# [Numpy-discussion] Python function for line intersection??

Happyman bahtiyor_zohidov at mail.ru
Tue Oct 8 09:15:54 EDT 2013

``` Hello,

I am having trouble with solving line intersection problem. I would solve it using standard functions which may already exist in Python library.
Let me explain it below:
I have sets of lines A(x,y) and B(x,y) and one map as a matrix form, also with its resolution dx, dy which can be changed.
I wanted to calculate all intersected points of line with the map depending on dx, dy value. I already did it, but two problems:
1) When some coordinate value (x or y) are zero, the program returns wrong answer. For example, distance is zero, but it is not zero in fact.
2) How can I optimize my code (using Python standard library), if possible.

Or is there standard Python library for that purpose???

import numpy as np

def intrsctd_pnts(map, dx, dy, A, B, line_number):

height, width = np.shape(map)

# slope of each line
m = (B[:, 1] - A[:, 1]) / (B[:, 0] - A[:, 0])
b = A[:, 1] - m * A[:, 0]

lx_min = np.minimum(A[:,0], B[:,0])
lx_max = np.maximum(A[:,0], B[:,0])
ly_min = np.minimum(A[:,1], B[:,1])
ly_max = np.maximum(A[:,1], B[:,1])

lx_floor = np.ceil(lx_min /dx)*dx
lx_ceil = np.floor(lx_max /dx)*dx
ly_floor = np.ceil(ly_min /dy)*dy
ly_ceil = np.floor(ly_max /dy)*dy

distance = []
i_pixel = []
intersect_point = []
for i in range(line_number):
AB = []
# calculate all intersected x coordinates
x = np.arange(lx_floor[i], lx_ceil[i]+dx, dx)
y = m[i] * x + b[i]
AB = zip(x, y)
# calculate all intersected y coordinates
y = np.arange(ly_floor[i], ly_ceil[i]+dy, dy)
x = (y - b[i]) / m[i]
AB.extend(zip(x, y))
AB.append((A[i,0], A[i,1]))
AB.append((B[i,0], B[i,1]))
AB.sort()
AB = np.asarray(AB)
intersect_point.append(AB)
# compute distance between two points
dist_x = np.diff(AB[:,0])
dist_y = np.diff(AB[:,1])
distance.append( np.sqrt((dist_x)**2 + (dist_y)**2) )

# FIND pixel value where line intersects that pixel
col = (np.floor( min(AB[:,0]) / dx)).astype(int)
row = (np.floor( min(AB[:,1]) / dy)).astype(int)

# FIND  pixel to which this lines belong
i_pixel.append(col + width*row)

return distance, i_pixel, intersect_point

def main():
# INPUTS:
map = np.array( [ [ 4.5,  4.5,  4.5,  3.4],
[ 3.9,  4.5,  5.2,  4.5],
[ 3.9,  3.9,  2.5,  2.2],
[ 3.4,  3.9,  2.9,  2.2],
[ 2.5,  3.4,  2.2,  1.4],
[ 2.5,  2.2,  2.5,  1.2] )
dx = dy = 0.5
A = np.array( [ [ 0. , 0. ],
[ 1.9 , 0.] ])

B = np.array( [ [ 1.1 , 2.3],
[ 1.3 , 1.3] ])

line_number = len(A)  # or len(B)

distance, pixels, int_points = intrsctd_pnts(map, dx, dy, A, B, line_number)

##  distance should not be zero

if __name__ == '__main__':
main()

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