Efficient plotting the functions with discontinuities based on combined sampling

Tomáš Bayer


This article presents  new algorithm for interval plotting of
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).


adaptive sampling; combined sampling; recursive approach; stack; discontinuity; polygonal approximation; visualization; map projection; plotting; GIS;


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