Abstract
This chapter discusses the basic principles of the σ-tree. The σ-tree is a symbolic hierarchical representation of a 3D space. The structure of the hierarchy is logically designed to support spatial reasoning and query techniques and serves therefore as a spatial data model. The chapter focuses on three basic concepts of σ-tree: the universal, the cluster, and the spatial model. The basic idea behind the σ-tree is simply to describe the universe in terms of a technique similar to that of using “lego” blocks in conjunction with symbolic algebra. Two query techniques, which are both recursive are introduced in the chapter, of which the first is concerned with the σ-tree, while the second is developed for a related structure called VPT. The two data models presented in the chapter, i.e., the σ-tree and the VPT models are similar in that they both demonstrate how queries can be formulated and answered in a qualitative way, which is a unique characteristic that most query languages of today do not possess. Both data models are also similar in that they permit application of recursive queries; they differ in that only the σ-tree model is generalized into three dimensions.
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