How to calculate line line intersection

Support
1

I got 2 lines and each line was defined by two points.
I’m trying to compute the intersection of the two lines with code below:

img1Line1P1 = [35.522341272816135, 244.0, -81.8808026069687]
img1Line1P2 = [36.1800944701046, 231.0, -81.31657002936069]
img2Line1P1 = [72.34037273903428, 244.0, -81.8925739257786]
img2Line1P2 = [70.43558942657907, 231.0, -81.32453925781688]

u = vtk.mutable(0)
v = vtk.mutable(0)

intersectType = vtk.vtkLine().Intersection(
img1Line1P1, img1Line1P2, img2Line1P1, img2Line1P2, u, v)
target11 = [img1Line1P1[i]+u*(img1Line1P2[i]-img1Line1P1[i]) for i in range(3)]
target12 = [img2Line1P1[i]+v*(img2Line1P2[i]-img2Line1P1[i]) for i in range(3)]
target1 = [(target11[i]+target12[i])/2 for i in range(3)]

print(intersectType)
print(u,v)
print(target11)
print(target12)
print(target1)

img1Line1P1 = [35.5223, 244, -81.8808]
img1Line1P2 = [36.4701, 231, -81.3736]
img2Line1P1 = [72.3401, 244, -81.8927]
img2Line1P2 = [70.4352, 231, -81.3244]

u = vtk.mutable(0)
v = vtk.mutable(0)

intersectType = vtk.vtkLine().Intersection(
img1Line1P1, img1Line1P2, img2Line1P1, img2Line1P2, u, v)
target11 = [img1Line1P1[i]+u*(img1Line1P2[i]-img1Line1P1[i]) for i in range(3)]
target12 = [img2Line1P1[i]+v*(img2Line1P2[i]-img2Line1P1[i]) for i in range(3)]
target1 = [(target11[i]+target12[i])/2 for i in range(3)]

print(intersectType)
print(u,v)
print(target11)
print(target12)
print(target1)

Output of code above goes like:

0
14.367889142863488 14.367746083471086
[44.972866294820804, 57.217441142774646, -73.7739714811047]
[44.97292976164488, 57.21930091487587, -73.73119604989571]
[44.97289802823284, 57.21837102882526, -73.7525837655002]
0
12.902095599460948 12.899676454379204
[47.7509062091691, 76.27275720700769, -75.33685711195344]
[47.76750632205291, 76.30420609307035, -74.56181387097621]
[47.759206265611006, 76.28848165003902, -74.94933549146482]

As you can see, even with a tiny difference of the points coordinates, the intersection calculated was totally different, especially with the Y-axis.

I was wondering if my code is the correct way to calculate the intersection of two 3D lines? How to get the correct result?

2

Hi,
Maybe I’m wrong but it seems that if intersectType == 0 it means no intersection.

3

Intersection type is for finite line(or line segment) intersection and my purpose is to find the intersection of two infinite line.

As you can see the u and v calculated are beyond [0, 1], this is why vtkLine::Intersection() returns 0.

Plus, these two lines are skew lines so there is no intersection in the 3D space. But since vtkLine::Intersection() calculates the intersection of two 3D lines by projecting them to a plane, it does find a point which is closest to both two lines and I call it intersection

4

The question was also asked and answered on the Slicer forum: