Abstract
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 C1 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 C1 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 C1 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.
Highlights
Computer Aided Geometric Design (CAGD) is a field initially developed to introduce computer-based applications to industries such as automotive, aerospace and shipbuilding
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 CC1 continuity
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
Summary
Computer Aided Geometric Design (CAGD) is a field initially developed to introduce computer-based applications to industries such as automotive, aerospace and shipbuilding. The construction of scattered data interpolation using Bézier triangular patches can be described as follows:. Saaban et al [17] described the positivity preserving property by using quintic triangular Bézier patches. The surface is constructed by using convex combination of quintic triangular Bézier patches They used the real data collected from rainfall at various stations in West Peninsular Malaysia. Awang and Rahmat [18] focused on the developing a smooth surface using two processes which are the derivative estimation and the surface interpolation using the cubic Bѐzier triangular patch. The comparison described in Saaban et al [12] generalized positivity-preserving schemes for triangular Bѐzier patches of CC1 and CC2 scattered data interpolants are presented. Three methods of CC1 schemes using cubic Bѐzier triangular patches and one CC2 scheme using quantic Bѐzier triangular patches is compared
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