### Plotting the map projection graticule involving discontinuities based on combined sampling

#### Abstract

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.

#### Keywords

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