Geographic information systems (GIS) have become increasingly important in helping us understand complex social, economic, and natural dynamics where spatial components play a key role. The critical algorithms used in GIS, however, are notoriously difficult to both teach and understand, in part due to the lack of a coherent representation. GIS Algorithms attempts to address this problem by combining rigorous formal language with example case studies and student exercises. Using Python code throughout, Xiao breaks the subject down into three fundamental areas:  • Geometric Algorithms  • Spatial Indexing  • Spatial Analysis and Modelling With its comprehensive coverage of the many algorithms involved, GIS Algorithms is a key new textbook in this complex and critical area of geography.

# Chapter 6: Quadtrees

A quadtree uses both X and Y coordinates to index geospatial data, which is a different strategy from the k-D tree where only one dimension is used at a time. In order to use both coordinates, a node in a quadtree partitions the area into four parts, which, depending on different design ideas and rules, might be further partitioned into four smaller parts. The idea of quadtrees can be applied to not only points, but also higher-dimensional geometric objects such as lines and polygons, and different data models such as the raster model. In the GIS literature, the use of quadtrees in raster data has probably received the most attention, arguably due to the fact that raster is a useful data model for ...

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