The quadcode and its arithmetic
Communications of the ACM
Adjacency detection using quadcodes
Communications of the ACM
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Overlapping linear quadtrees: a spatio-temporal access method
Proceedings of the 6th ACM international symposium on Advances in geographic information systems
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
An effective way to represent quadtrees
Communications of the ACM
Algorithms for Joining R-Trees and Linear Region Quadtrees
SSD '99 Proceedings of the 6th International Symposium on Advances in Spatial Databases
Speeding up construction of PMR quadtree-based spatial indexes
The VLDB Journal — The International Journal on Very Large Data Bases
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The usual quadtree node non-pointer codification is based on interleaved binary representations of node coordinates, in such a way that every operation that concerns to the spatial position or to the specific orientation of the region represented by the node needs to undo this interleaving process. So, the computation time of such operations is linear with the node depth. In this paper an alternative codification is presented called “non-interleaved codification”. The new codification has a simpler management and a higher intuitiveness than current codifications that use the interleaving approach. The proposed codification is more efficient than previous ones for the following set of operations: generating the node codes from the spatial coordinates, recovering original coordinates from the node codes, and performing topological operations where explicit or implicit reference is made to node location, for instance, checking if two nodes are adjacent, evaluating distances between nodes, evaluating relative orientation, etc. The proposed codification performs all these operations in O (1) time, independently from the node depth.