A Matrix-Based Structure for Vario-Scale Vector Representation over a Wide Range of Map Scales: The Case of River Network Data

The representation of vector data at variable scales has been widely applied in geographic information systems and map-based services. When the scale changes across a wide range, a complex generalization that involves multiple operations is required to transform the data. To present such complex generalization, we proposed a matrix model to combine different generalization operations into an integration. This study was carried on a set of river network data, where two operations, i.e., network pruning accompanied with river simplification, were hierarchically constructed as the rows and columns of a matrix. The correspondence between generalization operations and scale, and the scale linkage of multiple operations were also explicitly defined. In addition, we developed a vario-scale data structure to store the generalized river network data based on the proposed matrix. The matrix model was validated and assessed by a comparison with traditional methods that conduct generalization operations in sequence. It was shown that the matrix model enabled complex generalization with good generalization quality. Taking advantage of the corresponding vario-scale data structure, the river network data could be obtained at any arbitrary scale, and the vario-scale representation was achieved across a wide scale range.