Abstract
Automatic multiple geographical feature label placement (MGFLP) is a combinatorial optimization problem shown to be an NP-hard problem, and it is a challenge in automatic cartography. Many automatic label placement algorithms for point, line, and area features were put forward. It is a common way to use multiple candidate positions (MCP) for label placement, but the research in this way mostly focuses on point features and does not take all three types of features and all the possible candidate positions into account on the map. Therefore, in this paper, the concept of degrees of spatial freedom for feature label placement is proposed based on the idea of degrees of freedom of mechanical motion. We define the degrees of freedom (DOF) and its space for feature labels on a planar map so as the potential space, including all the optional candidate positions of each feature label, can be standardized. Based on two degrees of freedom (2-DOF) space, feature reference position (FRP), and certain buffer distance (CBD) from FRP, we studied the methods including generating, calculating, evaluating, and selecting MCP for feature label. By using and improving the discrete differential evolution genetic algorithm (DDEGA), we carried out MGFLP experiments on the same dataset used by DDEGA algorithm. The results show that: 1) although the MCP based on the 2-DOF space increase the complexity of the NP-hard problem, however, the obtained results by optimizing the performance of the algorithm and increasing the number of candidate positions are still better than the traditional 8-candidate positions model. 2) In the same 2-DOF space, increasing the candidate positions from less to more along each direction of the 2-DOF space improves the quality of label placement.
Highlights
Accurate positioning of the labels on the map is one of the fundamental steps to visualize map information clearly, and it requires great attention from the cartographers
WORK Due to the lack of the insufficient degree of freedom space and the uncertainty of multiple candidate positions (MCP), the degree of freedom space for feature label placement is expanded from one degree to two degrees of freedom (2-DOF) space
Of generating, calculating, evaluating, and selecting MCP for feature label placement are studied to determine a proper method of generating multiple candidate positions for multiple geographical features
Summary
Accurate positioning of the labels on the map is one of the fundamental steps to visualize map information clearly, and it requires great attention from the cartographers. Since the 1960s, many studies have been done on automatic label placement of features. Automatic labeling is still a technical problem, which is one of the hotspots in computer graphics. The most common challenges on automatic label placement are label conflict, label-feature conflict, and association of label features. Many attempts have been made through decades of research to address these obstacles in automatic cartography. It has been proven that label placement is a non-deterministic polynomial-time hard (NP-hard) problem [1]. It is extremely difficult to estimate the ideal label position
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