... generalize directly to more than two dimen- sions: simple, straightforward extensions to the above algorithms immediately yield range-searching methods which work for more than two dimensions. However, ... space dictates that some caution is called for and that the performance characteristics of the algorithms might be difficult to predict for a particular application. To implement the grid method ... determining whether any two out of a set of N objects intersect in time proportional to N log N, based on algorithms presented by M. Shamos and D. Hoey in a seminal paper in 1976. First, we’ll consider...