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13 Aug 2022 05:45:32 EDT (-0400)
  Celtic knots (Message 4 to 13 of 13)  
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From: BayashiPascal
Subject: Re: Celtic knots
Date: 23 Dec 2021 19:45:00
Message: <web.61c517849e179f66c7449d78e0f8c582@news.povray.org>
"Mediat" <med### [at] hotmailfr> wrote:
> I'll be glad to answer every question you have, basically I used the algorithm
> described on page 33 of https://www.maths.ed.ac.uk/~v1ranick/knots/celtic.pdf to
> build an array of "codes" (1= left, 2= up, 4=right, 8= down) each code + (i+j)%2
> (where i and j are the coordintes in the array),  gives the kind of brick and
> its orientation.
>
> for instance the array of the lower left knot is :
>
> 3 2 2 2 2 6
> 1 0 0 0 4 5
> 1 0 0 0 4 5
> 5 1 0 0 0 4
> 5 1 0 0 0 4
> 9 8 8 8 8 12
>
> Do not hesitate to ask ...

Hi Mediat,
Thanks for the link. Knot theory is not my cup of tea but that looks an
interesting read. I keep it for reference and hope to have time later to dive
into it.
The algorithm on p.33 is a nice one: simple and efficient ! However I can't see
if the authors also give instructions on how to place the barriers at the
beginning of the algorithm (I confess I haven't spent much time looking for it).
How have you done yourself ? Do you set them manually ?
Regards,
Pascal


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From: Mediat
Subject: Re: Celtic knots
Date: 26 Dec 2021 02:45:00
Message: <web.61c81c919e179f6611d3eb285020ebe1@news.povray.org>
Hi Pascal,

In the algorithm you can place the barriers wherever you want as long as you
respect the rules.
In my program, so far, you choose the symetries you want, then the process is
random.

Best regards and happy new year


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From: Paolo Gibellini
Subject: Re: Celtic knots
Date: 27 Dec 2021 06:28:07
Message: <61c9a347@news.povray.org>
Il 22/12/2021 14:54, Mediat ha scritto:
 > Hi every one
 >
 > To learn about Celtic knot : https://en.wikipedia.org/wiki/Celtic_knot
 >
 > Basically, to draw a celtic knot you need to handle 4 different 
shapes (the
 > building blocks) that we call "brick":
 >
 > 1) the "corner" (from the center of a side to the center of an 
adjacent side)
 > which exists in two different directions.
 > 2) the "straight" (from the center of a side to the center of the 
opposite side)
 > which exists in two different directions.
 > 3) the "diagonal" (from a vertex to the opposite vertex) which exists 
in two
 > different directions.
 > 4) the "bend" (from a vertex to the center of a non adjacent side) 
which exists
 > in eight different directions/symmetries.
 >
 > In my generator I designed 8 different types of straights and 
diagonals, 4
 > different types of corners and 4 different types of bends.
 >
 > I added to the previous bricks,
 > 1) 5 different types of "crossings" (the way the cords crosses), one 
of them is
 > the historical crossing: one cord goes over the other one.
 > 2) 5 different types of "muffs"  (the way a bend connects to another 
brick on
 > its ends tha lies on a side)
 >
 > Before I publish the program I'm eager to answer questions and more 
than that,
 > to read remarks and requests.
 >
 > For the time being the program deals only with rectangular shapes, it 
should be
 > feasible to enhance it to handle rectangular shapes with rectangular 
holes, but
 > not to handle circles or triangles.

A very nice work!
The flat crossings seem more realistic, are you also able to rise up the 
crossings of the cylindrical ropes?

Paolo


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From: Mediat
Subject: Re: Celtic knots
Date: 27 Dec 2021 08:30:00
Message: <web.61c9bfa99e179f6611d3eb285020ebe1@news.povray.org>
> The flat crossings seem more realistic, are you also able to rise up the
> crossings of the cylindrical ropes?


Hi Paolo,

I Hope this image is the right answer

Best regards

Philippe


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From: Paolo Gibellini
Subject: Re: Celtic knots
Date: 31 Dec 2021 06:59:51
Message: <61cef0b7$1@news.povray.org>
Il 27/12/2021 14:29, Mediat ha scritto:
 >
 >> The flat crossings seem more realistic, are you also able to rise up the
 >> crossings of the cylindrical ropes?
 >
 >
 > Hi Paolo,
 >
 > I Hope this image is the right answer
 >
 > Best regards
 >
 > Philippe

Really nice!

Paolo


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From: Bald Eagle
Subject: Re: Celtic knots
Date: 8 Jan 2022 11:40:00
Message: <web.61d9bd329e179f661f9dae3025979125@news.povray.org>
"Mediat" <med### [at] hotmailfr> wrote:

> Before I publish the program I'm eager to answer questions and more than that,
> to read remarks and requests.

This is very nice.   I'm interested in seeing less-square, more-rectangular
shapes, and some directed-path examples, such as an excluded center (a knotwork
border) and maybe some sort of X or cross where the edge centers or corners are
excluded.

Could this be used to generate a tilable pattern, such as to cover a plane or
UV-map a cylinder?

Thanks!


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From: Mediat
Subject: Re: Celtic knots
Date: 10 Jan 2022 05:15:00
Message: <web.61dc07199e179f6611d3eb285020ebe1@news.povray.org>
Hi Eagle (I'm the bald one ;-))

1) Here is an example of a rectangular shape.
2) Crosses and holes shoud be easy to add
3) A tilable pattern should be easy to create as we can enforce X and Y symmetry


I must admit that I don't feel very motivated to enhance my program as it
doesn't seem to interest many people

Thanks for your interest

Best regards

Philippe


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From: Mediat
Subject: Re: Celtic knots
Date: 10 Jan 2022 16:00:00
Message: <web.61dc9d629e179f6611d3eb285020ebe1@news.povray.org>
Hi Bald

I couldn't resist;-)

Best regards

Philippe


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From: Bald Eagle
Subject: Re: Celtic knots
Date: 10 Jan 2022 18:05:00
Message: <web.61dcbb2b9e179f661f9dae3025979125@news.povray.org>
"Mediat" <med### [at] hotmailfr> wrote:
> Hi Bald
>
> I couldn't resist;-)
>
> Best regards
>
> Philippe

Nice.
I did a search, figuring that someone had covered this topic before.   The only
thing I found was a post from Mike Williams 20 years ago.    Then there's the
usual KnotPlot, etc that export to POV-Ray.

Now, with regard to interest, keep in mind that you're currently in a
microscopic corner of the internet here, and you might try showing off your
renders in some other venues, especially if there are sites where people would
have a _specific_ interest in celtic knotwork.

I've laid out a few of these by hand, and the usual method employs some gridwork
and "walls" to break up the plait.  Thinking about it from that aspect, it would
be like a maze-solving algorithm.

Also, folks interesting in generating custom celtic knotwork would likely want
to print the result out in the more typical 2D B&W format with the
over-and-under effect represented by simple whitespace.  I guess an orthographic
camera and a flat black cylinder on a white background would accomplish that.

- BW


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From: Mediat
Subject: Re: Celtic knots
Date: 11 Jan 2022 10:30:00
Message: <web.61dda2429e179f6611d3eb285020ebe1@news.povray.org>
Just because I like it ;-)


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