Commun. Comput. Phys., 2 (2007), pp. 545-576.


Use of the Spatial kD-Tree in Computational Physics Applications

A. Khamayseh 1*, G. Hansen 2

1 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
2 Multiphysics Methods Group, Idaho National Laboratory, Idaho Falls, ID, USA.

Received 13 July 2006; Accepted (in revised version) 8 November 2006
Available online 4 December 2006

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 ($sk$D-tree) for use by various applications when a general domain search is required. The $sk$D-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 $sk$D-tree of geometric objects, intersection query, containment query, and nearest neighbor query operations.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Geometric query, bounding volume hierarchy, $sk$D-tree, containment query, mesh generation, $h$-refinement, remapping.

*Corresponding author.
Email: khamaysehak@ornl.gov (A. Khamayseh), Glen.Hansen@inl.gov (G. Hansen)
 

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