Decades ago, I was working on a project to find the best
way to equidistribute a large number of points on a sphere.
We were looking for "random unit vectors".
(This had to do with choosing "random" orientations for a pot
containing a seed to see if the seed would sprout and grow
without benefit of gravity, the random orientation being
the best on earth simulation of no gravity at all. If
you are wondering, almost all kinds of seeds sprout intitially but only
some kinds of plants to grow. The others get all confused about
which way is up, and die. But some apparently are seeking not up but
warmth and they will grow if provided with one direction being more
towards warmth than others, a warmth gradient as it were, the
gravitational gradient being not used. This all had to do with the
space program of course though equally of course the space program
did not get to the point-not yet and probably not ever--that
gardening or farming in space was being attempted in any serious way, if
at all).
What we came up with is that the locations of the centers
of an icosahedron's faces--or equivalently at the vertices of a
dodecahedron --is a good way. If you need more points, then
there is no "canonical" choice(and no one is going to "discover"
any more Platonic solids--there aren't any more!). But you can
do reasonably well by just equidistributing in some sense
within the faces of an icosahedron but varying the distribution a
bit in each face.
Actually, once you get beyond the 20 speakers this gives you
(centers of the icosahedron faces), it probably does not matter
too much how you do it in detail. Not for the plants anyway
and probably not for Ambisonics. It would be tempting NOT
to vary the in-face distributions just for computational convenience!
Robert
On Wed, 10 Jul 2013, Martin Leese wrote:
"Michael Chapman" wrote:
Martin Leese wrote:
In general, for Ambisonics, you should
distribute the speakers as evenly as possible.
Aim for the faces of a platonic solid; visit:
http://en.wikipedia.org/wiki/Platonic_solid
Problem is ... despite many claims to be on the verge of discovering new
ones;-)> ...that Plato did not have many solids . . .
I _thought_ the consenus on this list (no howls of derision, please) was
edging towards three rings ... though without looking back, whether that
was 6-8-6 or something else ...?
Just a two pennies' worth,
I did not make myself sufficiently clear.
Aiming for a Platonic solid is just a goal, not a
destination. I was trying to suggest that
achieving an even distribution is important,
and was not trying to dictate strict adherence
to a fixed rule.
Note that with only three rings, you are limited
to second-order height. This may or may not
be a problem. 24 speakers is almost 5
squared, so fourth-order full-sphere could be
attempted.
Regards,
Martin
--
Martin J Leese
E-mail: martin.leese stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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