spline interpolation

Spline interpolation is a mathematical technique used to create a smooth curve that passes through a set of known data points. Imagine connecting dots with flexible, curved segments that fit each point precisely, while ensuring the overall path is smooth without sharp angles. These segments, called splines, are typically piecewise polynomial functions, often cubic, which blend seamlessly at the data points. Spline interpolation allows us to estimate intermediate values accurately and smoothly between known data, making it useful in applications like computer graphics, data fitting, and engineering design.