Polygons.py

"""
Some tools for computing various properties of polygons
Author: Travis Dick (travis.barry.dick@gmail.com)
"""

import numpy as np

def polygon_descriptors(corners):
    """ Computes the area, perimeter, and center of mass of a polygon.
    
    Parameters:
    -----------
    corners : (2,n) numpy array
      The vertices of the polygon. Should be in clockwise or
      counter-clockwise order.
    
    Returns:
    --------
    A tuple (perimeter, area, (center of mass x, center of mass y)).
    """
    n_points = corners.shape[1]
    p, a, cx, cy = 0, 0, 0, 0
    for i in xrange(n_points):
        j = (i+1) % n_points
        dot = corners[0,i]*corners[1,j] - corners[0,j]*corners[1,i]
        a += dot
        cx += (corners[0,i] + corners[0,j]) * dot
        cy += (corners[1,i] + corners[1,j]) * dot
        p += np.linalg.norm(corners[:,i] - corners[:,j])
    a /= 2
    cx /= 6*a
    cy /= 6*a
    a = abs(a)
    return (p, a, (cx,cy))