centroid and area of a polygon

centroid and area of a polygon

from Points import *


def centroid(pgon):
    """
    Calculates the centroid and area of a polygon. Input
     pgon: a list of Point objects
    Output
     A: the area of the polygon
     C: the centroid of the polygon
    """
    numvert = len(pgon)
    A = 0
    xmean = 0
    ymean = 0
    for i in range(numvert-1):
        ai = pgon[i].x*pgon[i+1].y - pgon[i+1].x*pgon[i].y
        A += ai
        xmean += (pgon[i+1].x+pgon[i].x) * ai
        ymean += (pgon[i+1].y+pgon[i].y) * ai
    A = A/2.0
    C = Point(xmean / (6*A), ymean / (6*A))
    return A, C

# TEST


if __name__ == "__main__":
    points = [ [0,10], [5,0], [10,10], [15,0], [20,10],
               [25,0], [30,20], [40,20], [45,0], [50,50],
               [40,40], [30,50], [25,20], [20,50], [15,10],
               [10,50], [8, 8], [4,50], [0,10] ]
    polygon = [ Point(p[0], p[1]) for p in points ]
    print(centroid(polygon))