Center of gravity of a polygon

Question

I am trying to write a PHP function that will calculate the center of gravity of a polygon.

I\'ve looked at the other similar questions but I can\'t seem to find a s

Answer 1

Since we are all having so much fun implementing this algo in different languages, here is my version I knocked up for Python:

def polygon_centre_area(vertices: Sequence[Sequence[float]]) -> Tuple[Sequence[float], float]:
    x_cent = y_cent = area = 0
    v_local = vertices + [vertices[0]]

    for i in range(len(v_local) - 1):
        factor = v_local[i][0] * v_local[i+1][1] - v_local[i+1][0] * v_local[i][1]
        area += factor
        x_cent += (v_local[i][0] + v_local[i+1][0]) * factor
        y_cent += (v_local[i][1] + v_local[i+1][1]) * factor

    area /= 2.0
    x_cent /= (6 * area)
    y_cent /= (6 * area)

    area = math.fabs(area)

    return ([x_cent, y_cent], area)