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.

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In this study, a new cubic Timmer triangular patch is constructed by extending the univariate cubic Timmer basis functions. The best scheme that lies towards the control polygon is cubic Timmer curve and surface compared to the other methods. From the best of our knowledge, nobody has extended the univariate cubic Timmer basis to the bivariate triangular patch. The construction of the proposed cubic Timmer triangular patch is based on the main idea of the cubic Ball and cubic Bezier triangular patches construction. Some properties of the new cubic Timmer triangular patch are investigated. Furthermore, the composite cubic Timmer triangular patches with parametric continuity (C1) and geometric continuity (G1) are discussed. Simple error analysis between the triangular patches and one test function is provided for each continuity type. Numerical and graphical results are presented by using Mathematica and MATLAB.

This paper discusses the application of the new cubic Timmer triangular patches constructed by Ali et al. [1] to interpolate the irregularly scattered data with C 1 continuity. In order to apply the cubic Timmer triangular patches for scattered data interpolation, the data is first triangulated by using the Delaunay algorithm, and then the sufficient condition for C 1 continuity is derived along the adjacent triangles. Two methods will be used to calculate the cubic Timmer ordinates on each triangle. The convex combination between three local schemes Ti , i = 1,2,3 will be used to produce the C 1 surface everywhere. The proposed scheme will be tested to visualize one energy data set with irregular shape properties. Numerical and graphical results are presented by using MATLAB. Comparisons between the proposed scheme and existing schemes such as cubic Ball and cubic Bézier triangular patches are also carried out. The results indicate that the surface produced by cubic Timmer triangular patch is better than surface produced using cubic Ball and cubic Bezier triangular patches with overall coefficient of determination R2 value obtained to be larger than 0.9234.