Use of the Spatial KD-Tree in Computational Physics Applications

Use of the Spatial KD-Tree in Computational Physics Applications

Year:    2007

Communications in Computational Physics, Vol. 2 (2007), Iss. 3 : pp. 545–576

Abstract

The need to perform spatial queries and searches is commonly encountered within the field of computational physics. The development of applications ranging from scientific visualization to finite element analysis requires efficient methods of locating domain objects relative to general locations in space. Much of the time, it is possible to form and maintain spatial relationships between objects either explicitly or by using relative motion constraints as the application evolves in time. Occasionally, either due to unpredictable relative motion or the lack of state information, an application must perform a general search (or ordering) of geometric objects without any explicit spatial relationship information as a basis. If previous state information involving domain geometric objects is not available, it is typically an involved and time consuming process to create object adjacency information or to order the objects in space. Further, as the number of objects and the spatial dimension of the problem domain is increased, the time required to search increases greatly. This paper proposes an implementation of a spatial k-d tree (skD-tree) for use by various applications when a general domain search is required. The skD-tree proposed in this paper is a spatial access method where successive tree levels are split along different dimensions. Objects are indexed by their centroid, and the minimum bounding box of objects in a node are stored in the tree node. The paper focuses on a discussion of efficient and practical algorithms for multidimensional spatial data structures for fast spatial query processing. These functions include the construction of a skD-tree of geometric objects, intersection query, containment query, and nearest neighbor query operations.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2007-CiCP-7918

Communications in Computational Physics, Vol. 2 (2007), Iss. 3 : pp. 545–576

Published online:    2007-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    Geometric query bounding volume hierarchy skD-tree containment query mesh generation h-refinement remapping.