Given a polygon with weighted vertices, calculate a value for an interior point

I want to be able to find out the value of a point inside a polygon if I have assigned weights to its vertices.

In the figure below, some weights have been applied to the green dots. For some red interior point, I need to calculate

I have use the inverse of the distance from the point to a vertex as my correction factor.

This is my code so far to get the weighted value at one red point:

def add_weights(poly, weights):
poly.weights = [float(w) for w in weights]+[weights[0]] #need to add the first weight
# at the end to account for
# the first point being added to close the loop

def distance(a,b):
dist = ( (b.x - a.x)**2 + (b.y - a.y)**2 )**0.5
if dist == 0: dist = 0.000000001
return dist

def get_weighted_sum(poly, point):
return sum([poly.weights[n]/distance(point,p) for n,p in enumerate(poly.points_shapely) if poly.weights[n] != 'nan'])

def get_weighted_dist(poly, point):
return sum([1/distance(point,p) for n,p in enumerate(poly.points_shapely) if poly.weights[n] != 'nan'])

def get_point_weighted_value(poly, point):
return get_weighted_sum(poly,point)/get_weighted_dist(poly,point)


Note that my polygon can be irregular. Also, not all the vertices might have a weight, in which case the vertex is skipped for the calculation: in the example above it would mean that the value of the weight would only be calculated using two vertices rather than three.

And this is a test code sample:

import shapely.geometry as shapely

class MyPoly(shapely.Polygon):
def __init__(self,points):
closed_path = list(points)+[points[0]]
super(MyPoly,self).__init__(closed_path)
self.points = closed_path
self.points_shapely = [shapely.Point(p[0],p[1]) for p in closed_path]

def convert_to_shapely_poly(poly):
poly_shapely = MyPoly(poly)
return poly_shapely

#inputs
poly = [[0,0],[5,10],[10,0]]

#conversion to shapely format
mypoly = convert_to_shapely_poly(poly)

#adding weights to the vertices of the polygone
add_weights(mypoly,[2,11,5])

#calculate the weighted value of a point inside the polygon:
get_point_weighted_value(mypoly,shapely.Point(7,2))


Any suggestion on improving this code would be welcome!

• Welcome, does this code work? Take a look in help. – Raystafarian Sep 16 '16 at 16:01
• After reading you description thrice, I still had no idea what you program does. There is no such thing as a »value of a point«. Points only have coordinates. Functions, such as a sum of distances, evaluate to a value at a specific point. – Rainer P. Sep 16 '16 at 16:31
• Sorry about that, I have edited the figure I hope that it makes more sense now. By "value of a point" I mean that I arbitrarily decided that each point (with x,y coordinates) would be associated to a value, which is my weight. – Sorade Sep 16 '16 at 16:51
• In Rev 2, the formula in the diagram doesn't make sense, so I've tried to interpret it. Also, "not all vertices might have a weight" — does that mean that its weight is 1? – 200_success Sep 16 '16 at 17:02
• No it means that the vertex is skipped for the calculation. In the example above it would mean that the value of the weight would only be calculated using two vertices rather than three. – Sorade Sep 16 '16 at 17:05