Subject: Summary: Smallest rectangular Box

From: Friedrich Ackermann <[email-masked]>
Date: Wed, 12 Jun 1996 13:59:46 +0200 (MET DST)

Hi,

sorry that I didn't answer the  first time,  but  I am nearly sure
that the posted answers  concerning the question  how to determine
the smallest rectangular  box  containing a  set  of 3D points are
w r o n g.  E.g. it is obvious that the suggested "principal axis"
algorithms can not work,  because the  principal axis are affected
also by "interior"  points  that don't affect the correct position
of the rectangular box searched for (only points at the "boundary"
are important for this box).
I'm no expert, but I would have a look at a book like
	@book{prepa85,
	author = {Preparata, F. P. and Shamos, M. I.},
	title = {Computational Geometry. {A}n Introduction},
	publisher = {New York: Springer},
	year = {1985}
	}
to get an idea of  a correct answer.   I  think  the  faces of the
rectangular  box  are  related to the faces of the boundary of the
convex hull of the point set.

Hope that helps,

	Friedrich Ackermann

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Friedrich Ackermann
Applied Computer Science
Bielefeld University
P.O. 100131
D-33501 Bielefeld
Phone: +49 521 106 2938 (2935)
Fax: +49 521 106 2992
email: [email-masked]
http://www.TechFak.Uni-Bielefeld.DE/techfak/persons/friedric/
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