interpolatsioonipunkte

Interpolatsioonipunkte, often translated as interpolation points, are specific data points used in interpolation techniques. Interpolation is a method of constructing new data points within the range of a discrete set of known data points. These known points, the interpolation points, serve as anchors for the interpolation process. The choice of interpolation points and the method used to connect them significantly influence the accuracy and smoothness of the resulting interpolated curve or surface.

Common interpolation methods include linear interpolation, polynomial interpolation, and spline interpolation. Linear interpolation uses two points to define a straight line, and any point between them is estimated based on its position along that line. Polynomial interpolation uses a polynomial function that passes through a set of interpolation points. Higher-order polynomials can fit more points but may lead to oscillations (Runge's phenomenon). Spline interpolation uses piecewise polynomial functions, which are typically of lower degree and joined smoothly at specific points, often referred to as "knots" or, in this context, interpolation points.

The accuracy of interpolation depends heavily on the density and distribution of the interpolation points. A denser and more evenly distributed set of points generally leads to a more accurate interpolation. Conversely, sparse or unevenly spaced points can result in significant errors. Interpolation points are fundamental in various fields, including computer graphics, numerical analysis, signal processing, and data analysis, where it's necessary to estimate values between known measurements.