### Efficient plotting the functions with discontinuities based on combined sampling

#### Abstract

the function $y=f(x)$ based on the combined sampling. The proposed

method synthesizes uniform and adaptive sampling approaches and provides

a more compact and efficient function representation. During the combined

sampling, the polygonal approximation with a given threshold $\overline{\alpha}$

between adjacent segments is constructed. The automated detection

and treatment of discontinuities based on $LR$ criterion are involved.

Two implementations, the recursive-based and stack-based, are introduced.

Finally, several tests of the proposed algorithms for different functions

involving discontinuities and several map projection graticules are

presented. The proposed method may be applied in geoinformatic for

more efficient sampling the curves (map projection graticules, contour

lines, or buffers).

#### Keywords

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