MATLAB Code Implementation for Surface Fitting

While numerous surface fitting programs are available online, many contain critical errors that affect their performance and reliability. To address these issues, I have systematically corrected and enhanced these programs through several key improvements. The modifications include implementing robust numerical algorithms such as least-squares fitting with regularization to prevent overfitting, optimizing matrix operations for better computational efficiency using MATLAB's vectorization capabilities, and adding proper error handling mechanisms. The corrected implementation now features enhanced polynomial fitting functions (polyfitn) and spline-based approaches (spapi) with improved parameter validation. The program incorporates advanced fitting techniques including Gaussian process regression and radial basis function interpolation for complex surface patterns. These enhancements not only significantly improve fitting accuracy but also increase computational performance by optimizing memory allocation and reducing redundant calculations. Additionally, I've added comprehensive documentation and user-friendly interfaces that simplify parameter configuration and result visualization. The improved code structure allows both professional researchers and enthusiasts to easily utilize these tools for various applications including 3D data modeling, topographic mapping, and scientific data analysis. The uploaded corrected versions include detailed examples demonstrating proper usage of key functions like fit and scatteredInterpolant for different data types and fitting scenarios. These comprehensive modifications have transformed the surface fitting programs into more robust, accurate, and accessible tools, representing significant advancements for both academic research and practical applications in data modeling and analysis.