MATLAB-based Cubic Spline Interpolation Algorithm Implementation

This document presents a comprehensive implementation of cubic spline interpolation algorithm using MATLAB, enabling readers to gain deeper insights into both the theoretical foundations and practical execution of this method. We begin by explaining the fundamental concepts and mathematical formulations of cubic spline interpolation, including the derivation of piecewise cubic polynomials and continuity conditions. The implementation section details how to program this algorithm in MATLAB environment, covering key functions such as data input handling using arrays, boundary condition specification (natural, clamped, or not-a-knot), and the construction of tridiagonal systems for solving spline coefficients. We demonstrate practical coding techniques including vectorization for efficient computation and visualization using MATLAB's plot functions to display interpolation results. Additionally, we analyze the algorithm's performance characteristics in real-world applications, discussing its advantages in smoothness preservation and limitations in computational complexity. Several worked examples illustrate how to apply this program to solve practical engineering problems, such as trajectory planning and sensor data smoothing. Through this documentation, readers will acquire solid understanding of cubic spline interpolation's core principles and programming techniques, establishing a foundation for advanced research and application development.