Python: checking if point is inside a polygon

Question

I have a class describing a Point (has 2 coordinates x and y) and a class describing a Polygon which has a list of Points which correspond to corners (self.corners) I need to check if a Point is in a Polygon

Here is the function that is supposed to check if the Point in in the Polygon. I am using the Ray Casting Method

def in_me(self, point):
        result = False
        n = len(self.corners)
        p1x = int(self.corners[0].x)
        p1y = int(self.corners[0].y)
        for i in range(n+1):
            p2x = int(self.corners[i % n].x)
            p2y = int(self.corners[i % n].y)
            if point.y > min(p1y,p2y):
                if point.x <= max(p1x,p2x):
                    if p1y != p2y:
                        xinters = (point.y-p1y)*(p2x-p1x)/(p2y-p1y)+p1x
                        print xinters
                    if p1x == p2x or point.x <= xinters:
                        result = not result
            p1x,p1y = p2x,p2y
         return result

I run a test with following shape and point:

PG1 = (0,0), (0,2), (2,2), (2,0)
point = (1,1)

The script happily returns False even though the point it within the line. I am unable to find the mistake

Answer 1

I would suggest using the Path class from matplotlib

import matplotlib.path as mplPath
import numpy as np

poly = [190, 50, 500, 310]
bbPath = mplPath.Path(np.array([[poly[0], poly[1]],
                     [poly[1], poly[2]],
                     [poly[2], poly[3]],
                     [poly[3], poly[0]]]))

bbPath.contains_point((200, 100))

(There is also a contains_points function if you want to test for multiple points)

Answer 2

I'd like to suggest some other changes there:

def contains(self, point):
    if not self.corners:
        return False

    def lines():
        p0 = self.corners[-1]
        for p1 in self.corners:
            yield p0, p1
            p0 = p1

    for p1, p2 in lines():
        ... # perform actual checks here

Notes:

• A polygon with 5 corners also has 5 bounding lines, not 6, your loop is one off.
• Using a separate generator expression makes clear that you are checking each line in turn.
• Checking for an empty number of lines was added. However, how to treat zero-length lines and polygons with a single corner is still open.
• I'd also consider making the lines() function a normal member instead of a nested utility.
• Instead of the many nested if structures, you could also check for the inverse and then continue or use and.

Answer 3

Steps:

• Iterate over all the segments in the polygon
• Check whether they intersect with a ray going in the increasing-x direction

Using the intersect function from This SO Question

def ccw(A,B,C):
    return (C.y-A.y) * (B.x-A.x) > (B.y-A.y) * (C.x-A.x)

# Return true if line segments AB and CD intersect
def intersect(A,B,C,D):
    return ccw(A,C,D) != ccw(B,C,D) and ccw(A,B,C) != ccw(A,B,D)

def point_in_polygon(pt, poly, inf):
    result = False
    for i in range(len(poly.corners)-1):
        if intersect((poly.corners[i].x, poly.corners[i].y), ( poly.corners[i+1].x, poly.corners[i+1].y), (pt.x, pt.y), (inf, pt.y)):
            result = not result
    if intersect((poly.corners[-1].x, poly.corners[-1].y), (poly.corners[0].x, poly.corners[0].y), (pt.x, pt.y), (inf, pt.y)):
        result = not result
    return result

Please note that the inf parameter should be the maximum point in the x axis in your figure.