Construction of C1 Rational Bi-Quartic Spline With Positivity-Preserving Interpolation: Numerical Results and Analysis - Abdul Karim, Samsul Ariffin; Saaban, Azizan; Nguyen, Van Thien (Frontiers in Physics, 2021)
It is essentially that from the observed data sets, we should be able to produce curves surfaces that have same characteristics as the original data sets. For instance, if the given data is positive, then the resulting curve or surface must be positive on entire given intervals i.e., everywhere. In this study, a new partial blended rational bi-quartic spline with C1 continuity is constructed through partially blended scheme. This rational spline is defined on four corners of the rectangular meshes. The sufficient condition for the positivity of rational bi-quartic spline is derived on four boundary curves network. There are eight (8) free parameters that can be used for shape modification. The first order partial derivatives are estimated by using numerical techniques. We also show that the proposed scheme is local quadratic reproducing such that it can exactly reproduce the quadratic surface. We test the proposed scheme to interpolate various types of positive surface data. Based on statistical indicators such as root mean square error (RMSE) and coefficient of determination (R2), we found that the proposed scheme is on par with some established schemes. In fact, it requires less CPU times (in seconds) to generate the interpolating surface on rectangular meshes. Furthermore, by combining the statistical indicators result and graphically visualizing of the test functions, the proposed method has the capability to reconstruct very comparable smoothing interpolating positive surfaces compared to some existing schemes. This finding is significant in producing a better interpolating surfaces for computer graphics applications since the proposed scheme has smaller error compared with existing schemes.