Efficient plotting the functions with 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: adaptive sampling; combined sampling; recursive approach; stack; discontinuity; polygonal approximation; visualization; map projection; plotting; GIS
• Online Access: https://ojs.cvut.cz/ojs/index.php/gi/article/view/4938

This article presents  new algorithm for interval plotting of<br />the function $y=f(x)$ based on the combined sampling. The proposed<br />method synthesizes uniform and adaptive sampling approaches and provides<br />a more compact and efficient function representation. During the combined<br />sampling, the polygonal approximation with a given threshold $\overline{\alpha}$<br />between adjacent segments is constructed. The automated detection<br />and treatment of discontinuities based on $LR$ criterion are involved.<br />Two implementations, the recursive-based and stack-based, are introduced.<br />Finally, several tests of the proposed algorithms for different functions<br />involving discontinuities and several map projection graticules are<br />presented. The proposed method may be applied in geoinformatic for<br />more efficient sampling the curves (map projection graticules, contour<br />lines, or buffers).