Area of a Polygon

• The traditional method to determine the area of a polygon is as follows.

  1. Observe that the origin forms a triangle when combined with any edge of the polygon.
  2. Find the signed area of each of those triangles, using a 2x2 determinant.
  3. Add the areas.

• The above may be speeded up by taking the edges in twos and finding the areas of successive quadrilaterals, plus perhaps one final triangle.

• Here is a fortran subroutine. Note that, apart from the input validity check and the return, there are only SEVEN lines of executable code. C Area.f Return the area of a polygon C C INPUTS: Array X with the X coords, and Y with the Y coords. C N: Number of verts. C OUT: The area. C C If there is only one connected component, the first vertex must be C repeated as the last vertex. C C The polygon can have multiple separate components, possibly nested, C provided that each component has its first vertex repeated as the last C vertex of that component. The vertices of each outside component must C be listed in positive order, those of any immediately contained C component in negative order, etc. C C Wm. Randolph Franklin, wrfATecse.rpi.edu, (518) 276-6077; Fax: -6261 C ECSE Dept., 6026 JEC, Rensselaer Polytechnic Inst, Troy NY, 12180 USA C C Last modified: Fri Sep 30 14:33:18 1994 C C This is modelled on a function that I wrote about 1971. C C FUNCTION AREA(X,Y,N) DIMENSION X(1), Y(1) AREA=0.0 IF (N-3) 1,1,2 1 WRITE(2,3) N 3 FORMAT(19HUnusual value of N=,I10,17H in call to AREA.) RETURN 2 IF(N-1000000) 7,1,1 7 DO4I=3,N,2 4 AREA=AREA+(X(I-2)-X(I))*Y(I-1)-(Y(I-2)-Y(I))*X(I-1) IF (MOD(N,2)) 6,5,6 5 AREA=AREA+X(N-1)*Y(N)-Y(N-1)*X(N) 6 AREA=AREA*0.5 RETURN END