[SOLVED] Numpy and line intersections

Issue

How would I use numpy to calculate the intersection between two line segments?

In the code I have `segment1 = ((x1,y1),(x2,y2))` and `segment2 = ((x1,y1),(x2,y2))`. Note `segment1` does not equal `segment2`. So in my code I’ve also been calculating the slope and y-intercept, it would be nice if that could be avoided but I don’t know of a way how.

I’ve been using Cramer’s rule with a function I wrote up in Python but I’d like to find a faster way of doing this.

Solution

``````#
# line segment intersection using vectors
# see Computer Graphics by F.S. Hill
#
from numpy import *
def perp( a ) :
b = empty_like(a)
b[0] = -a[1]
b[1] = a[0]
return b

# line segment a given by endpoints a1, a2
# line segment b given by endpoints b1, b2
# return
def seg_intersect(a1,a2, b1,b2) :
da = a2-a1
db = b2-b1
dp = a1-b1
dap = perp(da)
denom = dot( dap, db)
num = dot( dap, dp )
return (num / denom.astype(float))*db + b1

p1 = array( [0.0, 0.0] )
p2 = array( [1.0, 0.0] )

p3 = array( [4.0, -5.0] )
p4 = array( [4.0, 2.0] )

print seg_intersect( p1,p2, p3,p4)

p1 = array( [2.0, 2.0] )
p2 = array( [4.0, 3.0] )

p3 = array( [6.0, 0.0] )
p4 = array( [6.0, 3.0] )

print seg_intersect( p1,p2, p3,p4)
``````