Area of Polygon - C++ - c++

Question

I'm trying to write a code to calculate the area of a polygon, but it looks like something isn't adding up. Might be that the formula is off, or I need to use the absolute value function?
double polygon_area(int actual_size, double x[], double y[])
{
printf("In polygon.area\n"); //Initial basic test
int i;
double area;
area = 0.0;
for (i = 0; i <= max_size; i = i + 1)
{
area = (x[i + 1] + x[i]) * (y[i + 1] - y[i]);
area = (area * 0.50);
}
printf("The area of the polygon is %lf \n", area);
return (area);
}

Answer 1

Problems that I see:
You are computing the area as if there are max_size elements to compute the area from. I think you need to use actual_size.
Since C++ indices for arrays start with 0, they need to stop at actual_size-1, not actual_size. Instead of
for (i = 0; i <= max_size; i = i + 1)
use
for (i = 0; i < actual_size; ++i)
// Using ++i is more idiomatic that using i = i + 1
Computation of area is wrong. Replace the lines:
area = (x[i + 1] + x[i]) * (y[i + 1] - y[i]);
area = (area * 0.50);
by
area += 0.5*(the area term);
Calculation of the area term needs to use wrap around indices. Say you have 5 points. When processing the 5-th point, you have to use indices 4 and 0, not 4 and 5.
Instead of
x[i + 1] + x[i]) * (y[i + 1] - y[i]);
use
x[(i + 1)%actual_size] + x[i]) * (y[(i + 1)%actual_size] - y[i]);
The computation for the area term needs to be fixed. Instead of using
0.5*(x2 + x1) * (y2 - y1))
you need to use:
0.5*(x1.y2 - x2.y1)
Here's a simplified version of the function:
double polygon_area(int actual_size, double x[], double y[])
{
printf("In polygon.area\n");
double area = 0.0;
for (int i = 0; i < actual_size; ++i)
{
int j = (i + 1)%actual_size;
area += 0.5 * (x[i]*y[j] - x[j]*y[i]);
}
printf("The area of the polygon is %lf \n", area);
return (area);
}