Amidst the chaos of RL, (I moved over the weekend) I managed to work out a
reliable placement of a sphere tangent to all 4 faces of any irregular
tetrahedron.
I worked out some macros to generate the determinant of a 4x4 matrix, based on
the Laplace expansion, or expansion by minors, but for whatever reason that
didn't play nicely with my tetrahedra.
I might have to shovel a lot of output to the debug stream and work out a smaple
problem by hand to see if there's a bug somewhere.

I modified some code from John Burkardt, and that seemed to work, so ...


It's immediately apparent that there will be large gaps between such spheres in
a random tetrahedral "mesh", and these guys have done some work on that next
step:
http://www.afhalifax.ca/magazine/wp-content/sciences/EmpilementDeDisques/ProducingPacking/Initialization.pdf

certainly one can see how the Delaunay-optimized triangles make the incircles
pack much more nicely, so that's a fairly important first-step to filling space
by this method.

Wondering how Ari's doing....    :D

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