Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!uunet!mcsun!unido!gmdzi!wittig
From: wittig@gmdzi.UUCP (Georg Wittig)
Newsgroups: comp.graphics
Subject: Re: AREA MEASUREMENT OUT OF POLYGON-CONTOUR DATA
Message-ID: <3192@gmdzi.UUCP>
Date: 10 Aug 90 09:58:57 GMT
References: <dick.650211355@prisma>
Distribution: comp.graphics
Organization: GMD - The German National Research Center for Computer Science
Lines: 53

dick@prisma.cv.ruu.nl (Dick Bakker) writes:

>I am looking for a method to calculate the area of a 
>contour out of the polygon-data that describes the 
>contour.

>e.g. I have 100 points that describe a contour (x,y-
>coordinates) and I'd like to calculate the area of it.

>Does anyone know an algorithm that can do such a thing?

>Thanks in advance,
>				Dick Bakker 

Let the polygon be the sequence {(X[i], Y[i]) | i = 0 ... N-1}
For each I in 0 ... N-2 there exists a trapezium with the 4 corners
	(X[I  ], 0     ),
	(X[I+1], 0     ),
	(X[I+1], Y[I+1]),
	(X[I  ], Y[I  ])
The area of it is	( X[I+1] - X[I] ) * ( Y[I] + Y[I+1] ) / 2
(i.e., height * length of the center line).

So, if your points are stored as floating point, your program could be

	double area, *px, *py;
	area = 0.0;					/* if polygon is open */
--or--	area = (X[N-1] - X[0]) * (Y[N-1] + Y[0] );	/* if it is closed */

	for (px = &X[N-2], py = &Y[N-2];   px >= X;   --px, --py)
		area += ( px[0] - px[1] ) * ( py[0] + py[1] );
	area *= 0.5;

If your coordinates are integers, then it is wise, not to divide by 2
because of the rounding errors. Just store the value that isn't divided by
2; so you avoid rounding errors. When the value of the area is printed to
the user, it can be divided by 2 in the print statement:

	long area, *px, *py;
	area=0L;					/* if polygon open */
--or--	area = (X[N-1] - X[0]) * (Y[N-1] + Y[0] );	/* if pol. closed */

	for (px = &X[N-2], py = &Y[N-2];   px >= X;   --px, --py)
		area += ( px[0] - px[1] ) * ( py[0] + py[1] );
	...
	printf ("area is %ld\n", area/2);


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