# Checking if a point is inside a polygon

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### Question :

Checking if a point is inside a polygon

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 is 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

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)

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`.

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.

I was trying to solve the same problem for my project and I got this code from someone in my network.

``````#!/usr/bin/env python
#
# routine for performing the "point in polygon" inclusion test

# This code may be freely used and modified for any purpose
# providing that this copyright notice is included with it.
# SoftSurfer makes no warranty for this code, and cannot be held
# liable for any real or imagined damage resulting from its use.
# Users of this code must verify correctness for their application.

# translated to Python by Maciej Kalisiak <mac@dgp.toronto.edu>

#   a Point is represented as a tuple: (x,y)

#===================================================================

# is_left(): tests if a point is Left|On|Right of an infinite line.

#   Input: three points P0, P1, and P2
#   Return: >0 for P2 left of the line through P0 and P1
#           =0 for P2 on the line
#           <0 for P2 right of the line
#   See: the January 2001 Algorithm "Area of 2D and 3D Triangles and Polygons"

def is_left(P0, P1, P2):
return (P1[0] - P0[0]) * (P2[1] - P0[1]) - (P2[0] - P0[0]) * (P1[1] - P0[1])

#===================================================================

# cn_PnPoly(): crossing number test for a point in a polygon
#     Input:  P = a point,
#             V[] = vertex points of a polygon
#     Return: 0 = outside, 1 = inside
# This code is patterned after [Franklin, 2000]

def cn_PnPoly(P, V):
cn = 0    # the crossing number counter

# repeat the first vertex at end
V = tuple(V[:])+(V[0],)

# loop through all edges of the polygon
for i in range(len(V)-1):   # edge from V[i] to V[i+1]
if ((V[i][1] <= P[1] and V[i+1][1] > P[1])   # an upward crossing
or (V[i][1] > P[1] and V[i+1][1] <= P[1])):  # a downward crossing
# compute the actual edge-ray intersect x-coordinate
vt = (P[1] - V[i][1]) / float(V[i+1][1] - V[i][1])
if P[0] < V[i][0] + vt * (V[i+1][0] - V[i][0]): # P[0] < intersect
cn += 1  # a valid crossing of y=P[1] right of P[0]

return cn % 2   # 0 if even (out), and 1 if odd (in)

#===================================================================

# wn_PnPoly(): winding number test for a point in a polygon
#     Input:  P = a point,
#             V[] = vertex points of a polygon
#     Return: wn = the winding number (=0 only if P is outside V[])

def wn_PnPoly(P, V):
wn = 0   # the winding number counter

# repeat the first vertex at end
V = tuple(V[:]) + (V[0],)

# loop through all edges of the polygon
for i in range(len(V)-1):     # edge from V[i] to V[i+1]
if V[i][1] <= P[1]:        # start y <= P[1]
if V[i+1][1] > P[1]:     # an upward crossing
if is_left(V[i], V[i+1], P) > 0: # P left of edge
wn += 1           # have a valid up intersect
else:                      # start y > P[1] (no test needed)
if V[i+1][1] <= P[1]:    # a downward crossing
if is_left(V[i], V[i+1], P) < 0: # P right of edge
wn -= 1           # have a valid down intersect
return wn
``````