Augmented reality requires real and virtual objects to be registered in three dimensions from any viewing direction. Therefore, accurate, large field of regard head tracking is needed. As a part of a research effort to design probes to track the position and orientation of the head of a user in a virtual environment, an algorithm is provided for the uniform distribution of an arbitrary number of beacons on a spherical probe using simulated annealing. The validity of the algorithm is tested by comparison to the tetrahedron, octahedron, and icosahedron, which are spherical equivalents. Additionally, variations upon the cooling schedule implemented in the algorithm and the effects upon the resulting point distributions are examined. Finally, a successfully constructed head-tracking probe is presented and the generalization of the algorithm to probes of other shapes is discussed.