# Infinity point how it defined - Secp256K Curve

I have problem with point infinity. How to solve it?

Curve Secp256k

# A Python3 program to check if a given point
# lies inside a given polygon
#
# for explanation of functions onSegment(),
# orientation() and doIntersect()

# Define Infinity (Using INT_MAX
# caused overflow problems)
INT_MAX = 9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

def onSegment(p: tuple, q: tuple, r: tuple) -> bool:
r"""
Check whether point q lies on line segment 'pr'
"""
if (q[0] <= max(p[0], r[0]) and
q[0] >= min(p[0], r[0]) and
q[1] <= max(p[1], r[1]) and
q[1] >= min(p[1], r[1])):
return True
return False

def orientation(p: tuple, q: tuple, r: tuple) -> int:
r"""
Return the orientation of the ordered triple (p, q, r).

The orientation is encoded as:

- 0 if p, q and r are collinear
- 1 if they turn clockwise
- 2 if they turn counterclockwise
"""
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
return 2

def doIntersect(p1, q1, p2, q2):
# Find the four orientations needed for
# 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 p2 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:
r"""
Check whether the point p lies inside
the polygon defined by points.
"""
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 infinity - how to define this point?

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

# Driver code
if __name__ == '__main__':
# i: 1
x = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
# i: 2
x2 = 0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5
y2 = 0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a
# i: 3
x3 = 0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9
y3 = 0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672
# i: 4
x4 = 0xe493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13
y4 = 0x51ed993ea0d455b75642e2098ea51448d967ae33bfbdfe40cfe97bdc47739922
# i: 5
x5 = 0x2f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4
y5 = 0xd8ac222636e5e3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6
# i: 6
x6 = 0xfff97bd5755eeea420453a14355235d382f6472f8568a18b2f057a1460297556
y6 = 0xae12777aacfbb620f3be96017f45c560de80f0f6518fe4a03c870c36b075f297

polygon1 = [(x, y), (x2, y2), (x4, y4), (x5, x5), (x6, y6)]

p = (x3, y3)
if is_inside_polygon(points=polygon1, p=p):
print ('Yes')
else:
print ('No')

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I think your function onSegment checks whether q is in the rectangle with corners p and r and horizontal and vertical sides; not whether it is on the segment from p to r.