Data Sets for Bivariate Normal Distribution Approximation Using Cubic q- Bézier Triangular Patch

In this study, scattered data sets were generated to evaluate the performance of the proposed method under different sample sizes. The data points were randomly sampled from a bivariate normal distribution and restricted to the rectangular computational domain [0,1]×[0,1].[0,1]\times[0,1].[0,1]×[0,1]. Three different scattered data configurations were considered, consisting of n=36,n=65, and n=100 sample points, respectively. These sample sizes were selected to represent relatively sparse, moderate, and denser distributions of scattered data over the unit square domain. The points were generated according to a bivariate normal distribution so that the spatial locations are not uniformly distributed, thereby producing a more realistic scattered-data setting. This type of distribution allows some regions of the domain to contain relatively dense clusters of points, while other regions may be more sparsely populated. For each data set, the sampled points were used as interpolation or approximation nodes for testing the accuracy and stability of the proposed scheme. By considering 36, 65, and 100 scattered points, the effect of increasing data density on the numerical results can be examined. In particular, the comparison among these three data sets provides insight into how the method behaves when the number of available scattered data points increases.