Hermite interpolation

Hermite interpolation is a mathematical technique used to construct a smooth curve through a set of points, not only matching the points' positions but also their slopes or rates of change at those points. Imagine plotting a curve that passes through specific locations, while also ensuring the curve's direction at each point aligns with the given slope. This method is useful when you want the interpolated curve to accurately reflect both the data's value and its behavior, resulting in a more precise and smoothly connected representation than simple point-to-point interpolation.