Efficient plotting the functions with discontinuities based on combined sampling

Abstract

This article presents new algorithm for interval plotting ofthe function $y=f(x)$ based on the combined sampling. The proposedmethod synthesizes uniform and adaptive sampling approaches and providesa more compact and efficient function representation. During the combinedsampling, the polygonal approximation with a given threshold $\overline{\alpha}$between adjacent segments is constructed. The automated detectionand 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 functionsinvolving discontinuities and several map projection graticules arepresented. The proposed method may be applied in geoinformatic formore efficient sampling the curves (map projection graticules, contourlines, or buffers).

Keywords

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