## Algorithmic Foundation of Multi-Scale Spatial RepresentationWith the widespread use of GIS, multi-scale representation has become an important issue in the realm of spatial data handling. However, no book to date has systematically tackled the different aspects of this discipline. Emphasizing map generalization, Algorithmic Foundation of Multi-Scale Spatial Representation addresses the mathematical basis of multi-scale representation, specifically, the algorithmic foundation. Using easy-to-understand language, the author focuses on geometric transformations, with each chapter surveying a particular spatial feature. After an introduction to the essential operations required for geometric transformations as well as some mathematical and theoretical background, the book describes algorithms for a class of point features/clusters. It then examines algorithms for individual line features, such as the reduction of data points, smoothing (filtering), and scale-driven generalization, followed by a discussion of algorithms for a class of line features including contours, hydrographic (river) networks, and transportation networks. The author also addresses algorithms for individual area features, a class of area features, and various displacement operations. The final chapter briefly covers algorithms for 3-D surfaces and 3-D features. Providing a thorough treatment of low-level algorithms, Algorithmic Foundation of Multi-Scale Spatial Representation supplies the mathematical groundwork for multi-scale representations of spatial data. |

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Algorithm Based analysis angle applied area features automated averaging boundary bounding box buildings Cartographic Cartographic Journal Cartography and Geographic cell centroid cluster coefficients collapse contour lines convex hull coordinates corner detection criterion critical points cubic function curvature curved line Delaunay triangulation dilation displacement elimination Equation example filtering follows fractal dimension frequency function Gaussian Gaussian function generalisation Geographic Information Systems geometric transformations illustrated in Figure Li-Openshaw algorithm line features line smoothing linear mathematical mathematical morphology McMaster medial axis morphological multi-scale representation natural principle number of points Openshaw operation original line parameters Pattern Recognition Perkal algorithm perpendicular distance pixel point features point-reduction algorithms raster mode rectangle region-of-support represented Reprinted result road segments scale-driven scale-space selective omission sequential set of points shape shown in Figure shows skeleton smaller scale spatial data split structuring element template thematic thickening topological triangle types typification vector Voronoi diagram wavelet Weibel