Fourier-based multi-scale representation and progressive transmission of cartographic curves on the internet

ABSTRACT

Automatic generation of multi-scale representations from the same spatial data source has been the research focus in map generalization for a long time. Based on the Fourier technique, this paper proposes a continuous, multi-scale representation model for progressive transformation of cartographic curves on the Internet. In our method, all the curves, whether closed or open, are depicted as periodical functions which are further expressed as Fourier series. The convergence degrees of the Fourier series are explored for different kinds of curves, and truncating frequencies are derived based on the similarity between the original and reconstructed curves. Using information theory and the Radical Law in cartography, the relationship between map scales and Fourier frequencies is established. Based on the proposed multi-scale model, we also introduce the principles and implementation of a progressive transmission method. Our method is evaluated using the contours from a topographic map. The results show that our model is a valid approach to multi-scale representation of cartographic curves.

KEYWORDS:

• Map generalization
• periodical functions
• reconstruction
• Fourier series
• Radical Law

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which helped improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the Natural Science Foundation of China [project number 41371183]; self-determined research funds of CCNU from the colleges’ basic research and operation of MOE [project number CCNU15A02004]; the “One Hundred Talents Program” of the Chinese Academy of Sciences, and the National Science Foundation, China [grant number 41531180].