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Re: How to increase area of irregular polygon?


On Tue, 11 Feb 2003 10:00:26 +0000 (UTC), Garry Helzer
<gah at math.umd.edu> wrote:

>Steve,
>
>If you operate on an object with a linear transformation the 
>area/volume of the image is the original area/volume multiplied by the 
>determinant of the matrix of the linear transformation.
[snip]
>You now have rescaled the object without moving its center of gravity. 
>This is the "fix" mentioned below.

Gray:
	Right. I knew that but the poster didn't say he wanted the
centroid invariant.
	Rather than think of the determinant, I find it much simpler
just to use the fact that the area of anything with constant shape
goes as the square of its linear dimensions. This would also work for
3-D (with the cube), etc., and one can find the centroid in the same
way.


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