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Interpolation techniques are methods used to estimate unknown values that fall between known data points. These techniques are fundamental in various fields, including mathematics, computer graphics, statistics, and signal processing. The core idea is to construct a function that passes through a given set of data points and then use this function to predict values at intermediate locations.

One of the simplest interpolation methods is linear interpolation. It assumes a straight line between two known points and estimates the value at any point along that line by proportional scaling. For more complex curves, polynomial interpolation is used, where a polynomial function is fitted to a set of data points. Lagrange interpolation and Newton's divided differences are common algorithms for constructing such polynomials. Spline interpolation, particularly cubic splines, offers a more flexible approach by using piecewise polynomial functions that are joined smoothly at the data points, avoiding the oscillations that can occur with high-degree global polynomials.

Other interpolation techniques include nearest neighbor interpolation, which simply assigns the value of the closest known data point, and trigonometric interpolation, which uses sine and cosine functions. The choice of interpolation technique often depends on the nature of the data, the desired accuracy, and computational efficiency. For instance, in image processing, different interpolation methods can affect the smoothness and sharpness of scaled images. In scientific data analysis, interpolation helps to fill gaps in measurements or to create continuous representations from discrete samples.