be iterations).
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Tom Melly <tom### [at] tomandlucouk> wrote:
> Well, you can't have iterations in an iso. I've wondered if, provided you
> were willing to accept a fairly low number of iterations, it would still be
> possible by nesting the iterations (which would no longer be iterations).
Well, I believe you can trick POV into using recursive functions, you
need to break the recursion using the if() "function". You have to
declare the function as something else first, a completely empty function
will work, then you follow it with a recursive declaration.
--
Christopher James Huff - chr### [at] maccom
Home Page: http://homepage.mac.com/chrishuff/
POV-Ray TAG e-mail: chr### [at] povrayorg
POV-Ray TAG web site: http://tag.povray.org/
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Chris Huff" <chr### [at] maccom> wrote in message
news:3af7cbc7@news.povray.org...
>
> Well, I believe you can trick POV into using recursive functions, you
> need to break the recursion using the if() "function". You have to
> declare the function as something else first, a completely empty function
> will work, then you follow it with a recursive declaration.
>
Can you post a small sample of this?
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Tom Melly wrote:
>
> "Nekar Xenos" <j-p### [at] citywalkcoza> wrote in message
> news:3af65116@news.povray.org...
> >
> > > I don't think isos work with complex numbers
> >
> > So you can't do iso-mandelbrots?
> >
>
> Well, you can't have iterations in an iso. I've wondered if, provided you
> were willing to accept a fairly low number of iterations, it would still be
> possible by nesting the iterations (which would no longer be iterations).
If you get last version of POVMan, then you can use specific shader type
iso_function for isosurface potential calculation. Shader language
supports for and while cycles, so it is quite easy write 'recursive'
iso-functions. POVMan documentation contains example of menger sponge,
where you can specify iteration depth by setting shader input parameter
and watch, how sponge disappears...
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
