A Homotopic Approach to Cartographic Generalization
نویسندگان
چکیده
Given a collection of objects on a map, we seek a method of enlarging the objects over time so that these objects are still visible when the map is zoomed out. This question is brought to rigor as well-defined problems in homotopic deformation. We ask the objects, over time, to preserve topology, area-ratios and relative position. A solution is conjectured, using differential methods, leading to possible applications to cartograms. The problem is also extended to include the notion of epsilon-separation.
منابع مشابه
How the Quality of Cartographic Generalization Is Assured – the Approach with an Automatic Cartographic Generalization Chain
As one of the key techniques in multi-representation database, GIS, mapmaking and Digital Earth, automatic cartographic generalization has been intensively researched since decades. Current developments worldwide have been concentrated on the efforts towards adaptive and easily embeddable automatic generalization modules or services. Based on an analysis of the common rules concerning the quali...
متن کاملShape deformation in continuous map generalization
Given a collection of regions on a map, we seek a method of altering the regions over time so they are still visible when the map is scaled. This is formalized and brought to rigor as well-defined problems in homotopic deformation. We ask the regions to preserve topology, area-ratios and relative position as they change over time. A solution is conjectured, using differential methods, leading t...
متن کاملGenetic agent approach for improving on-the-fly web map generalization
The utilization of web mapping becomes increasingly important in the domain of cartography. Users want access to spatial data on the web specific to their needs. For this reason, different approaches were appeared for generating on-the-fly the maps demanded by users, but those not suffice for guide a flexible and efficient process. Thus, new approach must be developed for improving this process...
متن کاملHybrid approach for optimizing on-the-fly web map generalization
Abstract The creation of the map on-the-fly becomes today an important domain in cartography. Thousands of the users need access to spatial data on the web specific to their needs. This requires generating a map in real time. Different approaches appeared for optimizing the on-the-fly generation maps, but those not suffice for guiding a powerful and efficient process. Thus, a new approach must ...
متن کاملB-spline Curve Fitting: Application to Cartographic Generalization of Maritime Lines
Generalization is the process of abstraction applied when the scale of a map is changed. It involves modifications of data in such a way that the data can be represented in a smaller space, while best preserving geometric as well as descriptive characteristics. A map is an abstracted model representing the geometric reality. The smaller the scale, the more schematic the representation. Line car...
متن کامل