Plotting the map projection graticule involving discontinuities based on combined sampling


  • Tomáš Bayer Department of Applied Geoinformatics and Cartography, Charles University in Prague



digital cartography, mathematical cartography, adaptive sampling, graticule, meridians, parallels, recursive approach, map projection, great circle, discontinuity, visualization, sphere,


This article presents  new algorithm for interval plotting the projection graticule on the interval $\varOmega=\varOmega_{\varphi}\times\varOmega_{\lambda}$ based on the combined sampling technique. The proposed method synthesizes uniform and adaptive sampling approaches and treats discontinuities of the coordinate functions $F,G$. A full set of the projection constant values represented by the projection pole $K=[\varphi_{k},\lambda_{k}]$, two standard parallels $\varphi_{1},\varphi_{2}$ and the central meridian shift $\lambda_{0}^{\prime}$ are supported. In accordance with the discontinuity direction it utilizes a subdivision of the given latitude/longitude intervals $\varOmega_{\varphi}=[\underline{\varphi},\overline{\varphi}]$, $\varOmega_{\lambda}=[\underline{\lambda},\overline{\lambda}]$ to the set of disjoint subintervals $\varOmega_{k,\varphi}^{g},$$\varOmega_{k,\lambda}^{g}$ forming tiles without internal singularities, containing only "good" data; their parameters can be easily adjusted. Each graticule tile borders generated over $\varOmega_{k}^{g}=\varOmega_{k,\varphi}^{g}\times\varOmega_{k,\lambda}^{g}$ run along singularities. For combined sampling with the given threshold $\overline{\alpha}$ between adjacent segments of the polygonal approximation the recursive approach has been used; meridian/parallel offsets are $\Delta\varphi,\Delta\lambda$. Finally, several tests of the proposed algorithms are involved.


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