Optimal angular sampling for 3D volume matching and faster fitting of 3D structures into cryogenic electron microscopy data

A numerical algorithm to generate a set of optimal 3D rotations is presented. A list is created, with each new rotation found in a way to minimise the gap in angular coverage for a global angular search or a local angular refinement problem. Efficiency can be gained by combining rotations in groups when fitting molecular density representations to an experimental electron density map in cryo electron microscopy, and this algorithm also works for those combined rotations. Lists of optimal rotations written as quaternions and code to generate those lists are provided. The maximum gap in the angular coverage decays as a reciprocal-cubic function of the number of rotations.