Abstract
Monotonicity preserving interpolation is very important in many sciences and engineering based problems. This paper discuss the monotonicity preserving interpolation for monotone data set by using C 2 rational cubic spline interpolant (cubic/quadratic) with three parameters. The data dependent sufficient conditions for the monotonicity are derived with two degree freedom. Numerical results suggests that the proposed C 2 rational cubic spline preserves the monotonicity of the data and outperform the performance of the other rational cubic spline schemes in term of visually pleasing.
Highlights
Visualizing the scientific data is important in computer graphics and geometric modeling areas
In Sarfraz et al [19] the rational cubic spline with quadratic denominator has been used for monotonicity with C2 continuity – without any degree freedom
Abbas et al [1] discussed the monotonicity by using C2 rational cubic spline with two free parameters
Summary
Visualizing the scientific data is important in computer graphics and geometric modeling areas. One of the requirements for scientific visualization is that the ability of the interpolating scheme to preserves the geometric properties of the data sets. Fritsch and Carlson [8] constructed the monotonic cubic Hermite spline polynomial to preserve monotone data set. Their scheme have some drawback such as it require the modification of the first derivatives if shape violation is found. Monotonicity preserving for curves and surfaces by utilizing rational cubic spline with quadratic denominator- without any degree freedom i.e. no free parameters for shape modification. Sarfraz [18] discussed the used of rational cubic spline (cubic/cubic) for monotonicity preserving with C 2 continuity but his schemes not received much attention since there are no degree freedom. (iii) Our scheme has two degree freedom there are no degree freedom in the works of Sarfraz [18], Delbourgo and Gregory [6,7] and Gregory [9]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
