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14 Jul 2024 06:35:02 EDT (-0400)
  "Minimalistic" intersection of 3 cubes (Message 1 to 1 of 1)  
From: Lars R 
Subject: "Minimalistic" intersection of 3 cubes
Date: 6 Sep 2022 04:36:33
Message: <63170691$1@news.povray.org>
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:

	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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