       Re: Parsing polygon lists

• To: mathgroup at smc.vnet.net
• Subject: [mg8993] Re: [mg8963] Parsing polygon lists
• From: Fabian Haas <b5hafa at rz.uni-jena.de>
• Date: Tue, 7 Oct 1997 03:35:40 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Russell Towle <rustybel at foothill.net> wrote:

>Hi all,
>
>I wish to optimize the task of, given a large list of polygons in 3-space,
>some of which may fall into coincidence in pairs, to delete any such pairs
>from the list. The polygons are lists of vertices, and each vertex is a
>list of three real numbers.
>
>My current method is as follows, using a function "facent" which finds the
>centers of polygons:
>
>1. Find the centers of each polygon in the list 'a':
>centfaces =3D Map[ facent[#]&,  a];(*no problem here*)
>
>2. Find the positions in the list of face centers wherein one face center
>equals another:
>qaz =3D Table[ Position[ centfaces, x_ /; x=3D=3Dcentfaces[[i]] ], {i,=
Length[ a
>]} ];(*slow*)
>
>3. Drop the duplicate pairs:
>red =3D Flatten[ DeleteCases[ qaz, x_ /; Length[ x ]=3D=3D2] ];(*OK as is*)
>
>After step (3), I can construct a new list of polygons by writing a[[red]].
>
>The main problem is step (2), which is terribly slow. At times the number
>of polygons may exceed three or four thousand or more. I am using version
>2.2.2.
>
>Russell Towle
>Giant Gap Press:  books on California history, digital topographic maps
>P.O. Box 141
>Dutch Flat, California 95714
>------------------------------
>Voice:  (916) 389-2872
>e-mail:  rustybel at foothill.net
>------------------------------

Well, I am not sure but you might also try the  Complement function, see=
details in the reference manual.
You might need to remove the Polygon by a replacement rule Polygon[a_] -> a=
(rules are generally slower than function) of by a Map[ #[]&,=
Polygonlist ]
The point is that Complement does not realize that {{a,b,c}, {d,e,f}} is=
equal to {{d,e,f}, {a,b,c}} in our sense here, so I added a line that sorts=
thinks:
list/.If[ a < d, {{a,b,c}, {d,e,f}}, {{d,e,f}, {a,b,c}}].
That works fine for my purposes but I dont know how efficient it works with=
3 to 4000 polygons. You might check that with Timing function.

=46abian

-------------------------------------------------------------------------
Dipl.Biol. Fabian Haas, MPhil
Institut f=FCr Spezielle Zoologie und Evolutionsbiologie
Erbertstr. 1
D-07743 Jena
b5hafa at pop3.uni-jena.de
http://www.zoo.uni-jena.de/~fabian/
Deutschland / Germany
TEL  ++ 49 3641 630 424
=46AX  ++ 49 3641 630 392
:-)  (-:
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```

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