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From: "Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid>
Newsgroups: comp.soft-sys.matlab
Subject: Re: volume of a pyramid
Date: Fri, 23 Nov 2007 02:52:51 +0000 (UTC)
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"Pinpress " <nospam__@yahoo.com> wrote in message <fi5aof$gp
$1@fred.mathworks.com>...
> Hi,
> 
> Anyone knows how to calculate the volume of a 3D ultrasound
> imaging volume, like the one in the following figure:
> 
> http://www.gehealthcare.com/usen/ultrasound/education/images/u3d4d/
fig2.jpg
> 
> Or any pointer to useful links would be much appreciated. 
> thanks and happy Thanksgiving!
--------
  You haven't stated explicitly what shape your image has.  It looks like a solid 
defined by projecting a spherical quadrilateral surface inwards along radial 
lines to a smaller spherical quadrilateral.  Is that correct?

  If so, then its volume can be calculated in terms of the area of the outer 
quadrilateral:

 V = a*R/3*(1 &#8211; (r/R)^3)

Where R is the outer radius, r the inner radius, and a the outer area.

  As for computing a, it is equal to

 a = R^2*(A + B + C + D &#8211; 2*pi)

where A, B, C, and D are the four angles in radians at the four vertices of the 
outer quadrilateral.

  So your problem becomes that of determined what those four angles are.  
There is no way of determining them without additional information about 
that quadrilateral.

Roger Stafford