Real-time approximation of molecular interaction interfaces based on hierarchical space decomposition

The interaction interface between two molecules can be represented as a bisector surface equidistant from the two sets of spheres of varying radii representing atoms. We recursively divide a box containing both sphere-sets into uniform pairs of sub-boxes. The distance from each new box to each sphere-set is conservatively approximated by an interval, and the number of sphere-box computations is greatly reduced by pre-partitioning each sphere-set using a kd-tree. The subdivision terminates at a specified resolution, creating a box partition (BP) tree. A piecewise linear approximation of the bisector surface is then obtained by traversing the leaves of the BP tree and connecting points equidistant from the sphere-sets. In 124 experiments with up to 16,728 spheres, a bisector surface with a resolution of 12⁴ of the original bounding box was obtained in 28.8 ms on average.