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Re: Volume by four vectors [message #41226]

Sun, 17 October 2004 07:35

ed
Messages: 3
Registered: October 2004

Junior Member

Sander,

Uhoh! It's a volume with 5 vertices, obviously not cube-like in any
way. But I guess you can dissect it into irregular tetrahedrons and
use that Francesca formula for each one. The volume of the original
solid may not be convex in general, which might lead to negative
tetrahedral volumes, but I suspect, even then the sum of the volumes
will be correct.

Ed

Sander Roosendaal <sander@wereldraadsel.nl> wrote in message news:<kfn242-pe3.ln1@wereldraadsel.demon.nl>...
> Many thanks, Ed.
> Just the hint I needed.
>
> Ed Schmahl wrote:
>
>> Dear Sander,
>>
>> Interesting geometry problem. The volume you're talking about is an
>> irregular polyhedron--the generalization of a cube. You can dissect
>> the volume into
>> irregular tetrahedra, each bounded by 4 triangles, two triangles on
>> each face.
>> Pick an origin inside of the hexahedron, and since there are 6 faces,
>> there
>> will be 12 (irregular) tetrahedra, each with a common vertex at the
>> origin.
>> Obviously the location of the origin is irrelevant, but if it is
>> outside of
>> the hexahedron, some of the tetrahedra will have negative volumes.
>>

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[Message index]

		Re: Volume by four vectors By: ed on Sun, 17 October 2004 07:35
		Re: Volume by four vectors By: Sander Roosendaal on Thu, 14 October 2004 12:11
		Re: Volume by four vectors By: Sander Roosendaal on Thu, 14 October 2004 09:52
		Re: Volume by four vectors By: ed on Wed, 13 October 2004 14:02

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