Extremal Scattered Data Interpolation in $$\mathbb {R}^3$$ Using Triangular Bézier Surfaces

2015 ◽  
pp. 304-311
Author(s):  
Krassimira Vlachkova
Keyword(s):  
Scattered Data ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Bézier Surfaces ◽  
Bezier Surfaces

scholarly journals Error estimates for scattered data interpolation on spheres

1999 ◽  
Vol 68 (226) ◽  
pp. 733-748 ◽  
Author(s):  
Kurt Jetter ◽  
Joachim Stöckler ◽  
Joseph D. Ward
Keyword(s):  
Error Estimates ◽  
Scattered Data ◽  
Data Interpolation ◽  
Scattered Data Interpolation

scholarly journals Scattered Data Interpolation Using Rational Quartic Triangular Patches With Three Parameters

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 44239-44262 ◽  
Author(s):  
Nur Nabilah Che Draman ◽  
Samsul Ariffin Abdul Karim ◽  
Ishak Hashim
Keyword(s):  
Scattered Data ◽  
Data Interpolation ◽  
Scattered Data Interpolation

scholarly journals Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 159 ◽  
Author(s):  
Fatin Amani Mohd Ali ◽  
Samsul Ariffin Abdul Karim ◽  
Azizan Saaban ◽  
Mohammad Khatim Hasan ◽  
Abdul Ghaffar ◽  
...  
Keyword(s):  
Convex Combination ◽  
Scattered Data ◽  
Coefficient Of Determination ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Digital Elevation ◽  
Standard Set ◽  
C1 Continuity ◽  
Local Schemes ◽  
Corrected Scheme

This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R2). The higher R2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown’s validation.

scholarly journals Scattered Data Interpolation and Approximation with Truncated Exponential Radial Basis Function

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1101 ◽  
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu
Keyword(s):  
Radial Basis Functions ◽  
Radial Function ◽  
Dimensional Space ◽  
Level Set Methods ◽  
Scattered Data ◽  
Surface Modeling ◽  
Basis Functions ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Radial Basis

Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation effect, this is often accompanied by an ill-conditioned algebraic system. The exceedingly large condition number of the discrete matrix makes the numerical calculation time consuming. The paper introduces a truncated exponential function, which is radial on arbitrary n-dimensional space R n and has compact support. The truncated exponential radial function is proven strictly positive definite on R n while internal parameter l satisfies l ≥ ⌊ n 2 ⌋ + 1 . The error estimates for scattered data interpolation are obtained via the native space approach. To confirm the efficiency of the truncated exponential radial function approximation, the single level interpolation and multilevel interpolation are used for surface modeling, respectively.

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