[sdiy] solid geometry

[Glen]

At 03:40 PM 1/3/04 , John L Marshall wrote:

>I want to mount the speakers evenly distributed on the sphere. What is the
>formula for doing this?
>
>I have found formulas for dodecahedrons and icosahedrons but they describe
>12 and 20 flat surface solids.

I'm not a math wizard by any means, but I know the answer to this one, from
my experience working with POV-Ray raytracing software. The truth is, there
is NO formula that calculates the positions of an arbitrary number of
equi-distant points on the surface of a sphere. For certain numbers of
points, there *are* perfect solutions available. (I think 2, 3, or 6 points
have perfect solutions, for example.) Unfortunately, those cases are in the
minority.

For large numbers of points, most people end up using approximations that
suit their particular needs and personal tastes best. Some people base
their design on the math of geodesic domes. Others have ran a computer
simulation of N points, each with an imaginary electrical charge that makes
them repel each other. During the simulation, they place the points on the
sphere in an initially random position, and then let the simulation run for
a "reasonably long" time. The pattern of points that exists when the
simulation is stopped is fairly equidistant, but of course it won't be
perfectly equidistant, except for those certain values of N that happen to
have perfect solutions.

My advice would be to either settle for a reasonably close compromise, or
to restrict the number of speakers to those cases that actually have
perfect solutions. Just don't drive yourself crazy trying to achieve
perfectly equal placement for those cases where it's mathematically
impossible.  :)


later,
Glen