MATLAB Implementation of B-Spline and Hermite Curves with Code Explanations

This program implements B-spline and Hermite curve functionality using MATLAB. The B-spline implementation utilizes a recursive algorithm for curve interpolation, where the curve is generated through basis function calculations applied to given control points. B-splines are commonly used in 3D modeling, image processing, and computer-aided design applications due to their smoothness properties and local control characteristics. The implementation allows users to specify control point coordinates and degree parameters to generate smooth, continuous curves. Hermite curves employ a different mathematical approach using endpoints and their tangent vectors for interpolation. This implementation provides greater flexibility in controlling curve shape compared to B-splines, as it allows direct manipulation of both position and direction parameters at control points. The code includes functions for specifying initial and terminal points along with their corresponding tangent vectors, enabling precise curve shaping according to specific requirements. Users can select either B-spline or Hermite interpolation methods based on their application needs. The program includes visualization functions that plot the generated curves alongside control points for verification and analysis purposes. Key MATLAB functions implemented include bspline() for B-spline generation and hermite_curve() for Hermite interpolation, both supporting 2D and 3D coordinate systems with customizable resolution parameters for smooth curve rendering.