A method, termed approximate splitting, is proposed to model the node distribution that results when the PR quadtree is used to store point data drawn from a uniform distribution. This method can account for the aging and phasing phenomena which are common in most hierarchical data structures. Approximate splitting is also shown to be capable of being adapted to model the node distribution of t...

We give a closed-form expression for the average number of n-dimensional quadtree nodes (“pieces” or “blocks”) required by an n-dimensional hyperrectangle aligned with the axes. Our formula includes as special cases the formulae of previous efforts for two-dimensional spaces [8]. It also agrees with theoretical and empirical results that the number of blocks depends on the hypersurface of the h...

We explore the applicability of the quadtree encoding method to the run-time MPI collective algorithm selection problem. Measured algorithm performance data was used to construct quadtrees with different properties. The quality and performance of generated decision functions and in-memory decision systems were evaluated. Experimental data shows that in some cases, a decision function based on a...

This paper uniies the problems of variable block size motion estimation (VBSME) and region-based segmen-tation using a quadtree approach. The quadtree's nodes are each labeled providing region-based segmentation, and the same quadtree is also used for block motion estimation. The Lagrange multiplier method and a tree-pruning technique are used to nd the optimal tree which achieves the joint opt...

SAND is a spatial database and information browser system developed at University of Maryland which supports 2D and 3D data models. The experience in extending SAND to include a spherical data model thereby enabling SAND to perform spatial queries on spherical data and to browse their results in an incremental manner is described. The focus is on the issues that arise in adding a spherical data...

The new generation of spaceborne laser altimeter, the Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2), which can simultaneously generate reflections on water surface underwater, is a potential data source for exploring depth in nearshore environments. To achieve this scientific goal, accurate bathymetric photon extraction needed. This study proposed pre-pruning quadtree isolation (PQI) me...

Many algorithms exist for producing quality meshes when the input point cloud is known a priori. However, modern finite element simulations and graphics applications need to change the input set during the simulation dynamically. In this paper, we show a dynamic algorithm for building and maintaining a quadtree under insertions into and deletions from an input point set in any fixed dimension. ...