"Samuel B." <stb### [at] hotmailcom> wrote:

> It looks like a good solution, but I must admit I can't quite comprehend a lot
> of it. (I will keep trying, though.)

Apparently it is "the" solution, as I basically came across this exact equation
once when I was trying to save myself the trouble of re-deriving it.   :D

You have the "height" h of the arc, or depth that the circle/sphere pokes into
the object when it butts up against the edges.   Picture resting an oversize
ball in the mouth of a glass.

You also have the radius of the desired circle. r

We draw a chord perpendicular to the radius at height h, and use one half of
that as the leg of a triangle.  (L/2)  Drawing a line from the edge/circle
intersection to the circle center, we get the hypotenuse, which is just another
radius of the circle.

The other leg of the triangle is the radius minus the height of the arc.

Now you just do the Pythagorean theorem, and expand terms, simplify, and
rearrange to get r.

The diagram is messier because I used (L/2) instead of defining l = L/2, which
just makes the equation look a lot nicer.

Hope that helps.

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"Samuel B." <stb### [at] hotmailcom> wrote:

> Did you ever post the dual-lantern model? I can't remember if it was you, or
> someone else on another forum using Blender. /Somebody/ posted a lantern, that's
> all I know!


I did not - as it wasn't really a project for a render, but a desire to
construct an inexpensive and functional replacement for an expensive vintage
glass globe.

It's a Thermos 8326, which has a bit of a taper / cone shape.

I think I saw that maybe a new manufacture Coleman A200 would fit, but I have to
find one and measure it.

It's really just there to protect the fragile mantles from accidental damage or
insects flying in, while still letting the light out.

- BW

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Attachments:
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Preview of image 'thermos8326.png'

Thomas de Groot <tho### [at] degrootorg> wrote:
> Op 18-7-2023 om 02:27 schreef Samuel B.:
> > [...] It's a generic gothic/medieval window macro. [...]
>
> Aaah! I love this! Can it do the typically English 4-centered arch? I
> have been trying to write a macro lately but did not get very far.
>
> --
> Thomas

Well, you got me interested in the 4-centered arch. I found the following video
that explains how to make the underlying shape using a compass and straightedge:
https://www.youtube.com/watch?v=sgyYXKgs8gw

Basically, you start with the smallest circle's position and radius, and
eventually find the center of the 'X'. Then you use that to make a second
circle. As it turns out, the curved portion is made from just two perfect circle
segments.

I hope to get a proper object macro going soon. Not sure what the final geometry
will be, since there are smooth arches, chamfered and/or filleted arches,
bricked arches, stepped arches... and any combination of those and beyond...

Sam

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Preview of image '4centeredarchgeometry.jpg'

"Samuel B." <stb### [at] hotmailcom> wrote:
> Thomas de Groot <tho### [at] degrootorg> wrote:
> > Op 18-7-2023 om 02:27 schreef Samuel B.:
> > > [...] It's a generic gothic/medieval window macro. [...]
> >
> > Aaah! I love this! Can it do the typically English 4-centered arch? I
> > have been trying to write a macro lately but did not get very far.
> >
> > --
> > Thomas
>
> Well, you got me interested in the 4-centered arch. I found the following video
> that explains how to make the underlying shape using a compass and straightedge:
> https://www.youtube.com/watch?v=sgyYXKgs8gw
>
> Basically, you start with the smallest circle's position and radius, and
> eventually find the center of the 'X'. Then you use that to make a second
> circle. As it turns out, the curved portion is made from just two perfect circle
> segments.
>
> I hope to get a proper object macro going soon. Not sure what the final geometry
> will be, since there are smooth arches, chamfered and/or filleted arches,
> bricked arches, stepped arches... and any combination of those and beyond...
>
> Sam

Cool stuff Sam.

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Op 19/07/2023 om 23:52 schreef Samuel B.:
> Thomas de Groot <tho### [at] degrootorg> wrote:
>> Op 18-7-2023 om 02:27 schreef Samuel B.:
>>> [...] It's a generic gothic/medieval window macro. [...]
>>
>> Aaah! I love this! Can it do the typically English 4-centered arch? I
>> have been trying to write a macro lately but did not get very far.
>>
>> --
>> Thomas
> 
> Well, you got me interested in the 4-centered arch. I found the following video
> that explains how to make the underlying shape using a compass and straightedge:
> https://www.youtube.com/watch?v=sgyYXKgs8gw
> 
Yes, that is the procedure indeed.

> Basically, you start with the smallest circle's position and radius, and
> eventually find the center of the 'X'. Then you use that to make a second
> circle. As it turns out, the curved portion is made from just two perfect circle
> segments.
> 
> I hope to get a proper object macro going soon. Not sure what the final geometry
> will be, since there are smooth arches, chamfered and/or filleted arches,
> bricked arches, stepped arches... and any combination of those and beyond...
> 
> Sam
> 
Very good. Looking forward to it. thanks!

