is_inside_polygon.py

def onSegment(p:tuple, q:tuple, r:tuple) -> bool:
    """
    # https://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
    # Given three collinear points p, q, r, 
    # the function checks if point q lies
    # on line segment 'pr'
    """ 
     
    if ((q[0] <= max(p[0], r[0])) &
        (q[0] >= min(p[0], r[0])) &
        (q[1] <= max(p[1], r[1])) &
        (q[1] >= min(p[1], r[1]))):
        return True
         
    return False


def orientation(p:tuple, q:tuple, r:tuple) -> int:
    """
    To find orientation of ordered triplet (p, q, r).
    The function returns following values
    0 --> p, q and r are collinear
    1 --> Clockwise
    2 --> Counterclockwise
    # See https://www.geeksforgeeks.org/orientation-3-ordered-points/amp/
    # for details of below formula.
    """
    
     
    val = (((q[1] - p[1]) *
            (r[0] - q[0])) -
           ((q[0] - p[0]) *
            (r[1] - q[1])))
            
    if val == 0:
        return 0
    if val > 0:
        return 1 # Collinear
    else:
        return 2 # Clock or counterclock


def doIntersect(p1:tuple, q1:tuple, p2:tuple, q2:tuple) -> bool:    
    """
    The main function that returns true if
    the line segment 'p1q1' and 'p2q2' intersect.
    """
     
    # Find the 4 orientations required for
    # the general and special cases
    o1 = orientation(p1, q1, p2)
    o2 = orientation(p1, q1, q2)
    o3 = orientation(p2, q2, p1)
    o4 = orientation(p2, q2, q1)
 
    # General case
    if ((o1 != o2) and (o3 != o4)):
        return True
 
    # Special Cases
 
    # p1 , q1 and p2 are collinear and p2 lies on segment p1q1
    if ((o1 == 0) and onSegment(p1, p2, q1)):
        return True
 
    # p1 , q1 and q2 are collinear and q2 lies on segment p1q1
    if ((o2 == 0) and onSegment(p1, q2, q1)):
        return True
 
    # p2 , q2 and p1 are collinear and p1 lies on segment p2q2
    if ((o3 == 0) and onSegment(p2, p1, q2)):
        return True
 
    # p2, q2 and q1 are collinear and
    # q1 lies on segment p2q2
    if (o4 == 0) and (onSegment(p2, q1, q2)):
        return True
 
    return False


def is_inside_polygon(points:list, p:tuple) -> bool:
    """
    Returns true if the point p lies
    inside the polygon[] with n vertices
    """
    	
    n = len(points)
	
	# There must be at least 3 vertices in polygon
    if n < 3:
        return False
		
	# Create a point for line segment from p to infinite
    INT_MAX = 10000
    extreme = (INT_MAX, p[1])
    count = i = 0
	
    while True:
        next = (i + 1) % n
		
		# Check if the line segment from 'p' to
		# 'extreme' intersects with the line
		# segment from 'polygon[i]' to 'polygon[next]'
        if (doIntersect(points[i], points[next], p, extreme)):
							
			# If the point 'p' is collinear with line
			# segment 'i-next', then check if it lies
			# on segment. If it lies, return true, otherwise false
            if orientation(points[i], p, points[next]) == 0:
                return onSegment(points[i], p, points[next])
								
            count += 1
			
        i = next
		
        if (i == 0):
            break
		
	# Return true if count is odd, false otherwise
    return (count % 2 == 1)
    

if __name__ == '__main__':
    polygon1 = [ (0, 0), (10, 0), (10, 10), (0, 10) ]
        
    p = (1, 1)
    if (is_inside_polygon(points = polygon1, p = p)):
        print('Yes')
    else:
        print('No')