Shape preserving interpolation of positive and range-restricted data using quintic trigonometric Bézier curves

Abstract

This study proposes novel methods for preserving the shape of positive and range-restricted data using a quintic trigonometric Bézier curve with two shape parameters. Automated algorithms based on the shape-preserving condition are developed on one of the shape parameters, whereas the second shape parameter ensures the smoothness of the final interpolations. Hence, this scheme does not require manual adjustment on the control points. Datasets from the existing scheme are implemented to assess the efficiency of the proposed schemes. The results reveal that the shape-preserving C2 quintic trigonometric Bézier curves interpolations offer smooth interpolating curves and appear to be better than the existing schemes in terms of the complexity and flexibility offered to users. Furthermore, the developed schemes demonstrate good performance when applied to larger datasets. Finally, the proposed positivity-preserving scheme is also used to interpolate the daily COVID-19-related death data. Upon comparison with actual statistics, the developed scheme provides reliable answers with only slight deviations from the actual data. These findings imply that the proposed techniques can be used to interpolate missing data points in time-series analysis. Moreover, their performance on larger datasets suggests that they are robust and scalable, making them suitable for a wide range of applications.