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I have a real life problem. I have a segment representing a road that is defined by its geographic coordinates (let's call them p1_road_test and p2_road_test) and want to test whether it intersects with another set of segments (I gave all segments different coordinates to keep it simple) :

p1_road_test = np.array([1, 1]) # x, y value of point 1 of the road segment
p2_road_test = np.array([2, 4]) # x, y value of point 2 of the road segment

The other segments are defined by an original point (p_origin_test) and another point (p_moved_test) that describes to which position the original point has moved within a year:

p_origin_test = np.matrix([(3, 5, 6), (1, 1, 2)]) 
p_moved_test = np.matrix([(1,3, 3), (3, 3, 2)])
# basically, the original point (3, 1)  moved to position (1, 3) and spans the segment accordingly. (5, 1) moves to (3, 3) etc.

p_origin_test
Out[46]: 
matrix([[3, 5, 6],
        [1, 1, 2]])

p_moved_test Out[47]:  
matrix([[1, 3, 3],
        [3, 3, 2]])

I chose a numpy matrix to store the data to speed up the calculation, since I have 30000+ segments I need to test against the street segment. In the end I would like to know if the second segment will ever intersect with the street segment when it continues to move at this "velocity" (the p_moved was surveyed after a month).

I followed this post to calculate if two segments intersect and derive their s and t value. So far so good.

X1, Y1 = p1_road_test[0], p1_road_test[1]
X2, Y2 = p2_road_test[0], p2_road_test[1]

#count = 0
Segment1 = ((X1, Y1), (X2, Y2))
for i in range(0, np.shape(p_origin_test)[1]):
    X3, Y3 = p_origin_test[0, i], p_origin_test[1, i]
    X4, Y4 = p_moved_test[0, i], p_moved_test[1, i]
    Segment2 = ((X3, Y3), (X4, Y4))

    dx1 = X2 - X1
    dx2 = X4 - X3
    dy1 = Y2 - Y1
    dy2 = Y4 - Y3
    
    det = dx1 * dy2 - dx2 * dy1
    
    dx3 = X1 - X3
    dy3 = Y1 - Y3
    
    det1 = dx1 * dy3 - dx3 * dy1
    det2 = dx2 * dy3 - dx3 * dy2
    
    s = 3 / dx1
    t = 1 / dx1
    
    s = det1 / det
    t = det2 / det
    if s < 0.0 or s > 1.0 or t < 0.0 or t > 1.0:
        print('false', s, t)  # no intersect
    else:
        print(s, t)

which results in the anticipated output:

0.75 0.5
false 1.5 1.0
false 1.5555555555555556 0.3333333333333333

However, I would rather like to have another matrix as output with the same dimension as my input dataset (2, 30000) containing the s and t value since I will be needing it to further derive the "change per time unit". Also I know there is a more elegant way of doing this calculation than looping through the columns, but I can't figure it out.

I would really appreciate your input on this one.

I am working with Python 3.6.9 in Spyder3 on a Linux Mint 19.3.

ohnoinkimono
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1 Answers1

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I created two lists now,

s_list = []
t_list = []

stored the s and t value in it

[...]

if s < 0.0 or s > 1.0 or t < 0.0 or t > 1.0:
    print('false', s, t)  # no intersect
else:
    print(s, t)
s_list.append(s)
t_list.append(t)

and created a matrix out of this.

st_values = np.matrix([s_list, t_list])

Still, I am certain there is a better solution!?

ohnoinkimono
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