Dynamic Environmental Modeling by the C-Tree

Abstract

We introduce an e cient and robust spatial index to support a set of di erent queries, which is developed from G unther's Celltree 6 and the Monotonous Bisector Tree 11;16. In practice, huge scenes are manageable by using the paging{concept. For convex polyhedrons in N{dimensional real space and any L p {metric (1 p 1) we are able to show that the C-tree can be constructed in time O(n log n), linear space and logarithmic height, where n denotes the number of objects. Dynamic insertion of objects is performed in O(log 2 n) amortized worst{case time. Objects can be deleted in amortized O(n) or in amortized O(log 2 n) if the update of cluster radii can be delayed. In all cases logarithmic height and linear space requirements are preserved. (analogously for rSon(v)). a Always textually replace @ by the letter 'l' and 'r'. In the following we will use this shorter notation.