Example : I am flying a course of 045 degrees, at 3500 ft, someone else is flying a course of 135 degrees also at 3500 ft. Both of us are complying with the hemispherical rule, but we are potentially heading towards each other on a collision course.
I would recommend you review the extensive work done by Robert Patlovany by googling "Robert Patlovany collision", and also the work done by Russell A. Paielli.
The 1928 Australian invention, the Altimeter-Compass Cruising Altitude Rule (ACCAR), would be much safer.
Paielli's model, made in 2000, corroborated an earlier 1997 model by Patlovany showing that zero altitude error by pilots obeying the hemispherical cruising altitude rules resulted in six times more mid-air collisions than random cruising altitude. Similarly, Patlovany's computer model test of the Altimeter-Compass Cruising Altitude Rule (ACCAR) with zero piloting altitude error (a linear cruising altitude rule similar to the one recommended by Paielli), resulted in about 60% of the mid-air collisions counted from random altitude non compliance, or 10 times fewer collisions than the internationally accepted hemispherical cruising altitude rules. In other words, Patlovany's ACCAR alternative and Paielli's linear cruising altitude rule would reduce cruising midair collisions between 10 and 33 times, compared to the currently recognized, and internationally required, hemispherical cruising altitude rules, which institutionalize the navigation paradox on a worldwide basis.
The ACCAR alternative to the hemispherical cruising altitude rules, if adopted in 1997, could have eliminated the navigation paradox at all altitudes, and could have saved 342 lives in over 30 midair collisions (up to November 2006) since Patlovany's risk analysis proves that the current regulations increase the risk of a midair collision in direct proportion to pilot compliance.