Points on SO(3) with low logarithmic energy
Abstract
We describe several randomized collections of 3× 3 rotation matrices and analyze their associated logarithmic energy. The best one (i.e. the one attaining the lowest expected logarithmic energy) is constructed by choosing r spherical points, which come from the zeros of a randomly chosen degree r polynomial, and considering at each of these points a set of s evenly distributed rotation matrices. This construction yields a new upper bound on the minimal logarithmic energy of n=rs rotation matrices.
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