How to Calculate Centroid of polygon in C

Question

I'm trying to rotate the polygon around centroid but I confused about coding from formulas.

float x[32];
float y[32];
float cx=0;
float cy=0;
int j,n;
printf("How many angles :")
scanf("%d" ,&n);
//get (x[j],y[j]);
for (j=0; j<n; j++){
printf("x%d : ",j+1);
scanf("%f" ,&x[j]);
printf("y%d : ",j+1);
scanf(input, "%f" ,&y[j]);
}
//find a
//find cx
//find cy
printf("The centroid of the polygon is (%f,%f)",cx,cy);

centroid of polygon formulas
https://i.stack.imgur.com/qjezn.png

Answer 1

Here's the formula:

It's perhaps a little misleading because the formula requires a list of vertices from (x₀,y₀) to (x_n–1,y_n–1), but includes the values of x_n and y_n in the summations. What you have to do there is wrap around to the start of the list; i.e., (x_n,y_n) ≡ (x₀,y₀).

Here's some code that will do these calculations:

float a, cx, cy, t;
int i, i1;

/* First calculate the polygon's signed area A */

a = 0.0;
i1 = 1;
for (i=0; i<n; i++) {
  a += x[i] * y[i1] - x[i1] * y[i];
  i1 = (i1 + 1) % n;
}
a *= 0.5;

/* Now calculate the centroid coordinates Cx and Cy */

cx = cy = 0.0;
i1 = 1;
for (i=0; i<n; i++) {
  t = x[i]*y[i1] - x[i1]*y[i];
  cx += (x[i]+x[i1]) * t;
  cy += (y[i]+y[i1]) * t;
  i1 = (i1 + 1) % n;
}
cx = cx / (6.0 * a);
cy = cy / (6.0 * a);