Problem 44365. An asteroid and a spacecraft

Needs more test cases to eliminate the the trivial non-solution that exploits the lack of test cases.

This problem needs more test cases. My solution probably is not general, but it works without using all of its tests.

An interesting test case, for instance, would be (that my solution and many others would fail):

p0 = [1, 0, 0];
p1 = [ -1, 0, 0];
p2 = [ 0, 1, 0.5];
p3 = [ 0, -1, 0.5];
t0 = 0;
t1 = 1;
d = 1;
ok = false;

At half-way their path, asteroid and spacecraft will be at distance 0.5 of each other, violating the safe distance d=1, and without crossing paths.