Plotting the map projection graticule involving discontinuities based on combined sampling

• Main Author: Tomáš Bayer
• Format: Article
• Language: English
• Published: Czech Technical University in Prague 2018-07-01
• Series: Geoinformatics FCE CTU
• Subjects: digital cartography; mathematical cartography; adaptive sampling; graticule; meridians; parallels; recursive approach; map projection; great circle; discontinuity; visualization; sphere
• Online Access: https://ojs.cvut.cz/ojs/index.php/gi/article/view/4940

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