Quadratic and Cubic B-Spline Implementation

This is my original implementation of quadratic and cubic B-spline algorithms, designed for applications in wavelet transformations and curve fitting. The code includes core mathematical formulations and interpolation methods that can handle both second-order and third-order B-spline basis functions. Key features include parameterized knot vector generation, recursive de Boor algorithm implementation for efficient evaluation, and support for both uniform and non-uniform knot sequences. I encourage beginners to study this implementation as a reference point for understanding B-spline mathematics and computational approaches. The modular code structure allows easy modification of spline order, knot intervals, and boundary conditions. Users can extend functionality by incorporating additional optimization techniques, adaptive knot placement strategies, or integration with signal processing libraries for wavelet applications. The implementation demonstrates fundamental concepts including: - Basis function calculation using Cox-de Boor recurrence relations - Control point influence weighting for curve construction - Continuous curvature maintenance through parametric continuity - Efficient matrix operations for large-scale data fitting Developers can build upon this foundation to create customized solutions for specific engineering or scientific computing requirements.