Parameter Selection and Fitting Implementation for Bézier Curves

I have developed a custom MATLAB GUI that enables parameter selection and fitting capabilities for Bézier curves. This GUI allows users to interactively adjust Bézier curve parameters (including control points and degree) through slider controls and point manipulation interfaces to achieve desired curve shapes. The implementation utilizes MATLAB's App Designer framework with callback functions handling real-time curve updates using the standard Bézier algorithm: B(t) = Σ(i=0 to n) binom(n,i) * (1-t)^(n-i) * t^i * P_i, where P_i represents control points. Additionally, the fitting functionality employs optimization algorithms (such as least-squares fitting) to match Bézier curves with user-provided data points, enabling better understanding of data trends and patterns. Key functions include bezier() for curve generation, fminsearch() for parameter optimization, and plot() for real-time visualization. This GUI serves as a valuable tool for Bézier curve research and analysis within the MATLAB environment, particularly suitable for computer graphics and data approximation applications.