## 8 Conclusions  
In light of the importance of curve modeling in various fields, a \(C^{2}\) interpolation system is built utilizing a rational quadratic trigonometric function for the purpose of object form design. Convex hull, partition of unity, affine invariance, and variation decreasing are geometric properties of the curves achieved through the developed method. The suggested method is accommodating for numerous shape effects to change the object as desired locally or globally. The parameters in the recommended method are beneficial for several critical shape features, providing good control over the curve and allowing for shape modification as desired. Furthermore, the comparative study revealed that the proposed method is a superior alternative to RCS.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Data Used**} & **Time Passed by RCS** & **Time Passed by** & **Difference between the** \\  & **in Seconds** & **RQTS in Seconds** & **Times Passed in Seconds** \\ \hline Glass & 1.674103 & 1.349462 & 0.271486 \\ \hline Guitar & 1.860445 & 1.588977 & 0.291976 \\ \hline Butterfly & 0.796280 & 0.504304 & 0.36916 \\ \hline Ellipses & 0.852281 & 0.483121 & 0.245246 \\ \hline Egg & 0.480849 & 0.235603 & 0.513009 \\ \hline Fish & 1.531127 & 1.018118 & 0.271486 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Table of time passed by two splines.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\#} & **Parameter \(t\)** & **Uilized Function** & **RCS Computed Error** & **RQTS Computed Error** & **Error Difference Computed by Both Splines** \\ \hline
1 & \(-\pi\leq t\leq\pi\) & \(Sin(t)\) & \(5.7356\times 10^{-15}\) & \(5.6966\times 10^{-15}\) & 3.90 \(\times 10^{-17}\) \\ \hline
2 & \(-\pi\leq t\leq\pi\) & \(Cos(t)\) & \(1.2978\times 10^{-15}\) & \(1.2988\times 10^{-15}\) & \(-1.00\times 10^{-18}\) \\ \hline
3 & \(-\pi\leq t\leq\pi\) & \(Tan(t)\) & \(4.2201\times 10^{-15}\) & \(4.1914\times 10^{-15}\) & 2.87 \(\times 10^{-17}\) \\ \hline
4 & \(-\pi\leq t\leq\pi\) & \(Sec(t)\) & \(7.0537\times 10^{-16}\) & \(5.0171\times 10^{-16}\) & 2.04 \(\times 10^{-16}\) \\ \hline
5 & \(2\leq t\leq 10\) & \(Log(t)\) & \(2.2204\times 10^{-15}\) & \(2.2204\times 10^{-15}\) & 0.00 \(\times 10^{0}\) \\ \hline
6 & \(2\leq t\leq 10\) & \(\sqrt{t+6}+\left(t+2\right)^{2}\) & \(4.8317\times 10^{-13}\) & \(5.1159\times 10^{-13}\) & \(-2.84\times 10^{-14}\) \\ \hline
7 & \(2\leq t\leq 10\) & \(e^{t}\) & \(3.9654\times 10^{-10}\) & \(4.0018\times 10^{-10}\) & \(-3.64\times 10^{-12}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Table of error study, for RCS and RQTS, for a various functions.  
**Author Contributions:** Conceptualization, M.S.; methodology, M.S. and S.S.; software, S.S. and N.J.; validation, M.S., S.S. and N.J.; formal analysis, M.S.; investigation, M.S.; resources, M.S.; data curation, S.S.; writing--original draft preparation, S.S. and N.J.; writing--review and editing, M.S. and S.S.; visualization, S.S. and N.J.; supervision, M.S.; project administration, M.S.; funding acquisition, S.A. and A.M. All authors have read and agreed to the published version of the manuscript.  
**Funding:** Taif University Researchers Supporting Project number (TURSP-2020/305), Taif University, Taif, Saudi Arabia.  
**Acknowledgments:** Taif University Researchers Supporting Project number (TURSP-2020/305), Taif University, Taif, Saudi Arabia.  
**Conflicts of Interest:** The authors declare no conflict of interest.