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Can anybody bound the polyhedrons in shapes2.inc in POV-Ray 3.5?
I don't know how big to make the bounding objects.
It should of course be as precise as possible to get optimal rendering
speed.
Rune
--
3D images and anims, include files, tutorials and more:
Rune's World: http://rsj.mobilixnet.dk (updated Mar 19)
POV-Ray Users: http://rsj.mobilixnet.dk/povrayusers/
POV-Ray Ring: http://webring.povray.co.uk
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"Rune" <run### [at] mobilixnet dk> wrote in message
news:3cb81031$1@news.povray.org...
: I don't know how big to make the bounding objects.
For a Dodecahedron and Icosahedron I'd take a sphere { 0 1.2577 } and
for
a Octahedron a sphere { 0 1.73 }. The Tetrahedron is tricky.. a box?
Someone quick in math could calculate the difference of the volumes of
the shapes and the smallest box/sphere/whatever they fit in and see
thats the best result.
Ari-Matti
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Ari-Matti Leppanen wrote:
>
> "Rune" <run### [at] mobilixnetdk> wrote in message
> news:3cb81031$1@news.povray.org...
>
> : I don't know how big to make the bounding objects.
>
> For a Dodecahedron and Icosahedron I'd take a sphere { 0 1.2577 } and
> for
> a Octahedron a sphere { 0 1.73 }. The Tetrahedron is tricky.. a box?
> Someone quick in math could calculate the difference of the volumes of
> the shapes and the smallest box/sphere/whatever they fit in and see
> thats the best result.
>
> Ari-Matti
A quick look at shapes2.inc learns that those polyhedra are
circumscribed to a unit sphere.
Knowing the radius of the inscribed sphere it's rather easy to obtain
the radius of the circumscribed sphere for each of the polyhedra (not
the same sphere of course).
look at
http://mathforum.org/dr.math/faq/formulas/faq.polyhedron.html
calculate the ratio of the radius of the circumscribed and the inscribed
sphere.
You can bound the polyhedron by a sphere with a radius a little bit
larger than this ratio.
--
Herman Serras
Gent (Belgium)
http://cage.rug.ac.be/~hs/
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"Rune" <run### [at] mobilixnetdk> wrote in message
news:3cb81031$1@news.povray.org...
> Can anybody bound the polyhedrons in shapes2.inc in POV-Ray 3.5?
>
> I don't know how big to make the bounding objects.
I sometimes put my object inside a sphere pigment{rgbft 0.5} and look
for bits protruding. Not so easy if the object isn't regular.
Alf
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"Herman Serras" <Her### [at] pandorabe> wrote in message
news:3CB82C20.47AEA204@pandora.be...
: A quick look at shapes2.inc learns that those polyhedra are
: circumscribed to a unit sphere.
: http://mathforum.org/dr.math/faq/formulas/faq.polyhedron.html
Nice. So the bounding spheres are:
Tetrahedron sphere { 0, 3 }
Octahedron sphere { 0, 3/sqrt(3) }
Dodecahedron sphere { 0, 15/sqrt(75+30*sqrt(5)) }
Icosahedron sphere { 0, 15/sqrt(75+30*sqrt(5)) }
I'm still not sure if a box would be better. There's more empty space,
but the bounding bounds the bounded object yet with a box, so..
Ari-Matti
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"Herman Serras" wrote:
> http://mathforum.org/dr.math/faq/formulas/faq.polyhedron.html
Thanks!
Rune
--
3D images and anims, include files, tutorials and more:
Rune's World: http://rsj.mobilixnet.dk (updated Mar 19)
POV-Ray Users: http://rsj.mobilixnet.dk/povrayusers/
POV-Ray Ring: http://webring.povray.co.uk
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