YOu have the following options to check:
1. Do interpolation of the points along the path, if any point has 1, it is crossing the wall. Note that, for this you need to generate lot many points along the path so that a point lies on the yellow path.
2. Generate the points along the path, get the nearest neigboours to those points and see, any point is from yellow path.
3. Find the intersection between shortest paths and yellow paths. This would be better a solution.