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23 Apr 2024 13:23:10 EDT (-0400)
  Spherical triangle (Message 1 to 6 of 6)  
From: kurtz le pirate
Subject: Spherical triangle
Date: 8 Apr 2023 09:36:41
Message: <64316de9$1@news.povray.org>
Hello,


What method/object to use to make triangles from three points on a sphere?

After a long search on the web, I didn't find anything.


Thanks for your advice



-- 
Kurtz le pirate
Compagnie de la Banquise


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From: jr
Subject: Re: Spherical triangle
Date: 8 Apr 2023 10:40:00
Message: <web.64317b8d1ef881ca4301edef6cde94f1@news.povray.org>
hi,

kurtz le pirate <kur### [at] gmailcom> wrote:
> Hello,
> What method/object to use to make triangles from three points on a sphere?
> After a long search on the web, I didn't find anything.

I googled (quoted string) "spherical triangles", and found a page I can't read
but am sure you do :-).  hth.
<https://www.johndcook.com/blog/spherical_trigonometry/>


regards, jr.


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From: Bald Eagle
Subject: Re: Spherical triangle
Date: 8 Apr 2023 11:30:00
Message: <web.6431880b1ef881ca1f9dae3025979125@news.povray.org>
kurtz le pirate <kur### [at] gmailcom> wrote:
> Hello,
> What method/object to use to make triangles from three points on a sphere?
>
> After a long search on the web, I didn't find anything.


You could use a sphere and difference/intersection.
isosurface
parametric
polynomial
bicubic_patch
mesh

The mesh approach would likely involve using one of the many methods of starting
with a platonic solid and subdividing each face into more triangles and
normalizing the distance of the new vertices so that the triangles progressively
approximate the surface of the spherical triangle.

Heck, you could probably also use lathe and SOR.

Facetted_sphere or Ring_Sphere macros in shapes3.inc

- BW


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From: Leroy
Subject: Re: Spherical triangle
Date: 8 Apr 2023 18:35:00
Message: <web.6431e8511ef881ca40da5a51f712fc00@news.povray.org>
kurtz le pirate <kur### [at] gmailcom> wrote:
> Hello,
>
>
> What method/object to use to make triangles from three points on a sphere?
>
> After a long search on the web, I didn't find anything.
>
>
> Thanks for your advice
>
>
>
> --
> Kurtz le pirate
> Compagnie de la Banquise

It all depends on what you got and what you want.

There should be plenty of code out there that can place make a sphere out of
triangles. I use GEODESIC SHAPE GENERATOR FOR PERSISTENCE OF VISION 3.1x by by
Uwe Zimmermann, Stockholm, Sweden 1999. I Here's a copy if you need it.
 One thing the triangles that fit a sphere wont' be all the same size and shape.

Have Fun!


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Attachments:
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From: kurtz le pirate
Subject: Re: Spherical triangle
Date: 9 Apr 2023 12:44:55
Message: <6432eb87@news.povray.org>
Thank you for your answers ;)

Can be a beginning of solution: the spherical triangle is obtained by
the difference between the sphere and three planes defined by the normal
of the three vectors taken two by two.

Now I have to find out how to draw the arcs (not necessarily "great
circles") connecting the points.

Image of the first experiment here



-- 
Kurtz le pirate
Compagnie de la Banquise


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spherical02.jpg


 

From: Bald Eagle
Subject: Re: Spherical triangle
Date: 9 Apr 2023 15:55:00
Message: <web.643317271ef881ca1f9dae3025979125@news.povray.org>
kurtz le pirate <kur### [at] gmailcom> wrote:

> Now I have to find out how to draw the arcs (not necessarily "great
> circles") connecting the points.

You already have your planes, so find the mid point between two triangle
vertices and determine the depth of that arc.

Then it's a simple matter of calculating where the centers of the tori will be
and rotating and translating them into proper position.


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arccenter.png


 

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