Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation

Advances in Difference Equations

article

Karim, Samsul Ariffin Abdul¹  Saaban, Azizan²  Skala, Vaclav³  Ghaffar, Abdul⁴  Nisar, Kottakkaran Sooppy⁶  Baleanu, Dumitru⁷ 

[1] Fundamental and Applied Sciences Department and Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS;College of Arts and Sciences, Universiti Utara Malaysia;Department of Computer Science & Engineering, Faculty of Applied Sciences, University of West Bohemia;Informetrics Research Group, Ton Duc Thang University;Faculty of Mathematics & Statistics, Ton Duc Thang University;Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University;Department of Mathematics, Cankaya University;Institute of Space Sciences;Department of Medical Research, China Medical University Hospital, China Medical University

关键词: Cubic Bézier-like;    Bézier triangular;    Patches;    Scattered data interpolation;    Continuity;    Visualization;    Surface reconstruction;   

DOI  :  10.1186/s13662-020-02598-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper discusses the functional scattered data interpolation to interpolate the general scattered data. Compared with the previous works, we construct a new cubic Bézier-like triangular basis function controlled by three shape parameters. This is an advantage compared with the existing schemes since it gives more flexibility for the shape design in geometric modeling. By choosing some suitable value of the parameters, this new triangular basis is reduced to the cubic Ball and cubic Bézier triangular patches, respectively. In order to apply the proposed bases to general scattered data, firstly the data is triangulated using Delaunay triangulation. Then the sufficient condition for $C^{1}$ continuity using cubic precision method on each adjacent triangle is implemented. Finally, the interpolation scheme is constructed based on a convex combination between three local schemes of the cubic Bézier-like triangular patches. The detail comparison in terms of maximum error and coefficient of determination $r^{2}$ with some existing meshfree methods i.e. radial basis function (RBF) such as linear, thin plate spline (TPS), Gaussian, and multiquadric are presented. From graphical results, the proposed scheme gives more visually pleasing interpolating surfaces compared with all RBF methods. Based on error analysis, for all four functions, the proposed scheme is better than RBFs except for data from the third function. Overall, the proposed scheme gives $r^{2}$ value between 0.99920443 and 0.99999994. This is very good for surface fitting for a large scattered data set.

【 授权许可】

CC BY