I've found interesting to put a Peano's 2D Space-Filling Curve
on a height_field. Here it is.

Can anybody share ideas about where such a thing will be useful?


Gleb

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Gleb schrieb:

> I've found interesting to put a Peano's 2D Space-Filling Curve
> on a height_field. Here it is.
>

What exactly is a Peano 2D Space-Filling Curve?

>
> Can anybody share ideas about where such a thing will be useful?
>

Well, it does look like a pretty good terrain at least... ;)

Tim

--
Tim Nikias
Homepage: http://www.digitaltwilight.de/no_lights/index.html

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>What exactly is a Peano 2D Space-Filling Curve?
Well, it is a fractal curve which fill the 2D space
without holes. What is actually interesting:
it passes successively through neighbouring cells of a matrix.

You can try to look at examples e.g. here:

http://www.cut-the-knot.com/Curriculum/Geometry/Peano.html


atb,
Gleb
>
> What exactly is a Peano 2D Space-Filling Curve?
>
> Tim Nikias

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"Tim Nikias" <tim### [at] gmxde> ha scritto nel messaggio
news:3C4DC081.80FE4AB1@gmx.de...
> What exactly is a Peano 2D Space-Filling Curve?

A parametric curve G: [a,b] --> [x0,x1] x [y0,y1], iniective (but I'm not sure about
it) and, which is important, suriective. The English terms might differ from the
Italian ones so forgive me if what I've written sounds non-sense to you ;)
Well, I'm not sure whether what I've written has sense at all, but, to make a long
story short, Peano Curve is a curve whose support (again directly translated from an
Italian term) is a completely filled square.

--
#local j=text{ttf"arial""JRG".2,0}#local J=0;#while(J<10)#local R=0;#while
(R<2)#local G=0;#while(G<1)#if(inside(j<R,G.1>))object{j scale.025translate
<R-1G-J/20J/-40+2>pigment{rgb<9J>}}#debug"O"#else#debug" "#end#local G=G+
.025;#end#local R=R+.05;#debug"\n"#end#local J=J+1;#end// JRG

Home: http://digilander.iol.it/jrgpov  //New: Kitchen scene WIP

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very cool. it looks like the pelt of something prickly.



Gleb <gk1### [at] sotonacuk> wrote in message news:3c4dbf39@news.povray.org...
> I've found interesting to put a Peano's 2D Space-Filling Curve
> on a height_field. Here it is.
>
> Can anybody share ideas about where such a thing will be useful?
>
>
> Gleb
>
>
>

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"Ross Litscher" <lit### [at] osuedu> wrote in message
news:3c4dd986$1@news.povray.org...
> very cool. it looks like the pelt of something prickly.
Thanx. Hedgehog maybe?

Gleb

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"JRG" <jrg### [at] hotmailcom> wrote in message
news:3c4dcf33@news.povray.org...
> "Tim Nikias" <tim### [at] gmxde> ha scritto nel messaggio
> news:3C4DC081.80FE4AB1@gmx.de...
> > What exactly is a Peano 2D Space-Filling Curve?
>
> A parametric curve G: [a,b] --> [x0,x1] x [y0,y1], iniective (but I'm not
sure about
> it) and, which is important, suriective. The English terms might differ
from the

As I vaguely recall from my mathematical analysis courses, there cannot be a
continuous space-filling curve which is injective and surjective at the same
time. But I may be wrong...

Fernando.

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Yes, you're right. In fact I wasn't even sure about it.

--
#local j=text{ttf"arial""JRG".2,0}#local J=0;#while(J<10)#local R=0;#while
(R<2)#local G=0;#while(G<1)#if(inside(j<R,G.1>))object{j scale.025translate
<R-1G-J/20J/-40+2>pigment{rgb<9J>}}#debug"O"#else#debug" "#end#local G=G+
.025;#end#local R=R+.05;#debug"\n"#end#local J=J+1;#end// JRG

Home: http://digilander.iol.it/jrgpov  //New: Kitchen scene WIP


news:3c4e48a9@news.povray.org...
>
> "JRG" <jrg### [at] hotmailcom> wrote in message
> news:3c4dcf33@news.povray.org...
> > "Tim Nikias" <tim### [at] gmxde> ha scritto nel messaggio
> > news:3C4DC081.80FE4AB1@gmx.de...
> > > What exactly is a Peano 2D Space-Filling Curve?
> >
> > A parametric curve G: [a,b] --> [x0,x1] x [y0,y1], iniective (but I'm not
> sure about
> > it) and, which is important, suriective. The English terms might differ
> from the
>
> As I vaguely recall from my mathematical analysis courses, there cannot be a
> continuous space-filling curve which is injective and surjective at the same
> time. But I may be wrong...
>
> Fernando.
>

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