With the construction of spatial data infi＇astructure, automated topographic map generalization becomes an indispensable component in the community of cartography and geographic information science. This paper descri...With the construction of spatial data infi＇astructure, automated topographic map generalization becomes an indispensable component in the community of cartography and geographic information science. This paper describes a topographic map generalization system recently developed by the authors. The system has the following characteristics： 1） taking advantage of three levels of automation, i.e. fully automated generalization, batch generalization, and interactive generalization, to undertake two types of processes, i.e. intelligent inference process and repetitive operation process in generalization; 2） making use of two kinds of sources for generalizing rule library, i.e. written specifications and cartographers＇ experiences, to define a six-element structure to describe the rules; 3） employing a hierarchical structure for map databases, logically and physically; 4） employing a grid indexing technique and undo/redo operation to improve database retrieval and object generalization efficiency. Two examples of topographic map generalization are given to demonstrate the system. It reveals that the system works well. In fact, this system has been used for a number of projects and it has been found that a great improvement in efficiency compared with traditional map general- ization process can be achieved.展开更多
Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homoto...Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homotopy class of maps of Brower degree±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree±1 in a large family of maps from a torus into a sphere.展开更多
基金Under the auspices of the National Natural Science Foundation of China (No. 40301037), and a PolyU Project(G-T873)
文摘With the construction of spatial data infi＇astructure, automated topographic map generalization becomes an indispensable component in the community of cartography and geographic information science. This paper describes a topographic map generalization system recently developed by the authors. The system has the following characteristics： 1） taking advantage of three levels of automation, i.e. fully automated generalization, batch generalization, and interactive generalization, to undertake two types of processes, i.e. intelligent inference process and repetitive operation process in generalization; 2） making use of two kinds of sources for generalizing rule library, i.e. written specifications and cartographers＇ experiences, to define a six-element structure to describe the rules; 3） employing a hierarchical structure for map databases, logically and physically; 4） employing a grid indexing technique and undo/redo operation to improve database retrieval and object generalization efficiency. Two examples of topographic map generalization are given to demonstrate the system. It reveals that the system works well. In fact, this system has been used for a number of projects and it has been found that a great improvement in efficiency compared with traditional map general- ization process can be achieved.
基金supported by the Natural Science Foundation of China(No.11361073)supported by the Natural Science Foundation of Guangxi Province of China(No.2011GXNSFA018127)
文摘Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homotopy class of maps of Brower degree±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree±1 in a large family of maps from a torus into a sphere.
