We define a set of arbitrarily-shaped objects in R(d) to be a low-dens
ity environment if any axis-parallel hypercube intersects only few obj
ects of comparable or larger size. Generalizing and simplifying previo
us results for fat objects, we present a data structure for point loca
tion in a low-density environment, and we show how this data structure
can be extended to perform range search queries with query ranges of
size comparable to the smallest object.