# Cubic \(q\)-Bezier Triangular Patch for Scattered Data Interpolation and Its Algorithm
## 5 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Data Points**} \\ \cline{2-11} \(q\) **Value** & \multicolumn{3}{c}{**36**} & \multicolumn{3}{c}{**65**} & \multicolumn{3}{c}{**100**} \\ \cline{2-11}  & \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & \(\mathbf{F_{3}}\)



## 5 Conclusions

In conclusion, this study successfully extends the application of \(q\)-Bezier curves to a scattered data interpolation scheme on well-known mathematical functions as well as real-life data. The proposed interpolation scheme was constructed using three local schemes that are blended through a convex combination via an efficient algorithm. The performance of the scheme was rigorously tested with 36, 65, and 100 uniformly distributed data points. Our results indicate that the proposed scheme achieves optimal visualization and error analysis outcomes when the \(q\) parameter is set between 0.75 and 1. This finding suggests that the careful tuning of the \(q\) parameter is crucial for enhancing interpolation accuracy. The method presented in this paper is novel and still under exploration, particularly in finding the optimal \(q\) parameter. Our current approach is heuristic, and we recognize the need for a more systematic method to determine this parameter. One promising direction is to employ deep learning techniques, particularly Convolutional Neural Networks (CNNs) to optimize the \(q\) parameter. This approach involves training a CNN on a comprehensive dataset of scattered data points and their Delaunay triangulations to predict the optimal \(q\) parameter. Additionally, our study is limited by the relatively small number of data points. Increasing the dataset size could provide more comprehensive validation of the proposed scheme and enhance its applicability to a wider range of problems. Future research will also explore the application of the proposed scheme to image interpolation, particularly for RGB images. This extension could provide significant improvements in image processing tasks, where accurate interpolation is critical for enhancing image quality and resolution. Conceptualization, O.T. ; data curation, O.T. ; formal analysis, O.T. and S.A.A.K. ; funding acquisition, S.A.A.K. ; investigation, O.T. ; methodology, O.T. and S.A.A.K. ; project administration, S.A.A.K. ; software, O.T. and S.A.A.K. ; supervision, S.A.A.K. ; validation, O.T. and S.A.A.K. ; visualization, O.T. and S.A.A.K. ; writing--original draft, O.T. ; writing--review and editing, O.T. and S.A.A.K. All authors have read and agreed to the published version of the manuscript. This research was fully supported by the Ministry of Higher Education (MOHE) of Malaysia through Fundamental Research Grant Scheme [FRGS/1/2023/ICT06/ UMS/02/1] (New Scattered Data Interpolation Scheme Using Quasi Cubic Triangular Patches for RGB Image Interpolation) and Universiti Malaysia Sabah. Not applicable. The data are shared in this paper. The authors give special thanks to the Faculty of Computing and Informatics, Universiti Malaysia Sabah and School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia for the tremendous computing facility support. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} RBFs & Radial Basis Functions \\ SNRBFs & Square Normalized Radial Basis Functions \\ MLS & Moving Least Square \\ RMSE & Root Mean Square Error \\ CPU & Central Processing Unit \\ \end{tabular} 

## References

* [PERSON] and [PERSON] (1991) [PERSON]; [PERSON] Scattered data interpolation of large sets of scattered data. _Int. J. Numer. Methods Eng._**1991**, _15_, 1-691. * [PERSON] et al. (2019) [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON], [PERSON] Fast computation of triangular Shepard interpolants. _J. Comput. Appl. Math._**2019**, _354_, 457-470. [CrossRef]
* [PERSON] (2018) [PERSON] Local multilevel scattered data interpolation. _Eng. Anal. Bound. Elem._**2018**, _92_, 101-107.