# polygon_area

The area of a simple concave polygon is one half the sum of the cross products of the adjacent edges.

$$\large A=\frac{1}{2}\sum_{i=0}^{N-1}(x_iy_{i+1}-x_{i+1}y_i)$$

The sign of the result indicates the winding of the polygon, clockwise or counter-clockwise. Holes can be accounted for if the winding of the hole edges is the reverse of the perimeter edges.

NOTE: Be sure to use the absolute value of the return for the true area of the polygon.

polygon_area(polygon)
Returns the internal area of the given polygon.
COPY/// polygon_area(polygon)
//
//  Returns the internal area of the given polygon. The value may
//  positive or negative depending on the winding of the polygon.
//
//      polygon     ds_list of an ordered series of coordinate
//                  pairs defining the shape of a polygon
//
//  Polygons are closed figures with edges spanning consecutive
//  vertices and from the last vertex to the first. Polygons must be
//  simple, which means they cannot have edges that cross one another.
//
{
var a, i, j, x1, y1, x2, y2;
a = 0;
j = ds_list_size(argument0);
for (i=0; i<j div 2; i+=1)
{
x1 = ds_list_find_value(argument0, (2*i)   mod j);
y1 = ds_list_find_value(argument0, (2*i+1) mod j);
x2 = ds_list_find_value(argument0, (2*i+2) mod j);
y2 = ds_list_find_value(argument0, (2*i+3) mod j);
a += x1 * y2 - x2 * y1;
}
return a / 2;
}


Contributors: xot

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