Linear, Quadratic, and Cubic Bezier Curves: MATLAB Implementation

This MATLAB implementation demonstrates the generation of linear (1st-order), quadratic (2nd-order), and cubic (3rd-order) Bezier curves through parametric equations. The program utilizes control points to define curve shapes, where linear curves require 2 points, quadratic curves 3 points, and cubic curves 4 points. Key algorithms include De Casteljau's recursive subdivision method for precise curve calculation and Bernstein polynomial basis functions for smooth interpolation. The implementation features interactive control point adjustment, real-time curve rendering, and coordinate visualization through MATLAB's plotting functions. Users can modify control point coordinates to observe immediate changes in curve curvature and smoothness, making it suitable for computer graphics education, engineering design applications, and CAD prototyping. The code structure separates curve calculation modules from visualization components, allowing easy extension to higher-order Bezier curves through matrix operations and vectorized computations for optimal performance.