6 research outputs found
Partitioning space for range queries
Get PDFIt is shown that, given a set S of n points in R3, one can always find three planes that form an eight-partition of S, that is, a partition where at most n/8 points of S lie in each of the eight open regions. This theorem is used to define a data structure, called an octant tree, for representing any point set in R3. An octant tree for n points occupies O(n) space and can be constructed in polynomial time. With this data structure and its refinements, efficient solutions to various range query problems in 2 and 3 dimensions can be obtained, including (1) half-space queries: find all points of S that lie to one side of any given plane; (2) polyhedron queries: find all points that lie inside (outside) any given polyhedron; and (3) circular queries in R2: for a planar set S, find all points that lie inside (outside) any given circle. The retrieval time for all these queries is T(n)=O(na + m) where a= 0.8988 (or 0.8471 in case (3)) and m is the size of the output. This performance is the best currently known for linear-space data structures which can be deterministically constructed in polynomial time
Efficient contact determination between geometric models
Get PDFhttp://archive.org/details/efficientcontact00linmN
