I want to find an intersection point of two line segments, if one exists. Each line segment is represented by two endpoints. Each endpoint is represented as an ordered pair of numbers. There are no guarantees regarding the line segments (e.g., one or both line segments can be vertical or horizontal).

If multiple points of intersection exist, randomly return one of those intersection points. If no intersection exists, return None.

Pointing out any errors or potential improvements would be really appreciated.

from __future__ import division
from collections import namedtuple

Point = namedtuple('Point', 'x y')
Segment = namedtuple('Segment', 'ep1 ep2')

def find_slope(segment):
    Return the slope of the line segment, if it is defined. If it is
    undefined, return None.
    p1, p2 = segment.ep1, segment.ep2
    if p2.x - p1.x == 0.0:
        return None
        return (p2.y-p1.y) / (p2.x-p1.x)

def find_y_intercept(slope, point):
    Return the y-intercept of an infinite line with slope equal to slope that
    passes through point. If slope does not exist, return None.
    if slope is None:
        return None
        return point.y - slope*point.x

def order_segment(segment):
    Order endpoints in segment primarily by x position, and secondarily by y
    ep1, ep2 = segment.ep1, segment.ep2
    if (ep1.x > ep2.x or ep1.x == ep2.x and ep1.y > ep2.y):
        segment.ep1, segment.ep2 = segment.ep2, segment.ep1

def order_segments(segments):
    Order segments by each segment's first endpoint. Similar to order_segment,
    order primarily by first endpoint's x position, and secondarily by first
    endpoint's y position.
    seg1, seg2 = segments
    if (seg1.ep1.x > seg2.ep1.x or seg1.ep1.x == seg2.ep1.x
            and seg1.ep1.y > seg2.ep1.y):
        segments[0], segments[1] = segments[1], segments[0]

def on(point, segment):
    Return True if point lies on segment. Otherwise, return False.
    return (within(segment.ep1.x, point.x, segment.ep2.x) and
            within(segment.ep1.y, point.y, segment.ep2.y))

def within(p, q, r):
    Return True if q is between p and r. Otherwise, return False.
    return p <= q <= r or r <= q <= p

def find_intersection(segment1, segment2):
    Return an intersection point of segment1 and segment2, if one exists. If
    multiple points of intersection exist, randomly return one of those
    intersection points. If no intersection exists, return None.
    [s1, s2] = [find_slope(l) for l in [segment1, segment2]]
    [k1, k2] = [find_y_intercept(s, l[0])
                for s, l in [(s1, segment1), (s2, segment2)]]

    if s1 == s2:
        if k1 != k2:
            return None
        #  at this point, the two line segments are known to lie on the same
        #  infinite line (i.e. all of the endpoints are collinear)
        segments = [segment1, segment2]
        for segment in segments:
        intersection = segments[1].ep1
        #  assume segment 1 has slope and segment 2 doesn't
        s, x, k = s1, segment2.ep1.x, k1
        #  assumption wrong, segment 1 doesn't have a slope, but segment 2 does
        if s1 is None:
            s, x, k = s2, segment1.ep1.x, k2
        #  assumption wrong, segments 1 and 2 both have slopes
        elif s2 is not None:
            x = (k2-k1) / (s1-s2)
        y = s*x + k
        intersection = Point(x, y)

    if on(intersection, segment1) and on(intersection, segment2):
        return intersection
        return None
  • \$\begingroup\$ I haven't tested functionality, but your code is readable, clean, and well written. LGTM. The only nit I might have are about the s1, s2, k1, k2 variables, but for a function like this, I suppose they're fine. \$\endgroup\$
    – omgimanerd
    Commented Jul 15, 2017 at 0:02

2 Answers 2


I've not written much python, so I'm not qualified to comment on your coding style, etc. However, I do a lot of graphics work, and I can tell you that this is a lot more code than you should have to write for this task. It would be silly of me to repeat it all, but check out the answers to this question on Stack Overflow. You can see that it doesn't take more than a single function of about 10-20 lines.


The code looks okay, though a bit verbose, which isn't terrible, it's just not as nice to those with smaller screens :)

Some nits:

if a:
    return b
    return c

is the same as

if a:
    return b
return c

but the latter is a line shorter. You could make it even shorter in some cases by doing:

return b if a else c

but it may decrease legibility.

Also, it's complicated code, so could use some tests.

  • 1
    \$\begingroup\$ Actually I find the first style more explicit and thus more readable.. \$\endgroup\$
    – Pithikos
    Commented Mar 13, 2019 at 23:18
  • \$\begingroup\$ I agree with Pithikios \$\endgroup\$
    – k88
    Commented Apr 30, 2021 at 8:13

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