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I was modeling something the other day and wanted to autopmate the placement of
some pegs, and thought that finding the foci of an ellipse that's inscribed in
the region common to two overlapping boards would be a good way to place them.
No idea how to do it yet.
Take two boards - say 15 units x 1 unit, overlap them at 90 deg, you get a 1 by
1 unit square. Rotate 90 deg, and you fully align them to get 15 x 1 unit
rectangle. Somewhere in the middle you get a lot of diamonds/rhombi/etc.
Even just finding a function for the max and min vertical positions of the
overlapping region of the boards seemed an interesting problem.
Just far too many things to do IRL at the moment.
I thought perhaps someone would like to ponder the puzzle(s). :)
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From: Kevin Wampler
Subject: Re: Ellipse inscribed in 2 overlapping rectangles.
Date: 12 Jun 2018 12:58:13
Message: <5b1ffba5$1@news.povray.org>
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There's a discussion of this problem here:
https://math.stackexchange.com/questions/1971097/what-are-the-axes-of-an-ellipse-within-a-rhombus/1971327#1971327
They note that there are an infinite number of ellipses that you can
inscribe, so there isn't a unique answer unless you add another criteria.
On 6/5/2018 9:55 AM, Bald Eagle wrote:
>
> I was modeling something the other day and wanted to autopmate the placement of
> some pegs, and thought that finding the foci of an ellipse that's inscribed in
> the region common to two overlapping boards would be a good way to place them.
>
> No idea how to do it yet.
>
> Take two boards - say 15 units x 1 unit, overlap them at 90 deg, you get a 1 by
> 1 unit square. Rotate 90 deg, and you fully align them to get 15 x 1 unit
> rectangle. Somewhere in the middle you get a lot of diamonds/rhombi/etc.
>
> Even just finding a function for the max and min vertical positions of the
> overlapping region of the boards seemed an interesting problem.
>
> Just far too many things to do IRL at the moment.
> I thought perhaps someone would like to ponder the puzzle(s). :)
>
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Kevin Wampler <nob### [at] nowhere net> wrote:
> There's a discussion of this problem here:
>
https://math.stackexchange.com/questions/1971097/what-are-the-axes-of-an-ellipse-within-a-rhombus/1971327#1971327
> They note that there are an infinite number of ellipses that you can
> inscribe, so there isn't a unique answer unless you add another criteria.
Ha! Yes, I actually have that one open in my browser for further perusal.
I'm familiar with the criterion of the ellipse intersecting the midpoints of the
sides.
Just too, too many things going on and too little uninterrupted time where I'm
not ready to fall asleep at the keyboard....
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