From: George W. Hart <george_at_georgehart.com>

Date: Wed Jan 21 2004 - 19:45:15 EET

Date: Wed Jan 21 2004 - 19:45:15 EET

Bo Atkinson wrote:

*> ...It might be of interest that formZ, (with the latest version 4.x and
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*> latest pc hardware), was able to Boolean 343 soccer balls very easily.
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*> ... Yet to be fair, more
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*> experimentation is deserved before saying exactly where the limit is...
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Computing Boolean operations on objects defined by their surface

boundary can be "easy" or "hard" depending on how the faces and edges

intersect each other. Simpler algorithms have problems if some planes,

edges, or vertices are very close to coincident. In your model, it

appears that you made a regular 7x7x7 lattice of identical balls, so the

intersection geometry was the same in each case. That is fundamentally

no harder a test than the union of 27 balls in a 3x3x3 lattice---it just

repeats this same question many times.

For a better test, you could rotate each ball a random amount, scale it

slightly differently, and perturb its position a small random distance.

Then each intersection will be a slightly different problem for the

software to solve. In that case, I suspect there is a good chance that

at least one of them will expose a software problem. (But I would be

happy to hear otherwise...)

George

http://www.georgehart.com/

Received on Wed Jan 21 19:23:24 2004

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