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25 Jan 2022 14:34:28 EST (-0500)
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From: Mediat
Subject: Celtic knots
Date: 22 Dec 2021 08:55:00
Message: <web.61c32e10fda6d1e911d3eb285020ebe1@news.povray.org>
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.


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knot.jpg


 

From: BayashiPascal
Subject: Re: Celtic knots
Date: 22 Dec 2021 19:25:00
Message: <web.61c3c1bc9e179f66c7449d78e0f8c582@news.povray.org>
"Mediat" <med### [at] hotmailfr> wrote:
> 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.


Well done!

Having done something similar a few weeks ago I'm curious to know how you've
implemented it. Can you give more details ?

Pascal


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From: Mediat
Subject: Re: Celtic knots
Date: 23 Dec 2021 03:55:00
Message: <web.61c4387c9e179f6611d3eb285020ebe1@news.povray.org>
> Well done!
>
> Having done something similar a few weeks ago I'm curious to know how you've
> implemented it. Can you give more details ?


Hi Pascal,

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 ...


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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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Attachments:
Download 'pv8.png' (541 KB)

Preview of image 'pv8.png'
pv8.png


 

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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