Vec add(Vec a, Vec b)
{ return new Vec(a.x + b.x, a.y + b.y, a.z + b.z); }

becomes:

Vec add(Vec a, Vec b) {
  a.x += b.x;
  a.y += b.y;
  a.z += b.z;
  return a;

Another optimization is to replace the LinkedList with an ArrayList
and use .size() and .get() when iterating the list. Iterators are
slow.

Also remember to use the -server option when running the program, it
can improve performance significantly.

One other thing to try is to use float instead of double (if the
accuracy isn't needed). The latest Hotspot uses SSE, and this change
may have some effect on SSE optimizations.

Remember that the Hotspot JVM requires a quite long warmup before
compiling code, so if the program completes in a short time, you will
never reach the performance of C++.

With these optimizations I think the performance will be similar to
the C++ version.