Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Abstraction in Cartographic Generalization
ISMIS '00 Proceedings of the 12th International Symposium on Foundations of Intelligent Systems
GIS: A Computing Perspective, 2nd Edition
GIS: A Computing Perspective, 2nd Edition
Design and Implementation of Multi-scale Databases
SSTD '01 Proceedings of the 7th International Symposium on Advances in Spatial and Temporal Databases
GIScience'10 Proceedings of the 6th international conference on Geographic information science
Accentuating focus maps via partial schematization
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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Manual cartographic generalization is a simultaneous process. However, most automatic approaches so far have been sequential; generalization operators are applied one at a time in a certain order. This has been the case both for model generalization (generalization of the conceptual model) and graphic generalization. Our research seeks to demonstrate that the graphic part of cartographic generalization can be formulated as an optimization problem and accordingly be solved in a single step. This paper deals with several issues regarding this optimization approach. Firstly, a set of appropriate analytical constraints for the generalization process is given, as well as rules for when to apply these constraints. In our approach, we are limited to formulating these constraints on point locations. Secondly, least-squares adjustment is proposed to find the optimal solution according to the constraints. Finally, the conjugate-gradients method is recommended for solving the normal equations. A prototype system for simultaneous graphic generalization has been implemented in C++, which communicates with a commercial map production system. Results from three tests of the prototype system are included in the paper.