Points in which polygon

Question

I have several (order of M) points [(x0,y0),...,(xn,yn)]. I also have limited number of hexagons. I want to find each point falls in which hexagon. Using shapely this can be done for 1 point at a time so the loop below does the job. But is there any other way to do it faster?

from shapely.geometry import Point
from shapely.geometry.polygon import Polygon
zones = np.zeros(n)-1
for j,p in enumerate(points):
    point = Point(p)
    for i in range(len(poly_hex)): #poly_hex = list of hexagonal polygones
        polygon = Polygon(poly_hex[i])
        if polygon.contains(point):
            zones[j] = int(i)
            break

Answer 1

Some ideas to speed things up:

• Don't convert your hexagons to polygon = Polygon(poly_hex[i]) at each step of the inner loop. Calculate them once before the loop and store them in a list.
• As the surface of a hexagon is close to a circle, also make a list of just the centre and the radius of the hexagons. Inside the loop, first test the distance between the point p and the centre of each hexagon, comparing to the radius. Only in case p is less than the radius to the centre, do an explicit test to see whether it is inside the hexagon.
• If this still isn't fast enough, and depending on how small, and how far apart the hexagons are relative to your points, you could speed things up further with a quadtree or a grid. But this is less trivial. If most of the points are outside all hexagons, you could first test whether p is inside the convex hull of the hexagons.

Some remarks:

• I don't understand your zone[j] = int(i) . You convert i to an integer, while it already is an integer. Also, the way you store this, means a point can only be inside maximum one hexagon. Therefore, you can stop the loop as soon as you encountered such a hexagon. (There is also the rare case where a point is just on the edge between two hexagon. This might assign it to the first hexagon encountered. Or, due to rounding errors, even might have it outside both hexagons.)
• If you want to save the zones as integers, create it as: zones = np.zeros(n, dtype=int)-1 .
• If your hexagons form a regular hexagonal grid, you can find the exact hexagon simply from the x and y coordinates without the need for in-polygon testing.