POV-Ray : Newsgroups : povray.general : Unit cell of pavement pattern? Server Time: 15 Sep 2019 22:37:27 GMT
 Unit cell of pavement pattern? (Message 1 to 5 of 5)
 From: gregjohn Subject: Unit cell of pavement pattern? Date: 14 Aug 2019 20:25:07 Message:
```Hello, I was experimenting with the pavement pattern and number_of_sides 6.

I was trying to scale it to make its "tiles" be some precisely known size. But
for the life of me, I couldn't make it match up with any whole number fraction,
or factors of sqrt(3)/2 or pi or e!    Does anyone know a the size of the cell?
thanks.
```
 From: Le Forgeron Subject: Re: Unit cell of pavement pattern? Date: 15 Aug 2019 08:05:11 Message: <5d551237\$1@news.povray.org>
```Le 14/08/2019 Ã  22:22, gregjohn a Ã©critÂ :
> Hello, I was experimenting with the pavement pattern and number_of_sides 6.
>
> I was trying to scale it to make its "tiles" be some precisely known size. But
> for the life of me, I couldn't make it match up with any whole number fraction,
> or factors of sqrt(3)/2 or pi or e!    Does anyone know a the size of the cell?
> thanks.
>
>
You will never find it, it's too obvious.

The segment is 1 unit long.
```

Attachments:

Preview of image 'hex.png'

 From: Bald Eagle Subject: Re: Unit cell of pavement pattern? Date: 15 Aug 2019 10:20:01 Message:
```Le_Forgeron <jgr### [at] freefr> wrote:

> You will never find it, it's too obvious.
>
> The segment is 1 unit long.

That looks OK in the x direction, but in z, it's all off kilter.
I tried to puzzle it out yesterday, even looking at patterns.cpp, and doing an
overlay grid exactly like you have here, and couldn't get it to line up.
```
 From: Le Forgeron Subject: Re: Unit cell of pavement pattern? Date: 15 Aug 2019 11:29:38 Message: <5d554222\$1@news.povray.org>
```Le 15/08/2019 Ã  12:15, Bald Eagle a Ã©critÂ :
>
> Le_Forgeron <jgr### [at] freefr> wrote:
>
>> You will never find it, it's too obvious.
>>
>> The segment is 1 unit long.
>
> That looks OK in the x direction, but in z, it's all off kilter.
> I tried to puzzle it out yesterday, even looking at patterns.cpp, and doing an
> overlay grid exactly like you have here, and couldn't get it to line up.
>
>

on the z, it's an hexagon whose center is at 0. so there is an offset of
sqrt(3)/2  (0.866, sinus 60 degree) to find the next horizontal.

the width on z is 1.732 (sqrt(3)), but 2 on x for a single hexagon.

On the paving block, the x length is 3, but remains at sqrt(3) on z.
(a paving block is a block you can repeat to pave a plane)
```
 From: gregjohn Subject: Re: Unit cell of pavement pattern? Date: 15 Aug 2019 12:35:01 Message:
```Le_Forgeron <jgr### [at] freefr> wrote:
> Le 15/08/2019 Ã  12:15, Bald Eagle a Ã©critÂ :
> >
> > Le_Forgeron <jgr### [at] freefr> wrote:
> >
> >> You will never find it, it's too obvious.
> >>
> >> The segment is 1 unit long.
> >
> > That looks OK in the x direction, but in z, it's all off kilter.
> > I tried to puzzle it out yesterday, even looking at patterns.cpp, and doing an
> > overlay grid exactly like you have here, and couldn't get it to line up.
> >
> >
>
> on the z, it's an hexagon whose center is at 0. so there is an offset of
> sqrt(3)/2  (0.866, sinus 60 degree) to find the next horizontal.
>
> the width on z is 1.732 (sqrt(3)), but 2 on x for a single hexagon.
>
> On the paving block, the x length is 3, but remains at sqrt(3) on z.
> (a paving block is a block you can repeat to pave a plane)

Yes, thanks, after much tinkering, I found that

scale foo/sqrt(3)

makes a hexagon of size foo.
```