

While writing a generator for "rocks" (usable e.g. to render asteroids
etc. ;) ) I got an interesting optimization problem:
3 concentric, but randomly rotated, cubes of the same size intersects
each other. Which rotataions would give an object with minimal volume or
minimal circumsphere?
This way:
intersection
{
box { 1, +1 } // not rotated
box { 1, +1 rotate<X1, Y1, Z1> }
box [ 1, +1 rotate<X2, Y2, Z2> }
}
I wrote a program that choose X1,Y1,Z1, X2,Y2,Z2 randomly, and it
renders interesting objects, especially when the 3 cubes got different
colors, but I'd like to see how the optimal solution would look like and
how it can be calculated arithmetically.
Any ideas, suggestions?
Lars R.
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Download 'cubeintersection.png' (11 KB)
Download 'cubeintersection.pov.txt' (1 KB)
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