-- 
Thomas

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Thomas de Groot <tho### [at] degrootorg> wrote:
> Op 19/07/2023 om 23:52 schreef Samuel B.:
> > Thomas de Groot <tho### [at] degrootorg> wrote:
> >> Op 18-7-2023 om 02:27 schreef Samuel B.:
> >>> [...] It's a generic gothic/medieval window macro. [...]
> >>
> >> Aaah! I love this! Can it do the typically English 4-centered arch? I
> >> have been trying to write a macro lately but did not get very far.

> > I hope to get a proper object macro going soon. Not sure what the final geometry
> > will be, since there are smooth arches, chamfered and/or filleted arches,
> > bricked arches, stepped arches... and any combination of those and beyond...
> >
> [...] Very good. Looking forward to it. thanks!

Thank you. I got some work done on it today. Had to make it fit within a box and
margins. But, what kind of geometry to use? Many of the examples I've seen show
arches made from bricks. So, I guess that's what I will shoot for...

Sam

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Op 21/07/2023 om 00:56 schreef Samuel B.:
> Thomas de Groot <tho### [at] degrootorg> wrote:
>> Op 19/07/2023 om 23:52 schreef Samuel B.:
>>> Thomas de Groot <tho### [at] degrootorg> wrote:
>>>> Op 18-7-2023 om 02:27 schreef Samuel B.:
>>>>> [...] It's a generic gothic/medieval window macro. [...]
>>>>
>>>> Aaah! I love this! Can it do the typically English 4-centered arch? I
>>>> have been trying to write a macro lately but did not get very far.
> 
>>> I hope to get a proper object macro going soon. Not sure what the final geometry
>>> will be, since there are smooth arches, chamfered and/or filleted arches,
>>> bricked arches, stepped arches... and any combination of those and beyond...
>>>
>> [...] Very good. Looking forward to it. thanks!
> 
> Thank you. I got some work done on it today. Had to make it fit within a box and
> margins. But, what kind of geometry to use? Many of the examples I've seen show
> arches made from bricks. So, I guess that's what I will shoot for...
> 
> Sam
> 
I suppose that - like gothic windows or gates - they could be made also 
from stone and sculpted. See for example:
https://www.canterbury-archaeology.org.uk/four-centred-arch

Wood seems also to be widely used for indoor purposes.

But I see what you mean. The material can be an important (structural) 
element.

-- 
Thomas

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"Bald Eagle" <cre### [at] netscapenet> wrote:
> "Samuel B." <stb### [at] hotmailcom> wrote:
>
> > It looks like a good solution, but I must admit I can't quite comprehend a lot
> > of it. (I will keep trying, though.)
>
> Apparently it is "the" solution, as I basically came across this exact equation
> once when I was trying to save myself the trouble of re-deriving it.   :D

Thanks, I'll keep all this in mind for the future. I have a feeling that if our
respective solutions became more generalized and simplified, they would start
looking even more similar.

> > Did you ever post the dual-lantern model? [...]

> I did not - as it wasn't really a project for a render, but a desire to
construct an inexpensive and functional replacement for an expensive vintage
glass globe.

It's always nice when things can be brought into the real world like that. Did
you ever take a photo of it?

Sam

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Thomas de Groot <tho### [at] degrootorg> wrote:
> Op 21/07/2023 om 00:56 schreef Samuel B.:
> > Thomas de Groot <tho### [at] degrootorg> wrote:
> >> Op 19/07/2023 om 23:52 schreef Samuel B.:
> >>> Thomas de Groot <tho### [at] degrootorg> wrote:
> >>>> Op 18-7-2023 om 02:27 schreef Samuel B.:
> >>>>> [...] It's a generic gothic/medieval window macro. [...]
> >>>>
> >>>> Aaah! I love this! Can it do the typically English 4-centered arch? I
> >>>> have been trying to write a macro lately but did not get very far.
> >
> >>> I hope to get a proper object macro going soon. [...]
> >>>
> >> [...] Very good. Looking forward to it. thanks!
> >
> > [...] But, what kind of geometry to use? [...]
> >
> I suppose that - like gothic windows or gates - they could be made also
> from stone and sculpted. See for example:
> https://www.canterbury-archaeology.org.uk/four-centred-arch
>
> Wood seems also to be widely used for indoor purposes.
>
> But I see what you mean. The material can be an important (structural)
> element.
>
> --
> Thomas

I was mainly concerned about the shape itself, independent of structural
soundness. What is best for generic usage in POV-Ray? Probably just a basic
shape with beveling.

Got more done today, fixed some issues, and then I realized it could be made
more useful... so macro incoming, eventually ;)

Sam

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"Samuel B." <stb### [at] hotmailcom> wrote:

> > > Did you ever post the dual-lantern model? [...]
>
> > I did not - as it wasn't really a project for a render, but a desire to
> construct an inexpensive and functional replacement for an expensive vintage
> glass globe.
>
> It's always nice when things can be brought into the real world like that. Did
> you ever take a photo of it?
>
> Sam

No - with prices for even small pieces of pierced sheet metal being pretty
exorbitant, I'm still casting about for a suitable piece of scrap to repurpose.
I have plenty of other lanterns to use if the need arose, so no rush on the
Thermos.

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