Abstract
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.
Highlights
Many computer graphics and vision problems involve scattered data interpolation (SDI)
It is observed that the cubic Timmer triangular patches offer lower central processor unit unit (CPU) time as compared to the cubic Bezier and Ball triangular patches methods
The simulation error shows that the cubic Timmer triangular patches have the same values as obtained from Goodman and Said schemes
Summary
Many computer graphics and vision problems involve scattered data interpolation (SDI). SDI methods aims to build a smooth function from a set of data, which consist of functional values corresponding to points, which do not obey any structure or order between their relative locations. These methods have a wide range of uses in surface reconstruction, visualization, image restoration, computer graphics, surface deformation, image processing, engineering, and technology, etc. The most popular method that is usually used to generate the surface of scattered from the data points is Delaunay triangulation method [7]. It is a very famous method, applied to produce the triangle meshes, where vertices of the triangle are made up of the sample data points
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