Re: Math question: How to compute the area of polygons

[Gernot Lorenz]

Malte Brill wrote:

Hi List,

this one goes out to the math experts.
How does one compute the area ( I hope it is the correct Term for
flaecheninhalt in german) of a polygon with n sides.
(That would get me started.)

I want to extract all lines of 2 polygons by analysing their points,
evaluate the area of each of them with some magic formula I don�t know ;-)
and to figure out the area of the smallest polygon surrounding both of them.
 

Hallo Malte,
wenn sich das Polygon nicht schneidet, geht es folgenderma�en: Es wird 
in Dreiecke zerlegt (man nimmt ein Polygonpunkt und verbindet ihn mit 
allen anderen); angenommen, die Koordinaten der 3 Eckpunkte sind 
(ax,ay), (bx,by) und (cx,cy) dann gilt f�r den Fl�cheninhalt: F = 
[ax*(by - cy) + bx*(cy - ay) + cx*(ay - by)]/2.
Diese Berechnung mu� nun f�r alle entstandenen Dreiecke durchgef�hrt und 
die Ergebnisse addiert werden.
In English:
If the polygon does not cross itself, the following method helps: the 
polygon has to be divided into triangulars (choose one point of the 
polygon and connect it with all the others); supposed, the coordinates 
of the three triangular points are (ax,ay), (bx,by) und (cx,cy), then 
the area F will be calculated with [ax*(by - cy) + bx*(cy - ay) + cx*(ay 
- by)]/2.
This has to be done for all the triangulars and the areas have be added 
and give the total area.
( I know, bad English from "old Europe")

Gru�
Gernot
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