Re: Algorithm

From: Arthur J. O'Dwyer (ajo_at_nospam.andrew.cmu.edu)
Date: 02/17/05 

Date: Thu, 17 Feb 2005 14:41:01 -0500 (EST)

On Thu, 17 Feb 2005, Thomas Matthews wrote:
>
> TARUN SINHA wrote:
>> Hello All,
>> Currently I am Facing a Problem in Calculating a Polygonal
>> Area on Spheriod.
>> I want to find the area of any Irregular Polygon on Earth.Taken the
>> earth to be a sphere
>> I have search a lot in google and already Post a query.Does anyone have
>> an Algorithm for calculating the area.
>
> I don't understand how a polygonal area could be a different
> size if its on the surface of a sphere, cone or flat surface.

   Consider a triangle on the surface of a sphere with all three angles 90
degrees (an octant). This triangle has area equal to 1/8 the surface area
of the sphere. It can't even be drawn on a plane, because no planar
triangle can have angles that don't add up to 180 degrees.

> Given a square, which is a polygon, its area is:
> Area = length of side * length of side.

   Is it even possible to have a quadrilateral with four right angles on a
sphere? I don't think so; I think any non-trivial (non-zero--area)
quadrilateral will necessarily have an interior-angle sum greater than
360 degrees.

   Anyway, this looks very much like a problem Google can solve. Indeed,
searching for "area of polygon on surface of sphere" (no quotes) gives
a "Dr. Math" explanation as hit #3; and that page links to the MathWorld
definition page, complete with formula. If the OP still needs help,
he'd better explain what he's really trying to do.

-Arthur

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