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From: ken@turtlevax.UUCP (Ken Turkowski)
Newsgroups: net.math
Subject: Re: Surface Area Query
Message-ID: <964@turtlevax.UUCP>
Date: Mon, 18-Nov-85 14:55:05 EST
Article-I.D.: turtleva.964
Posted: Mon Nov 18 14:55:05 1985
Date-Received: Thu, 21-Nov-85 03:41:22 EST
References: <749@h-sc1.UUCP>
Reply-To: ken@turtlevax.UUCP (Ken Turkowski)
Distribution: net
Organization: CIMLINC, Inc. @ Menlo Park, CA
Lines: 32

In article <749@h-sc1.UUCP> riggsby@h-sc1.UUCP (andrew riggsby) writes:
>Is there a general method for determining the surface area of an arbitrary
>surface or solid similar to (or not similar, for that matter) using
>displacement to determine the volume of a solid.  Note that this includes
>2-d surfaces in E^3.

If you can determine the normal to the surface, you can use the divergence
theorem:
		 __ 
	integral \/ . A dV  = integral A . n dS
	   V			 S

Where V is the entire volume of the object,
S is the surface of the object,
__
\/ is the vector differential operator "del",
. is the dot product,
dV is an incremental volume of integration,
dS is an incremental surface of integration,
n is the normal to the surface,
and A is a vector function.

For your purposes, you would want to pick a function A such that
	A.n == 1


In some applications, doing a surface integral is easier than a volume
integral;  hopefully, for yours, a volume integral is easier.
-- 
Ken Turkowski @ CIMLINC (formerly CADLINC), Menlo Park, CA
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